{
  "format": "wai.qudit-conformance/1",
  "protocol": "wai.quantum.qudit/1",
  "about": "Qudit jobs (extensions/quantum-sim.md section 9): each dimension's constants at 2^-30, each vector's request with the result every conforming host gives (the members of a run's answer but engine, schema, energy and receipt), and requests a conforming host refuses, each with its code. Written by wai-quantum's tests/qudit_conformance.rs; results_blake3 is BLAKE3 over each vector's request and result as compact JSON, each followed by a newline.",
  "limits": {
    "amplitudes": 16777216,
    "gates": 65536,
    "shots": 1000000,
    "amplitudes_asked": 64,
    "work": 4294967296
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  "vectors": [
    {
      "name": "qubit-bell",
      "about": "d = 2 is circuit2: H then CNOT, the qubit simulator's amplitudes and counts",
      "request": {
        "d": 2,
        "qudits": 2,
        "gates": [
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        "shots": 1000,
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        "shots": 1000,
        "seed": 7,
        "counts": {
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        },
        "distinct_outcomes": 2,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
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        "accuracy": {
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          "bound_units": 3.8284271247461903,
          "outcomes": 1.4262002451611013e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-bell",
      "about": "three correlated outcomes, a third each",
      "request": {
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        "qudits": 2,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
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          },
          {
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            "qudits": [
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          }
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        "shots": 1000,
        "seed": 7,
        "amplitudes": [
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      "result": {
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        "gates": 2,
        "shots": 1000,
        "seed": 7,
        "counts": {
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          "11": 330,
          "22": 320
        },
        "distinct_outcomes": 3,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "00": {
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          "01": {
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          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "ququart-bell",
      "about": "four correlated outcomes; F_4's entries are exact",
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          "33": 243,
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        "distinct_outcomes": 4,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
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          "01": {
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          "outcomes": 4.214684873293863e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "six-level-bell",
      "about": "six correlated outcomes",
      "request": {
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        "gates": [
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        "shots": 1000,
        "seed": 7,
        "counts": {
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          "22": 182,
          "44": 171,
          "11": 163,
          "55": 149,
          "33": 148
        },
        "distinct_outcomes": 6,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "00": {
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          "01": {
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          "11": {
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          "amplitudes": 36,
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        "constants": {
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        },
        "work": 1324,
        "accuracy": {
          "class": "bit-exact",
          "bound": 4.287060177573639e-8,
          "bound_units": 46.031958146656834,
          "outcomes": 1.7148241077872255e-7,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qubit-ghz",
      "about": "d = 2 with the shift and the clock: X and Z",
      "request": {
        "d": 2,
        "qudits": 3,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
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          },
          {
            "gate": "csum",
            "qudits": [
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              1
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          },
          {
            "gate": "csum",
            "qudits": [
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              2
            ]
          },
          {
            "gate": "shift",
            "qudits": [
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            ]
          },
          {
            "gate": "clock",
            "qudits": [
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          }
        ],
        "shots": 2000,
        "seed": 3,
        "amplitudes": [
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          "011",
          "100",
          "111"
        ]
      },
      "result": {
        "answer": "run",
        "d": 2,
        "qudits": 3,
        "gates": 5,
        "shots": 2000,
        "seed": 3,
        "counts": {
          "011": 1032,
          "100": 968
        },
        "distinct_outcomes": 2,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "000": {
            "re": 0,
            "im": 0
          },
          "011": {
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          "100": {
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          "111": {
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        },
        "state": {
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          "amplitudes": 8,
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        "constants": {
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        },
        "work": 2064,
        "accuracy": {
          "class": "bit-exact",
          "bound": 4.6566128730773926e-9,
          "bound_units": 5.0,
          "outcomes": 1.8626451535677657e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-weyl-zx",
      "about": "Z X on F|0>: the Weyl relation's left side",
      "request": {
        "d": 3,
        "qudits": 1,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
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          },
          {
            "gate": "shift",
            "qudits": [
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          },
          {
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            "qudits": [
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        ],
        "shots": 0,
        "amplitudes": [
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      },
      "result": {
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        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
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        "work": 21,
        "accuracy": {
