Exact

Exact Union RegExp

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Transaction Science 72145ce6f9 WAI Quantum: the tracker's 49-qubit operator Loschmidt echo corrected loop by loop around belief propagation, and the four fast receipts sealed with the operator's key again ... quantum_bptn::clusters (written from J. Gray, G. Park, G. Evenbly, N. Pancotti, E. F. Kjonstad and G. K.-L. Chan 2025, and S. Midha and Y. F. Zhang 2025): Tns::expect_region_bp contracts any region exactly with belief propagation's messages on its boundary, which is the loop series restricted to the region summed to every order. Each piece is contracted from the leaves of a spanning tree to a root, the bonds the tree leaves out cut and summed over their ket and bra indices; every set of cuts that leaves a spanning tree (up to 20,000) is tried with every root against an estimate of the work and of the tables' memory, and the cheapest whose tables fit in 16 GiB is taken (RegionPlan). On the 49x648 echo at chi = 64 that halves the largest three-ring region's work (1.0e15 -> 4.9e14) and cuts another's by 4.5 (8.3e13 -> 1.8e13) against cutting the smallest bonds of a spanning tree of the largest. Combinations are summed as they come, each sum in a fixed order and each rescaling by a power of two: the same bits at any worker count and on every platform. Also loop_weight (a ring's own correction Z_l, the loop correlation check), counting_numbers and loop_cluster_terms (Gray et al.'s Algorithm 1), cluster_combine (product and sum formulas), short_cycles and cell_unions. tracker_ole mode loops: the arc through the observable's sites (order 0), then order k = the observable's ring F joined with every connected set of k - 1 other rings, closed under intersection and counted; regions past the run's work or memory budget are left out and named, and the order over the regions read is reported beside it. 49x648, chi = 64, 96, 128, 160, 192, 256, 320 (summed discarded weight 0.088 to 0.0015): order 1 (F exact) is the fast sweep's loop readout, the arc its arc bit for bit. Order 2 (F joined with D and with E, the two rings sharing a path with it) adds +0.0019, +0.0026, +0.0031, +0.0034, +0.0036, +0.0039, +0.0040, growing with chi, a nineteenth to a twelfth of what order 1 adds to the arc; at chi = 320 it reads 0.8235. On a line in the discarded weight through the last three chi (residual 3e-6) order 2 meets none discarded at 0.82251 (order 1: 0.81845, as before). The ring D gives almost all of it (DF over F +0.20 % at chi 64, +0.46 % at 320). Each ring's own Z_l is at most 2.8e-4 in size and falls with chi. Order 3 not reached: of its five three-ring regions only BDF fits the budgets run (6e12 to 2e13 multiply-adds), and it moves the value by at most 2e-10; at chi = 64 the others need 1.8e13 to 4.9e14 multiply-adds (ADF's tables 309 GB, past every host's cap), above chi = 64 1.4e14 to 1.2e16. Error estimate, with its assumption: if each order adds the same fraction of the one before as order 2 does of order 1 (Aitken's delta-squared on arc, order 1, order 2), the orders not run add 1.0e-4 at chi = 64 and 3.5e-4 at chi = 320, and the estimate extrapolates to 0.82287. That is an estimate, not a bound, and it is not tested against a third order here. Published: device 0.824, belief-propagation tensor networks 0.8203 (bond 192) and 0.8217 (bond 512), single-path Monte Carlo 0.808. 49x1296 and 70x1872: not converged (summed discarded weight 13 to 29), and order 2 there needs 6e13 to 1e14 multiply-adds at chi = 32, 1.6e15 at 48 and 1.6e16 at 64 (plan-only runs); the expansion corrects contraction, not truncation, so it cannot make those readings bound the echo. At chi = 96 all 24 numbers of the expansion have the same bits on Linux x86_64 (32 workers) and macOS arm64 (16 workers). Receipts: 49x648 loops at chi 96 and 128 sealed with the operator's key on Linux x86_64; chi 64, 160, 192, 256 and 320 with the demonstration key on macOS arm64. The four fast receipts cb44dd4a8 re-sealed with the demonstration key (49x648 chi 64 and 96, 49x1296 and 70x1872 chi 64) are