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The second version of the energy-landscape job (extensions/quantum-landscape-2.md), alongside the first, which answers byte for byte as before (register T1-1 and T4-5; holes H-7, H-9, R-30). - Each variable has its own cost, of either sign (`cost I C`; `cost C` may be below 0). A variable whose cost is below 0 is never 0 in a state of lowest energy, so `exactly K I J ...` (one-hot and cardinality) and `atmost 1 I J ...` lower exactly to couplings of -1 and whole-number fields; `#! check exactly` and `#! check atmost` grade an answer. - Kernels wai.quantum.landscape2/settle and /sample: each cell at its own cost; the settle move is the cell's lowest energy, a tie to 0 then to +, the first version's move wherever a cost is 0 or more. A request names the version with "protocol"; none is the first. - Joules: a run at temperature 0 priced at about 0.88 pJ an accumulate, the open FPGA member's measured settle figure, with its provenance, caveats and files under `evidence`; a run above it is "unpriced", with why and no figure. The first version keeps its rates (its replay lines hash whole answers) and its section 4.4 now says what stands behind them. - Ten worked examples: colouring (four regions, an odd ring of five, six regions, and four regions that all touch, which must fail), assignment at 3x3, 4x4 and 5x5, two in each row and column, four queens, and the assignment at temperature 0. Every lowest state solves each one marked as working where all arrangements are checked; seeds 1 to 100 at its own plan all solve it, and the two that must fail fail at all 100. The set states each one's reach. - The vector rule: quantum-conformance/landscape/vectors.json is frozen as it stood on 2026-11-10 and v2/vectors.json at publication, each BLAKE3 pinned (conformance2); the first version's section 9 states how its set changed on 11-06 and 11-09, and why. - Members: Member::protocols (provided; the first version by default). Only the CPU reference runs /2; the WebGPU, CUDA, Metal and FPGA members are certified on /1 alone and passed over for a /2 job, saying why. The FPGA member's label names the frozen /1 set. - Reach: the CLI (--protocol 2), the job service's /v1/landscape routes (stamped with the answer's version), Python (protocol=), npm and the desktop app carry /2; verify holds a /2 answer to its form. The MCP tool keeps to /1 (its output schema is landscape.v1.json) and a client sends no /2 job to a provider, whose description offers /1. - Registry: the two kernel labels; schemas/landscape.v2.json. Workflow pins updated. Co-Authored-By: Claude Opus 5.5 <[email protected]>
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Energy-landscape jobs: conformance and results
For the extension quantum-landscape. Reference: wai_quantum::quantum_landscape
and wai-quantum landscape. Everything here is the output of a command named below, on the code at the commit that
holds it. Every count is deterministic: the same command gives the same bytes on any machine. Wall-clock time is not,
and it is kept apart.
| file | what | made by |
|---|---|---|
vectors.json |
the conformance set a member is held to, §7 of the extension; frozen as it stood on 2026-11-10 (below) | wai-quantum landscape vectors |
v2/vectors.json |
the second version's set, §6 of quantum-landscape-2; frozen |
wai-quantum landscape vectors --protocol 2 |
table.json, table.md |
the scale table, below | wai-quantum landscape table --out DIR |
timing.json |
that table's wall-clock seconds a run, on one machine | the same command |
trial-assignment.json |
a trial outside the job form, below | wai-quantum landscape trial-assignment |
native-wasm.txt |
the browser build against the command line | wai-web/demo/verify_landscape_wasm.mjs, verify_landscape_page.mjs |
stated-result.md, reproduce.sh |
a stated result, and the script that checks it |
These are classical runs on a classical emulator, and nothing in them is a quantum effect.
Both sets are frozen
vectors.json is frozen as it stood on main on 2026-11-10 (sha256
1da13d2570eb5b1367d3017b465e1b6a199429210def0c4300dbc403413e3a8e), and v2/vectors.json at its
publication. The code pins each one's BLAKE3 digest (conformance2::VECTORS_1_BLAKE3, VECTORS_2_BLAKE3), and
tests/landscape2.rs fails on any difference: a change of any kind to either is a new version of the protocol. The
first set changed its form and grew three times after it was first published, with no expected bit of an earlier
vector changing; the first version's §9 lists each change and why. The FPGA member's grade names the set it was
earned on.