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          "bound": 9.847072980637845e-9,
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          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-weyl-wxz",
      "about": "omega X Z on F|0>: the Weyl relation's right side, the phase gate giving omega",
      "request": {
        "d": 3,
        "qudits": 1,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
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          {
            "gate": "clock",
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          {
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          {
            "gate": "phase",
            "qudits": [
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            "powers": [
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        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
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          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-fourier-powers",
      "about": "F, F^2 as the reflection, and F^3 as F's inverse",
      "request": {
        "d": 3,
        "qudits": 2,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
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            "power": 1
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          {
            "gate": "fourier",
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          {
            "gate": "fourier",
            "qudits": [
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            ],
            "power": 2
          },
          {
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            "qudits": [
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            ],
            "power": 3
          },
          {
            "gate": "shift",
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            "power": 2
          },
          {
            "gate": "fourier",
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            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
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            "power": 0
          }
        ],
        "shots": 500,
        "seed": 11,
        "amplitudes": [
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          "11",
          "12"
        ]
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 2,
        "gates": 7,
        "shots": 500,
        "seed": 11,
        "counts": {
          "11": 500
        },
        "distinct_outcomes": 1,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "00": {
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          },
          "01": {
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          },
          "11": {
            "re": 1073741825,
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          "12": {
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        "state": {
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          "amplitudes": 9,
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        "constants": {
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        },
        "work": 608,
        "accuracy": {
          "class": "bit-exact",
          "bound": 2.2550302979079213e-8,
          "bound_units": 24.21320345250915,
          "outcomes": 9.020121293334918e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "ququart-qft",
      "about": "F_4 on |2>: the two-qubit Fourier transform's column, exactly",
      "request": {
        "d": 4,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
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            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ]
          }
        ],
        "shots": 400,
        "seed": 5,
        "amplitudes": [
          "0",
          "1",
          "2",
          "3"
        ]
      },
      "result": {
        "answer": "run",
        "d": 4,
        "qudits": 1,
        "gates": 2,
        "shots": 400,
        "seed": 5,
        "counts": {
          "2": 116,
          "3": 103,
          "1": 93,
          "0": 88
        },
        "distinct_outcomes": 4,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 536870912,
            "im": 0
          },
          "1": {
            "re": -536870912,
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          },
          "2": {
            "re": 536870912,
            "im": 0
          },
          "3": {
            "re": -536870912,
            "im": 0
          }
        },
        "state": {
          "blake3": "59604053c18b3e49bafb0d18bd565d47e98da91da25cd30547807354cc04d036",
          "amplitudes": 4,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "0bc240d517a49c6052b02e972d0592f8b21b342c782f8770f845cc88e61045a3"
        },
        "work": 428,
        "accuracy": {
          "class": "bit-exact",
          "bound": 5.268356063861754e-9,
          "bound_units": 5.656854249492381,
          "outcomes": 2.107342431095817e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "ququart-exact",
      "about": "permutations and the roots ±1, ±i: the ideal state exactly, bound 0",
      "request": {
        "d": 4,
        "qudits": 3,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              0,
              1,
              2,
              3
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 3
          }
        ],
        "shots": 64,
        "seed": 9
      },
      "result": {
        "answer": "run",
        "d": 4,
        "qudits": 3,
        "gates": 6,
        "shots": 64,
        "seed": 9,
        "counts": {
          "223": 64
        },
        "distinct_outcomes": 1,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "521e81d1f5ab5853b5ef6681332e35cb701f4c930fab32376e9384a1412bc091",
          "amplitudes": 64,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "0bc240d517a49c6052b02e972d0592f8b21b342c782f8770f845cc88e61045a3"
        },
        "work": 576,
        "accuracy": {
          "class": "bit-exact",
          "bound": 0.0,
          "bound_units": 0.0,
          "outcomes": 0.0,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "six-level-roots",
      "about": "every root of d = 6 as a phase, and Z^3 = diag(1, -1, ...)",
      "request": {
        "d": 6,
        "qudits": 2,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ]
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              0,
              1,
              2,
              3,
              4,
              5
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              0
            ],
            "power": 5
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 3
          }
        ],
        "shots": 3000,
        "seed": 13,
        "amplitudes": [
          "00",
          "05",
          "50",
          "55"
        ]
      },
      "result": {
        "answer": "run",
        "d": 6,
        "qudits": 2,
        "gates": 6,
        "shots": 3000,
        "seed": 13,
        "counts": {
          "31": 522,
          "51": 514,
          "41": 503,
          "01": 494,
          "11": 489,
          "21": 478
        },
        "distinct_outcomes": 6,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "00": {
            "re": 0,
            "im": 0
          },
          "05": {
            "re": -2,
            "im": 0
          },