sealed with the operator's key again: re-run on Linux x86_64 in their committed settings, each request equal to the committed one and every number in each result the committed bits. Tests: clusters unit tests (a region holding every loop is exact whatever its cuts; worker-count bits; the cuts chosen cost no more than the largest bonds' tree's); tracker_reference: on a ladder of three squares order 2 is nearer the network's exact contraction than order 1 in four trials of six (summed distances: arc 3.43e-3, order 1 2.89e-3, order 2 1.85e-3), and the 49x648 loops receipts pinned. Change note: wai/changes/2026-11-14-wai-quantum-ole-loop-cluster-expansion.md. Co-Authored-By: Claude Opus 5.5 <[email protected]>		2026-11-14 08:34:52 -05:00
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equiv_bench	wai-quantum: the compilation flow's renaming test holds each exchange it names, and the benchmark note says what was measured	2026-11-13 18:03:08 -05:00
gbs_loops	quantum_gbs: a 2022 time-domain photonic boson sampler's samples against their exact ground truth	2026-11-12 02:44:00 -05:00
qec_memory	qec_memory: held-out shot windows, every decoder's predictions kept, and paired tests against the published decoders	2026-11-13 07:31:16 -05:00
svd	WAI Quantum: a fast deterministic dense SVD, and the all-to-all peaked 56x1917 read on a chain	2026-11-12 10:29:47 -05:00
tracker	WAI Quantum: the tracker's 49-qubit operator Loschmidt echo corrected loop by loop around belief propagation, and the four fast receipts sealed with the operator's key again	2026-11-14 08:34:52 -05:00
arch_factoring.rs	wai-quantum 0.3.29: the architecture around the code, priced, and the 2025 factoring machine re-run	2026-10-04 17:33:48 -04:00
bell.rs	wai-quantum circuit2: the crate's consumers follow the circuit's gateset	2026-10-09 11:19:49 -04:00
chem_dmrg.rs	wai-quantum 0.3.36: molecules and neural quantum states, held to exact answers	2026-10-05 16:15:50 -04:00
cutrank_gpu.rs	wai-quantum: the cut-rank table on the GPU, and the engine's cutrank_single method	2026-10-20 17:34:17 -04:00
cutrank_qasm.rs	wai-quantum 0.6.14: design critique, equivalence, alternatives and classical shortcuts across every surface; contraction trees that sweep along the line	2026-10-22 02:40:04 -04:00
dmrg_chain.rs	wai-quantum 0.3.34: ground states of spin chains by DMRG, held to exact answers	2026-10-05 09:50:20 -04:00
equiv_bench.rs	wai-quantum: the equivalence checker's rewriting contracts what it leaves, and runs over a published benchmark set with sealed receipts	2026-11-12 13:12:00 -05:00
estimate_calibration.rs	wai-quantum: resource estimation from programs, calibrated from the crate's own decoders	2026-10-27 23:44:27 -04:00
extension_points.rs	wai-quantum: the example's plan, a comment for a macro, and a type for the walk's step	2026-11-07 01:53:13 -05:00
fabric_state.rs	WAI Quantum cross-simulator: the engine's other methods against exact references, the integer reference to 22 qubits, GPU members, nightly	2026-11-11 18:52:55 -05:00
fabric_timing.rs	wai-quantum: auto places a state on a member only where the measurements say it is faster	2026-10-31 22:05:00 -04:00
gbs_check.rs	wai-quantum 0.3.27: Gaussian boson sampling, exactly	2026-10-04 16:19:25 -04:00
gbs_loops.rs	quantum_gbs: a 2022 time-domain photonic boson sampler's samples against their exact ground truth	2026-11-12 02:44:00 -05:00
gbs_sampler.rs	quantum_gbs_mps: the sampler's pair statistics net of sampling noise, and its verdicts corrected	2026-11-13 21:32:38 -05:00
landscape_solution.rs	wai-quantum: energy to solution for the landscape emulator, registered before the table is run	2026-11-11 10:24:37 -05:00
landscape_stage0.rs	wai-quantum: Stage 0 of the landscape emulator, run as registered: its data, its document and its CI job	2026-11-11 14:10:29 -05:00
ldpc_memory.rs	wai-quantum 0.3.30: qLDPC memory at circuit level, re-derived from the circuit up	2026-10-04 21:30:40 -04:00
noisy_bench.rs	wai-quantum: branching noisy trajectories (shots that share a history share a state)	2026-10-17 11:36:07 -04:00