The second version's worked examples
Ten programs, in wai-quantum/src/quantum_landscape/programs/2/, written with a cost for each variable and the
constraints exactly and atmost. Each one's reach in v2/vectors.json states how seeds 1 to 100 end at the
program's own plan; a test holds it to the code. Where every arrangement is checked, each one marked as working has
every lowest state solving its problem.
| example | variables | lowest, and how many lowest states solve it | seeds 1 to 100 |
|---|---|---|---|
colour-four |
12 | −35: 6 of 6, the six colourings | 100 solved |
colour-five-ring |
15 | −40: 30 of 30 | 100 solved |
colour-six |
18 | not enumerated; an answer that passes its check is a lowest state (quantum-landscape-2 §6) | 100 solved |
colour-four-all-touching |
12 | −36: 0 of 24, as it must (four regions that all touch need four colours) | 100 failed |
assign-3x3 |
9 | −21: 6 of 6 | 100 solved |
assign-4x4 |
16 | −48: 24 of 24 | 100 solved |
assign-5x5 |
25 | not enumerated; as colour-six |
100 solved |
two-in-each-row-and-column |
16 | −32: 90 of 90 | 100 solved |
four-queens |
16 | −84: 2 of 2 | 100 solved |
assign-3x3-settled |
9 | −21: 6 of 6, at temperature 0 | 100 failed: never rests |
These are a few small instances at one plan each, on the reference: they show that these landscapes express these problems and that this plan reached their lowest states. They say nothing of larger instances or of a device.
The worked examples
Fourteen programs, in wai-quantum/src/quantum_landscape/programs/. At seeds 1 to 20 each one marked as working is
solved every time, and each one marked as failing fails every time, for its stated reason (job::tests).
| example | variables | what it shows | result |
|---|---|---|---|
talks |
12 | three states: room A, room B or left out | lowest energy −10, reached at all 1,000 seeds tried |
clusters |
8 | signed clustering with a quarrel no split can settle | lowest energy −1, reached |
selection |
14 | six of fourteen that belong together | lowest energy −9, and the planted six |
chain |
8 | the deterministic mode with one end held | settles to the one lowest arrangement |
assign-2x2 |
4 | assignment written as sums, 2×2 | both lowest states are assignments |
blocks |
64 | eight blocks of eight: too many arrangements to check | the planted pattern, with 200 sweeps a start |
assign-3x3 |
9 | the same construction, 3×3 | fails: 21 lowest states, only 6 of them assignments |
colour-six |
6 | three colours, six regions | fails: none of the 6 lowest states is a colouring |
colour-four |
4 | three colours, four regions | fails: neither of the 2 lowest states is a colouring |
piles |
8 | two equal piles | fails: quantising to signs loses the sizes, and the answer has energy −7 on the weights as declared, against −130 |
cold-constraint |
4 | 2×2 assignment at temperature 0 | fails: never rests, flipping between two states |
cold-start |
12 | the talks at temperature 0, from all 0 | misses: stays at 0, energy 0 against −10 |
too-costly |
14 | the six of fourteen at too high a cost | fails: leaving everything out is the one lowest state |
typo |
3 | a misspelt statement | refused: Line 6: opposis not a statement epuML knows. Did you meanoppose? |
Where the truth exists and a program has its own check, every lowest arrangement is graded against it. That is how
assign-3x3 fails even when a run's answer happens to be an assignment: the landscape does not express the problem.
Native and WebAssembly
wai-web/demo/verify_landscape_wasm.mjs sends the same request to wai-quantum landscape call and to the browser build, and
compares the bytes: every example at its own temperature, at 0, at 0.5 and at a temperature given as text, a replay of 2,000 seeds
each, whole answers for 11 seeds, a sweep and a comparison. 700 answers the same bytes, 0 different, 104,000 seeded runs. In Chrome,
verify_landscape_page.mjs repeats the replays in the browser's own engine: 84 of 84 answers the same bytes, 19,500 seeded runs
(native-wasm.txt). The command line gives the same bytes on x86-64 Linux, arm64 Linux and arm64 macOS
(stated-result.md).
Two pinned digests hold this in the repository's checks. job::tests::every_platform_gives_the_same_bits covers every worked
example at three temperatures over 20 seeds, on Linux x86-64 and arm64, macOS arm64 and wasm32-wasip2 under wasmtime, in debug and
release builds. landscape_jobs_are_the_native_bits_in_wasm runs the browser build's own, over 3 seeds, in wai-web-wasm.yml.
The scale table
Four families, 8 to 128 variables (dense to 64), 5 instances each, 20 runs an instance and method, at 8 starts of 40 sweeps and of 320. Every method in a row has the budget of the sampling mode's run, where one operation is one coupling read, one cell updated or one move considered, whoever does it. The target is the exact lowest energy up to 16 variables, then a planted answer, or the best that long runs of simulated annealing and tabu search found, which proves nothing.