          "50": {
            "re": 0,
            "im": 0
          },
          "55": {
            "re": -2,
            "im": 0
          }
        },
        "state": {
          "blake3": "b4e5dda7a3853ac66995b624a137ebf01d1f8348d1463bd0307397f348a979b0",
          "amplitudes": 36,
          "norm2": 1073741828
        },
        "constants": {
          "blake3": "15f24f2b6546ea838e9360b122e4172c4574097c6fabc61cea0980c920596715"
        },
        "work": 3828,
        "accuracy": {
          "class": "bit-exact",
          "bound": 1.3698000121020534e-7,
          "bound_units": 147.0811563509681,
          "outcomes": 5.479200423678627e-7,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-seed-zero",
      "about": "the qutrit Bell pair at seed 0",
      "request": {
        "d": 3,
        "qudits": 2,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ]
          }
        ],
        "shots": 999,
        "seed": 0
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 2,
        "gates": 2,
        "shots": 999,
        "seed": 0,
        "counts": {
          "00": 336,
          "22": 336,
          "11": 327
        },
        "distinct_outcomes": 3,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "a701d2a787ddf4b8a83d161438eb016f8d041a1367f731be07c127f50115854a",
          "amplitudes": 9,
          "norm2": 1073741823
        },
        "constants": {
          "blake3": "2f4a3854c397f95e152396701355baab1c14f1ba5a735c0d34378fd71b571d72"
        },
        "work": 1053,
        "accuracy": {
          "class": "bit-exact",
          "bound": 1.1275151481664005e-8,
          "bound_units": 12.106601717798211,
          "outcomes": 4.51006061809141e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-seed-most",
      "about": "the qutrit Bell pair at the largest seed, 2^53 - 1",
      "request": {
        "d": 3,
        "qudits": 2,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ]
          }
        ],
        "shots": 999,
        "seed": 9007199254740991
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 2,
        "gates": 2,
        "shots": 999,
        "seed": 9007199254740991,
        "counts": {
          "11": 360,
          "00": 322,
          "22": 317
        },
        "distinct_outcomes": 3,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "a701d2a787ddf4b8a83d161438eb016f8d041a1367f731be07c127f50115854a",
          "amplitudes": 9,
          "norm2": 1073741823
        },
        "constants": {
          "blake3": "2f4a3854c397f95e152396701355baab1c14f1ba5a735c0d34378fd71b571d72"
        },
        "work": 1053,
        "accuracy": {
          "class": "bit-exact",
          "bound": 1.1275151481664005e-8,
          "bound_units": 12.106601717798211,
          "outcomes": 4.51006061809141e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-defaults",
      "about": "shots and seed left out: 1024 shots at seed 1; a power left out is 1",
      "request": {
        "d": 3,
        "qudits": 1,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ]
          }
        ]
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 1,
        "gates": 2,
        "shots": 1024,
        "seed": 1,
        "counts": {
          "1": 356,
          "2": 338,
          "0": 330
        },
        "distinct_outcomes": 3,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "0baf9bb5c565cc7f2072583f85c218f52b17c3496cfc0867fa55f92d2f06f166",
          "amplitudes": 3,
          "norm2": 1073741823
        },
        "constants": {
          "blake3": "2f4a3854c397f95e152396701355baab1c14f1ba5a735c0d34378fd71b571d72"
        },
        "work": 1042,
        "accuracy": {
          "class": "bit-exact",
          "bound": 9.847072980637845e-9,
          "bound_units": 10.573214103291196,
          "outcomes": 3.938829211648107e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "no-gates",
      "about": "the register |0...0>, measured",
      "request": {
        "d": 6,
        "qudits": 3,
        "gates": [],
        "shots": 10,
        "seed": 1,
        "amplitudes": [
          "000",
          "555"
        ]
      },
      "result": {
        "answer": "run",
        "d": 6,
        "qudits": 3,
        "gates": 0,
        "shots": 10,
        "seed": 1,
        "counts": {
          "000": 10
        },
        "distinct_outcomes": 1,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "000": {
            "re": 1073741824,
            "im": 0
          },
          "555": {
            "re": 0,
            "im": 0
          }
        },
        "state": {
          "blake3": "23ae46ffac0510f88784dcf24885c73635168b6478c4e8316614fd8fd8ac45bf",
          "amplitudes": 216,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "15f24f2b6546ea838e9360b122e4172c4574097c6fabc61cea0980c920596715"
        },
        "work": 442,
        "accuracy": {
          "class": "bit-exact",
          "bound": 0.0,
          "bound_units": 0.0,
          "outcomes": 0.0,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qubit-fourier-column",
      "about": "F|1>: a column of F_2, every entry as held",
      "request": {
        "d": 2,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 1
          }
        ],
        "shots": 600,
        "seed": 17,
        "amplitudes": [
          "0",
          "1"
        ]
      },
      "result": {
        "answer": "run",
        "d": 2,
        "qudits": 1,
        "gates": 2,
        "shots": 600,
        "seed": 17,
        "counts": {
          "1": 312,
          "0": 288
        },
        "distinct_outcomes": 2,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 759250125,
            "im": 0
          },
          "1": {
            "re": -759250125,
            "im": 0
          }
        },
        "state": {
          "blake3": "3d901bf5bf6f29e482f3695f68aa19bc9cb62d000e9a807b3ec64cf3f68454c9",
          "amplitudes": 2,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "fa5e6bc7fe53b14b4e5917caeb9b8028ae316c7f619bdd5c292565c9360b9dbf"
        },
        "work": 610,
        "accuracy": {
          "class": "bit-exact",
          "bound": 2.7939677238464355e-9,
          "bound_units": 3.0,
          "outcomes": 1.1175870910998253e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-fourier-column",
      "about": "F|1>: a column of F_3, every entry as held",
      "request": {
        "d": 3,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 1
          }
        ],
        "shots": 600,
        "seed": 17,
        "amplitudes": [
          "0",
          "1",
          "2"
        ]
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 1,
        "gates": 2,
        "shots": 600,
        "seed": 17,
        "counts": {
          "2": 213,
          "0": 198,
          "1": 189
        },
        "distinct_outcomes": 3,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 619925131,
            "im": 0
          },
          "1": {
            "re": -309962566,
            "im": 536870912
          },
          "2": {
            "re": -309962566,
            "im": -536870912
          }
        },
        "state": {
          "blake3": "2e037a40e768151862a937ce7755afbdb812526e360403e44126830a5d2cfa35",
          "amplitudes": 3,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "2f4a3854c397f95e152396701355baab1c14f1ba5a735c0d34378fd71b571d72"
        },