npu_onnx.rs	wai-quantum: the limb model in the portable format; f16_of at 2048	2026-10-14 10:03:55 -04:00
nqs_ground.rs	nqs_ground: a projected network up to 24 spins is held to its sector alone	2026-10-08 14:17:42 -04:00
otoc_spd.rs	WAI Quantum: OTOC(1) and OTOC(2) of the published echo circuits, on the state vector and by propagation, each run sealed in a receipt	2026-11-11 22:27:35 -05:00
otoc_sv.rs	WAI Quantum OTOC at 31 qubits: all 50 circuits' ΔC4, the four outside three standard errors named, and the spread's own uncertainty read as Student's t	2026-11-12 12:36:17 -05:00
otoc_tn.rs	WAI Quantum: OTOC(1) and OTOC(2) of the published echo circuits, on the state vector and by propagation, each run sealed in a receipt	2026-11-11 22:27:35 -05:00
patch_xeb.rs	wai-quantum: the remaining single findings	2026-11-10 18:10:29 -05:00
published_architectures.rs	wai-quantum: the published-architecture check, as its review asked	2026-11-06 08:00:15 -05:00
qec_frame.rs	WAI Quantum: measurement records from the frame simulator, the same bits on every machine, and cultivation circuits	2026-11-11 08:46:24 -05:00
qec_threshold.rs	wai-quantum 0.3.25: error correction at circuit level, sampled, modelled and decoded exactly	2026-10-04 14:21:56 -04:00
qio_gset.rs	wai-quantum 0.3.31: quantum-inspired optimisation, a re-runnable classical baseline	2026-10-05 05:27:49 -04:00
receipt.rs	wai-quantum circuit2: the crate's consumers follow the circuit's gateset	2026-10-09 11:19:49 -04:00
rv32_listing.rs	wai-quantum 0.5.2: the dataflow device's vector engine as a member	2026-10-15 01:49:20 -04:00
stablehlo_gate.rs	wai-quantum: the gate's products as a portable matrix-unit program	2026-10-15 10:06:50 -04:00
sv_bench.rs	wai-quantum: tiled multi-gate state-vector passes; vectorised wide-gate kernel	2026-10-17 11:21:27 -04:00
sv_run.rs	wai-quantum 0.3.28: the dense state vector at any angle, the same bits threaded or not	2026-10-04 17:01:39 -04:00
svd_bench.rs	WAI Quantum: quantum_svd reduces matrices past the caches in panels, and runs its inner loops on AVX2 where the processor has it	2026-11-13 10:32:22 -05:00
tdvp_quench.rs	wai-quantum 0.3.35: time evolution of spin chains by TDVP, held to exact answers	2026-10-05 11:13:38 -04:00
threshold.rs	wai-quantum 0.3.13: mixed states, and a bound that classical physics cannot reach	2026-09-07 03:47:38 -04:00
tn_cost.rs	wai-quantum tn: path search from independent restarts; the engine runs eight	2026-10-20 17:34:17 -04:00
tn_path.rs	wai-quantum 0.3.26: tensor-network contraction, hyper-optimised, sliced, bit-identical	2026-10-04 16:03:22 -04:00
tn_sweep.rs	wai-quantum 0.6.14: design critique, equivalence, alternatives and classical shortcuts across every surface; contraction trees that sweep along the line	2026-10-22 02:40:04 -04:00
tracker_guided.rs	WAI Quantum: published quantum-advantage instances reproduced, with an echo method and a loop readout	2026-11-11 21:49:12 -05:00
tracker_ole.rs	WAI Quantum: the tracker's 49-qubit operator Loschmidt echo corrected loop by loop around belief propagation, and the four fast receipts sealed with the operator's key again	2026-11-14 08:34:52 -05:00
tracker_peaked.rs	WAI Quantum: a fast deterministic dense SVD, and the all-to-all peaked 56x1917 read on a chain	2026-11-12 10:29:47 -05:00
tracker_su2.rs	WAI Quantum: published quantum-advantage instances reproduced, with an echo method and a loop readout	2026-11-11 21:49:12 -05:00
uf_bench.rs	wai-quantum 0.3.32: union-find decoding in near-linear time	2026-10-05 07:46:12 -04:00
utility.rs	wai-quantum 0.3.22: sparse Pauli dynamics at utility scale, and identical bits on every platform	2026-10-01 15:13:52 -04:00
utility_bptn.rs	wai-quantum 0.3.23: belief-propagation tensor networks, a second method for the same circuits	2026-10-01 20:40:14 -04:00
utility_mz.rs	wai-quantum 0.3.22: sparse Pauli dynamics at utility scale, and identical bits on every platform	2026-10-01 15:13:52 -04:00
xeb_sv.rs	wai-quantum: the cross-entropy reader takes circuits of up to 128 qubits; the 2024 three-patch circuits do not reproduce as read	2026-11-14 07:17:06 -05:00