Who reached the target more often, row by row, against the best of the three classical methods:
| the sampling mode | ahead | tied | behind | of |
|---|---|---|---|---|
| at the default start | 2 | 45 | 21 | 68 |
| at the hot start, the largest row of couplings | 0 | 38 | 30 | 68 |
Simulated annealing is the strongest method here: it is the best of the three, or level with the best, in 64 of the 68 rows, and it is ahead of the default start in 20 where the default start is ahead of it in 2. The two rows where the sampling mode is ahead of all three are ahead by one run of a hundred (clusters at 64 variables and 320 sweeps, sparse-glass at 32 and 40), which chance gives. Simulated annealing leads where it matters, at the larger sizes. At the default budget, at the largest size of each family:
| family | variables | default start | hot start | deterministic | simulated annealing | tabu search | greedy descent |
|---|---|---|---|---|---|---|---|
| clusters | 128 | 46 of 100 | 0 | 0 | 79 | 7 | 0 |
| sparse-glass | 128 | 36 | 0 | 0 | 71 | 5 | 0 |
| dense-glass | 64 | 81 | 4 | 0 | 97 | 54 | 91 |
| selection | 128 | 100 | 100 | 100 | 100 | 100 | 100 |
The deterministic mode, at temperature 0 from random starts, is far behind on all but the selection family, which is easy for everyone.
timing.json has wall-clock seconds a run on one shared machine. They depend on how each method here is written, and say nothing about a
device, so they are not a result.
What the table does not say. The operation count says nothing about what an operation costs in hardware, or about running cells side by side, which a machine would do and these methods do not.
The starting temperature
A solve with no t0 starts at the square root of the mean couplings a variable has, and at least 1. On instance 99 of three families at 32 and 64
variables, which the table's rows do not use, 40 runs at each start:
| held-out instance | lowest found | default start: runs at the lowest | hot start: runs at the lowest | start 1: runs at the lowest |
|---|---|---|---|---|
| clusters, 32 | −16 | 2: 40 of 40 | 9: 28 | 40 |
| clusters, 64 | −26 | 2: 28 | 8: 1 | 40 |
| sparse-glass, 32 | −19 | 2.449: 33 | 13: 15 | 38 |
| sparse-glass, 64 | −51 | 2.449: 40 | 12: 4 | 40 |
| dense-glass, 32 | −128 | 5.568: 39 | 31: 23 | 39 |
| dense-glass, 64 | −362 | 7.937: 38 | 63: 0 | 40 |
The hot start, the largest row of couplings, is far too hot at 64 variables, and worse at every size here. The default was chosen with this section in
view, and it is not the best start: a start of 1 does at least as well on all six, better on three of them (by 2 to 12 runs of 40), and on clusters at
64 by a wide margin. It stays where it is because it depends on the instance, and a fixed start of 1 would be too cold for a landscape of larger fields.
No instance here shows that; it is a judgement. wai-quantum landscape sweep tries the temperatures on a program of your own.
Assignment with a {0, +1} domain
wai-quantum landscape trial-assignment, outside the job form: the same assignment landscape, with each cell limited to 0 or +1. 40 runs a size, 8 starts of 60 sweeps.
| grid | lowest states (assignments among them) | three states | {0, +1} |
|---|---|---|---|
| 2×2 | 2 (2) | 40 of 40 | 40 of 40 |
| 3×3 | 21 (6) | 15 | 40 |
| 4×4 | 1,344 (24) | 1 | 40 |
| 5×5 | too many to check | 0 | 40 |
| 6×6 | 0 | 40 | |
| 8×8 | 0 | 40 |
So a {0, +1} domain fixes feasibility: the lowest states become exactly the assignments. It does not fix costs. With costs of 0 or 1 a cell, on 80 random instances, it found the cheapest assignment every time the cheapest cost 0, and never found a valid assignment when the cheapest cost more: the couplings are fixed at 1, so the constraint's weight is 1, and a cost of 1 ties with leaving a row empty. Costed assignment would need couplings above 1 or fractional fields, and this model has neither. The domain itself is a change to the cell, so it is a trial and not a kernel.
The joule line
On the twelve talks: 13,440 accumulates × about 0.41 pJ = about 5.5 nJ, priced. The same run's 320 sweeps need at least 320 clocks on that board, which draws about 3.1 W whatever it does: about 9.9 µJ of board power the priced line leaves out. A run's joules are not measured here, because no meter is attached to a run here.
A member's conformance
A member is held to vectors.json as §7 of the extension says, and the host finds its parity by running its kernels there: settle bit for bit
for a bit-exact settle kernel, every vector it takes, and it takes every vector whose field bound is at most 2³¹ − 1; chains bit for bit for a bit-exact
sampling kernel, the same way; otherwise the statistical battery, thirteen workloads of 20,000 chains each, each block's final states against its exact
distribution. wai-quantum/tests/landscape_conformance.rs reads the file as a member's checker would, from the file alone, and holds both parts to kernels
that are wrong in one way each. The vectors refuse a dropped carry in a 32 by 32 product, a cut point compared by its high word, fields held in 16 or 32
bits, a check of the fields that forgets the couplings, cells last to first, a draw counter that starts again at each of a device's windows of sweeps, a
run that stops after one window, chains past the first 64 left alone, a settle whose cells past 64 or 256 never move or that reports its end a sweep late,
and a member that declines below the line. The battery passes the reference's own kernel, one that colours its cells properly and one that takes its
cells last to first, and refuses kernels that move cells all at once, even then odd, ignore the schedule or keep only its end, clamp the table at 5,
sample the last sweep, hold their fields in 16 or 32 bits, or leave cells from the fifth on where they started.