        "work": 618,
        "accuracy": {
          "class": "bit-exact",
          "bound": 7.100146596280807e-9,
          "bound_units": 7.623724356957945,
          "outcomes": 2.8400586485947392e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-inverse-column",
      "about": "F-dagger|1>: a column of F_3's inverse, every entry as held",
      "request": {
        "d": 3,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 3
          }
        ],
        "shots": 600,
        "seed": 17,
        "amplitudes": [
          "0",
          "1",
          "2"
        ]
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 1,
        "gates": 2,
        "shots": 600,
        "seed": 17,
        "counts": {
          "2": 213,
          "0": 198,
          "1": 189
        },
        "distinct_outcomes": 3,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 619925131,
            "im": 0
          },
          "1": {
            "re": -309962566,
            "im": -536870912
          },
          "2": {
            "re": -309962566,
            "im": 536870912
          }
        },
        "state": {
          "blake3": "9f239c12809f179a07c6e2b2c098d64542c74342817ae6239e926352272b2c0c",
          "amplitudes": 3,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "2f4a3854c397f95e152396701355baab1c14f1ba5a735c0d34378fd71b571d72"
        },
        "work": 618,
        "accuracy": {
          "class": "bit-exact",
          "bound": 7.100146596280807e-9,
          "bound_units": 7.623724356957945,
          "outcomes": 2.8400586485947392e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "ququart-fourier-column",
      "about": "F|1>: a column of F_4, every entry as held",
      "request": {
        "d": 4,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 1
          }
        ],
        "shots": 600,
        "seed": 17,
        "amplitudes": [
          "0",
          "1",
          "2",
          "3"
        ]
      },
      "result": {
        "answer": "run",
        "d": 4,
        "qudits": 1,
        "gates": 2,
        "shots": 600,
        "seed": 17,
        "counts": {
          "2": 156,
          "3": 156,
          "0": 147,
          "1": 141
        },
        "distinct_outcomes": 4,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 536870912,
            "im": 0
          },
          "1": {
            "re": 0,
            "im": 536870912
          },
          "2": {
            "re": -536870912,
            "im": 0
          },
          "3": {
            "re": 0,
            "im": -536870912
          }
        },
        "state": {
          "blake3": "6582ee52e861d07c125664b864f8189f47a697e82b461087aa6e1c4a482eba46",
          "amplitudes": 4,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "0bc240d517a49c6052b02e972d0592f8b21b342c782f8770f845cc88e61045a3"
        },
        "work": 628,
        "accuracy": {
          "class": "bit-exact",
          "bound": 5.268356063861754e-9,
          "bound_units": 5.656854249492381,
          "outcomes": 2.107342431095817e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "six-level-fourier-column",
      "about": "F|1>: a column of F_6, every entry as held",
      "request": {
        "d": 6,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 1
          }
        ],
        "shots": 600,
        "seed": 17,
        "amplitudes": [
          "0",
          "1",
          "2",
          "3",
          "4",
          "5"
        ]
      },
      "result": {
        "answer": "run",
        "d": 6,
        "qudits": 1,
        "gates": 2,
        "shots": 600,
        "seed": 17,
        "counts": {
          "4": 111,
          "0": 103,
          "5": 102,
          "3": 99,
          "1": 95,
          "2": 90
        },
        "distinct_outcomes": 6,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 438353264,
            "im": 0
          },
          "1": {
            "re": 219176632,
            "im": 379625062
          },
          "2": {
            "re": -219176632,
            "im": 379625062
          },
          "3": {
            "re": -438353264,
            "im": 0
          },
          "4": {
            "re": -219176632,
            "im": -379625062
          },
          "5": {
            "re": 219176632,
            "im": -379625062
          }
        },
        "state": {
          "blake3": "ba01ac99b5b7e4f7c1b81d6265de3fc029838251d90fffdb19507d02d3226404",
          "amplitudes": 6,
          "norm2": 1073741822
        },
        "constants": {
          "blake3": "15f24f2b6546ea838e9360b122e4172c4574097c6fabc61cea0980c920596715"
        },
        "work": 654,
        "accuracy": {
          "class": "bit-exact",
          "bound": 1.9488911471471897e-8,
          "bound_units": 20.92605935115276,
          "outcomes": 7.795564664552292e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "six-level-inverse-column",
      "about": "F-dagger|1>: a column of F_6's inverse, every entry as held",
      "request": {
        "d": 6,
        "qudits": 1,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 3
          }
        ],
        "shots": 600,
        "seed": 17,
        "amplitudes": [
          "0",
          "1",
          "2",
          "3",
          "4",
          "5"
        ]
      },
      "result": {
        "answer": "run",
        "d": 6,
        "qudits": 1,
        "gates": 2,
        "shots": 600,
        "seed": 17,
        "counts": {
          "4": 111,
          "0": 103,
          "5": 102,
          "3": 99,
          "1": 95,
          "2": 90
        },
        "distinct_outcomes": 6,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "amplitudes": {
          "0": {
            "re": 438353264,
            "im": 0
          },
          "1": {
            "re": 219176632,
            "im": -379625062
          },
          "2": {
            "re": -219176632,
            "im": -379625062
          },
          "3": {
            "re": -438353264,
            "im": 0
          },
          "4": {
            "re": -219176632,
            "im": 379625062
          },
          "5": {
            "re": 219176632,
            "im": 379625062
          }
        },
        "state": {
          "blake3": "388630933c69df3439d11a1bfb4d743f65bdde6d687b4ad95660a213272daaad",
          "amplitudes": 6,
          "norm2": 1073741822
        },
        "constants": {
          "blake3": "15f24f2b6546ea838e9360b122e4172c4574097c6fabc61cea0980c920596715"
        },
        "work": 654,
        "accuracy": {
          "class": "bit-exact",
          "bound": 1.9488911471471897e-8,
          "bound_units": 20.92605935115276,
          "outcomes": 7.795564664552292e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qubit-walk",
      "about": "a walk of every gate on 4 qubits",
      "request": {
        "d": 2,
        "qudits": 4,
        "gates": [
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              0
            ],
            "power": 0
          },
          {
            "gate": "fourier",
            "qudits": [
              3
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              3
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              3
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              0,
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              3
            ],
            "powers": [
              0,
              0
            ]
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "fourier",
            "qudits": [
              3
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              3,
              0
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              3
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              3
            ],
            "powers": [
              0,
              1
            ]
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              0,
              0
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              3
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              3
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              0,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              3
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              0
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              3
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              3
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              0,
              0
            ]
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              1,
              0
            ]
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              1,
              1
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              1,
              1
            ]
          }
        ],
        "shots": 2000,
        "seed": 1
      },
      "result": {
        "answer": "run",
        "d": 2,
        "qudits": 4,
        "gates": 40,
        "shots": 2000,
        "seed": 1,
        "counts": {
          "1111": 1032,
          "0111": 968
        },
        "distinct_outcomes": 2,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "0aa957b2926f4cafaa8fc1a51107987dd50e858ee2bb380edc5db9175a7d74a0",
          "amplitudes": 16,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "fa5e6bc7fe53b14b4e5917caeb9b8028ae316c7f619bdd5c292565c9360b9dbf"
        },
        "work": 2416,
        "accuracy": {
          "class": "bit-exact",
          "bound": 6.199678638477233e-9,
          "bound_units": 6.656854249492381,
          "outcomes": 2.479871463078096e-8,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-walk",
      "about": "a walk of every gate on 4 qutrits",
      "request": {
        "d": 3,
        "qudits": 4,
        "gates": [
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              2,
              1,
              2
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              0
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 3
          },
          {
            "gate": "fourier",
            "qudits": [
              3
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              1,
              2,
              2
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              3
            ],
            "power": 3
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              3
            ],
            "power": 0
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              2,
              2,
              0
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              3,
              2
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              3
            ],
            "powers": [
              1,
              0,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              3
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 3
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 3
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 3
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              0
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              3,
              2
            ],
            "power": 2
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              0,
              1,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              0
            ],
            "power": 1
          },
          {
            "gate": "shift",
            "qudits": [
              3
            ],
            "power": 1
          },
          {
            "gate": "fourier",
            "qudits": [
              3
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              3
            ],
            "power": 1
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              3
            ],
            "powers": [
              1,
              1,
              0
            ]
          }
        ],
        "shots": 2000,
        "seed": 2
      },
      "result": {
        "answer": "run",
        "d": 3,
        "qudits": 4,
        "gates": 40,
        "shots": 2000,
        "seed": 2,
        "counts": {
          "2020": 87,
          "0201": 85,
          "1212": 83,
          "1202": 82,
          "1222": 82,
          "0001": 80,
          "0111": 80,
          "1012": 80,
          "0011": 79,
          "0121": 79,
          "1102": 79,
          "2120": 79,
          "2220": 77,
          "0221": 76,
          "2000": 76,
          "0021": 74,
          "1002": 74,
          "2110": 72,
          "1112": 70,
          "0101": 68,
          "2210": 68,
          "1122": 67,
          "2010": 65,
          "0211": 63,
          "1022": 62,
          "2100": 60,
          "2200": 53
        },
        "distinct_outcomes": 27,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "4adf1a43f5a3757090259e5b78278277b2dc49e57b258b7a8b087182499b8529",
          "amplitudes": 81,
          "norm2": 1073741820
        },
        "constants": {
          "blake3": "2f4a3854c397f95e152396701355baab1c14f1ba5a735c0d34378fd71b571d72"
        },
        "work": 6050,
        "accuracy": {
          "class": "bit-exact",
          "bound": 4.0247800800787827e-7,
          "bound_units": 432.1574704382658,
          "outcomes": 1.6099123560086069e-6,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "ququart-walk",
      "about": "a walk of every gate on 3 ququarts",
      "request": {
        "d": 4,
        "qudits": 3,
        "gates": [
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 3
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              3,
              1,
              1,
              1
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "shift",
            "qudits": [
              0
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 1
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              1,
              3,
              0,
              3
            ]
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              1,
              2,
              1,
              1
            ]
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 0
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 2
          },
          {
            "gate": "shift",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              0
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              2
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              0
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              3,
              1,
              3,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 2
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ],
            "power": 0
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              3,
              3,
              0,
              2
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ],
            "power": 0
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 2
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              1,
              3,
              2,
              2
            ]
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              3,
              0,
              3,
              0
            ]
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 1
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 0
          }
        ],
        "shots": 2000,
        "seed": 3
      },
      "result": {
        "answer": "run",
        "d": 4,
        "qudits": 3,
        "gates": 40,
        "shots": 2000,
        "seed": 3,
        "counts": {
          "123": 1253,
          "233": 252,
          "303": 248,
          "013": 247
        },
        "distinct_outcomes": 4,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "f3edb8450248b54f71e060e1f3bab3872c8ffd8ce80094ccab962531c67952d2",
          "amplitudes": 64,
          "norm2": 1073741824
        },
        "constants": {
          "blake3": "0bc240d517a49c6052b02e972d0592f8b21b342c782f8770f845cc88e61045a3"
        },
        "work": 4368,
        "accuracy": {
          "class": "bit-exact",
          "bound": 4.2146848510894035e-8,
          "bound_units": 45.254833995939045,
          "outcomes": 1.6858739759628984e-7,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "six-level-walk",
      "about": "a walk of every gate on 3 qudits of six levels",
      "request": {
        "d": 6,
        "qudits": 3,
        "gates": [
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 4
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 5
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              1
            ],
            "powers": [
              2,
              1,
              0,
              4,
              3,
              4
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              2,
              2,
              4,
              4,
              2,
              5
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              0
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 4
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 5
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 4
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 1
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              0
            ],
            "power": 5
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              0,
              5,
              2,
              1,
              4,
              2
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 5
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 5
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 5
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              2,
              0,
              5,
              2,
              0,
              2
            ]
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              3,
              5,
              5,
              1,
              4,
              5
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 4
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 5
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              0
            ],
            "power": 2
          },
          {
            "gate": "clock",
            "qudits": [
              0
            ],
            "power": 1
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 3
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ],
            "power": 1
          },
          {
            "gate": "fourier",
            "qudits": [
              0
            ],
            "power": 2
          },
          {
            "gate": "shift",
            "qudits": [
              1
            ],
            "power": 2
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 0
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ],
            "power": 0
          },
          {
            "gate": "phase",
            "qudits": [
              2
            ],
            "powers": [
              4,
              4,
              1,
              1,
              1,
              0
            ]
          },
          {
            "gate": "clock",
            "qudits": [
              2
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              1
            ],
            "power": 5
          },
          {
            "gate": "phase",
            "qudits": [
              0
            ],
            "powers": [
              5,
              4,
              1,
              5,
              1,
              0
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
            ],
            "power": 4
          },
          {
            "gate": "shift",
            "qudits": [
              2
            ],
            "power": 1
          }
        ],
        "shots": 2000,
        "seed": 4
      },
      "result": {
        "answer": "run",
        "d": 6,
        "qudits": 3,
        "gates": 40,
        "shots": 2000,
        "seed": 4,
        "counts": {
          "105": 346,
          "132": 346,
          "150": 345,
          "114": 341,
          "141": 320,
          "123": 302
        },
        "distinct_outcomes": 6,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "de1329ef361843d75e9536dfc9d9f8d8c826116f8b54d6f691df19db2ae9511c",
          "amplitudes": 216,
          "norm2": 1073741829
        },
        "constants": {
          "blake3": "15f24f2b6546ea838e9360b122e4172c4574097c6fabc61cea0980c920596715"
        },
        "work": 10640,
        "accuracy": {
          "class": "bit-exact",
          "bound": 5.164234028580268e-7,
          "bound_units": 554.5054065410645,
          "outcomes": 2.0656941448183693e-6,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qubit-wide",
      "about": "14 qubits spread over every outcome",
      "request": {
        "d": 2,
        "qudits": 14,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              1
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              2
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          },
          {
            "gate": "fourier",
            "qudits": [
              3
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              4
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              5
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              6
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              7
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              8
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              9
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              10
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              11
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              12
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              13
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              3,
              4
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              4,
              5
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              5,
              6
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              6,
              7
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              7,
              8
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          },
          {
            "gate": "csum",
            "qudits": [
              8,
              9
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          },
          {
            "gate": "csum",
            "qudits": [
              9,
              10
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              10,
              11
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          },
          {
            "gate": "csum",
            "qudits": [
              11,
              12
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          },
          {
            "gate": "csum",
            "qudits": [
              12,
              13
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              7,
              2
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            "power": 1
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          {
            "gate": "clock",
            "qudits": [
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            "power": 0
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          {
            "gate": "clock",
            "qudits": [
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            "power": 1
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          {
            "gate": "phase",
            "qudits": [
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            "powers": [
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              0
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          },
          {
            "gate": "csum",
            "qudits": [
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              7
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            "power": 0
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          {
            "gate": "csum",
            "qudits": [
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              4
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            "power": 0
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          {
            "gate": "phase",
            "qudits": [
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            "powers": [
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          },
          {
            "gate": "phase",
            "qudits": [
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            "powers": [
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          },
          {
            "gate": "clock",
            "qudits": [
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            "power": 1
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          {
            "gate": "phase",
            "qudits": [
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            "powers": [
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          },
          {
            "gate": "csum",
            "qudits": [
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            "power": 0
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          {
            "gate": "phase",
            "qudits": [
              13
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            "powers": [
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              1
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          }
        ],
        "shots": 300,
        "seed": 21
      },
      "result": {
        "answer": "run",
        "d": 2,
        "qudits": 14,
        "gates": 39,
        "shots": 300,
        "seed": 21,
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          "11111111100110": 1,
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        "distinct_outcomes": 297,
        "omitted_shots": 0,
        "outcomes": "each outcome is the qudits' digits, the highest-numbered qudit first",
        "state": {
          "blake3": "3d5073e1f8bb4b9dc33b42332b27f021d14fcfa6f50343a929ddd4817ce1c150",
          "amplitudes": 16384,
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        "constants": {
          "blake3": "fa5e6bc7fe53b14b4e5917caeb9b8028ae316c7f619bdd5c292565c9360b9dbf"
        },
        "work": 819500,
        "accuracy": {
          "class": "bit-exact",
          "bound": 2.3732620470214544e-6,
          "bound_units": 2548.27071919879,
          "outcomes": 9.493059452831305e-6,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "qutrit-wide",
      "about": "8 qutrits spread over every outcome",
      "request": {
        "d": 3,
        "qudits": 8,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
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          },
          {
            "gate": "fourier",
            "qudits": [
              1
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          },
          {
            "gate": "fourier",
            "qudits": [
              2
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          },
          {
            "gate": "fourier",
            "qudits": [
              3
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          },
          {
            "gate": "fourier",
            "qudits": [
              4
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          },
          {
            "gate": "fourier",
            "qudits": [
              5
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          },
          {
            "gate": "fourier",
            "qudits": [
              6
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          },
          {
            "gate": "fourier",
            "qudits": [
              7
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          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
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          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              3,
              4
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              4,
              5
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              5,
              6
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              6,
              7
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          },
          {
            "gate": "csum",
            "qudits": [
              2,
              1
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            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              3
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            "power": 0
          },
          {
            "gate": "clock",
            "qudits": [
              2
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            "power": 1
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          {
            "gate": "fourier",
            "qudits": [
              0
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            "power": 2
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          {
            "gate": "shift",
            "qudits": [
              2
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            "power": 2
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          {
            "gate": "csum",
            "qudits": [
              5,
              1
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            "power": 1
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          {
            "gate": "shift",
            "qudits": [
              0
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            "power": 0
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          {
            "gate": "csum",
            "qudits": [
              3,
              0
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            "power": 1
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          {
            "gate": "fourier",
            "qudits": [
              0
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            "power": 0
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          {
            "gate": "shift",
            "qudits": [
              2
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            "power": 0
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          {
            "gate": "clock",
            "qudits": [
              7
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            "power": 2
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          {
            "gate": "fourier",
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            "power": 0
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        ],
        "shots": 300,
        "seed": 21
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      "result": {
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        "shots": 300,
        "seed": 21,
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        "distinct_outcomes": 296,
        "omitted_shots": 0,
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        "state": {
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          "amplitudes": 6561,
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        "constants": {
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        "work": 256179,
        "accuracy": {
          "class": "bit-exact",
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          "outcomes": 9.436650461090378e-6,
          "note": "the amplitudes are the same integers on every host; the state is within bound (bound_units at 2^-30) of the ideal state in the 2-norm, each gate's rounding and constants added up as quantum-sim.md §9.4 states, and the counts are drawn from a law within outcomes of the ideal outcome distribution in total variation"
        }
      }
    },
    {
      "name": "ququart-wide",
      "about": "7 ququarts spread over every outcome",
      "request": {
        "d": 4,
        "qudits": 7,
        "gates": [
          {
            "gate": "fourier",
            "qudits": [
              0
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          },
          {
            "gate": "fourier",
            "qudits": [
              1
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          },
          {
            "gate": "fourier",
            "qudits": [
              2
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          },
          {
            "gate": "fourier",
            "qudits": [
              3
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          },
          {
            "gate": "fourier",
            "qudits": [
              4
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          },
          {
            "gate": "fourier",
            "qudits": [
              5
            ]
          },
          {
            "gate": "fourier",
            "qudits": [
              6
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          },
          {
            "gate": "csum",
            "qudits": [
              0,
              1
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              1,
              2
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              2,
              3
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              3,
              4
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              4,
              5
            ]
          },
          {
            "gate": "csum",
            "qudits": [
              5,
              6
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          },
          {
            "gate": "shift",
            "qudits": [
              5
            ],
            "power": 1
          },
          {
            "gate": "clock",
            "qudits": [
              1
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            "power": 0
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          {
            "gate": "clock",
            "qudits": [
              0
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            "power": 3
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          {
            "gate": "fourier",
            "qudits": [
              0
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            "power": 3
          },
          {
            "gate": "clock",
            "qudits": [
              1
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            "power": 1
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          {
            "gate": "csum",
            "qudits": [
              4,
              2
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            "power": 3
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          {
            "gate": "shift",
            "qudits": [
              3
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            "power": 2
          },
          {
            "gate": "fourier",
            "qudits": [
              0
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            "power": 0
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          {
            "gate": "phase",
            "qudits": [
              6
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            "powers": [
              2,
              3,
              3,
              2
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          },
          {
            "gate": "fourier",
            "qudits": [
              0
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            "power": 1
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          {
            "gate": "phase",
            "qudits": [
              4
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            "powers": [
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              0,
              1,
              2
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          },
          {
            "gate": "csum",
            "qudits": [
              6,
              5
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            "power": 0
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        ],
        "shots": 300,
        "seed": 21
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      "result": {
        "answer": "run",
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        "shots": 300,
        "seed": 21,
        "counts": {
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