WAI Extension: Energy-Landscape Jobs, Second Version (wai.quantum.landscape/2)

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Status: Draft. Reference: the quantum_landscape feature of wai-quantum (wai_quantum::quantum_landscape, its reader program::read_2 and its set conformance2), the command wai-quantum landscape … --protocol 2, and QuantumEngine.landscape in the browser build with the request’s protocol. Answer schema: wai-quantum/schemas/landscape.v2.json. Conformance set: quantum-conformance/landscape/v2/vectors.json.

Keywords MUST, MUST NOT, SHOULD and MAY are RFC 2119/8174.

0. What this version changes

The second version is the first (quantum-landscape) with four changes, and everything that text says holds here unless a section below says otherwise: the request and its limits (§2, §2.0 there), the grammar and its weights (§2.1, §2.2), the answer, its verdict and its replay digest (§3), the schedule, the draws, the cut points and the exponential (§4.2, Appendix A), the members, their checks and the audit (§5, §7.3), and the comparison (§6).

  1. A cost for each variable, of either sign (§1, §2). The first version has one cost c ≥ 0, so a variable is always free to be 0 at no cost, and a constraint over a group’s count cannot be written: colouring with interchangeable colours, assignment above a 2×2 grid and cardinality do not run there (its §8). A cost below 0 keeps a variable out of 0 in every state of lowest energy, and with it one-hot, at-most-one and exactly-K constraints are written with couplings of one sign and whole-number fields (§2.2).
  2. Kernels of its own (§4): wai.quantum.landscape2/settle and wai.quantum.landscape2/sample, which read each cell’s cost.
  3. Joules priced only at a rate with evidence in this repository (§4.3), never below what this project’s own hardware measured; a run above temperature 0, for which no such rate exists, is stated unpriced, with why, and no figure.
  4. A rule for its vectors the reference keeps (§7): the set is frozen, its digest pinned in the code, and any change to it is a new version of the protocol. The first version’s set is frozen the same way, as it stood on 2026-11-10.

The reference is a classical emulation, as the first version’s is. Its cells are three-state values sampled with classical random draws. Nothing here is a quantum effect, and no run of the reference involves any device but the machine it runs on.

1. The energy

E(s) = − Σ_{i<j} W_ij s_i s_j − Σ_i b_i s_i + Σ_i c_i · |s_i|,    s_i ∈ {−1, 0, +1}

The couplings and fields are the first version’s. Each variable has its own cost c_i, a whole number of either sign, at most 2⁴⁰ in size. This is the spin-1 model with a single-ion term on each site, of either sign.

A variable whose cost is below 0 is never 0 in a state of lowest energy: from a state where it is 0, taking the sign of its field h_i (or + where the field is 0) changes the energy by c_i − |h_i| ≤ −1.

2. The job

A request is the first version’s (its §2), and its protocol is required and MUST be wai.quantum.landscape/2. A request that gives no protocol, or the first version’s, is a job of the first version; a host that reads both versions reads it so, and its answer is that version’s, its bytes unchanged. A host MUST refuse any other protocol.

2.1. The program

The first version’s grammar (its §2.1), with cost widened and three statements added:

cost C             every variable's cost, a whole number of either sign
cost I C           variable I's own cost, a whole number of either sign; set twice, a warning, and the last holds
exactly K I J …    of these variables, exactly K hold +, and the others −
atmost 1 I J …     of these variables, at most one holds +, and the others −

K is a count ([0-9]+), from 0 to the number of variables named; the variables of a constraint are two or more, each named once. The checks gain two forms, each holding groups written as variables joined by -:

#! check exactly K 0-1-2 3-4-5    each group holds exactly K +, and its other members −
#! check atmost K 0-3 1-4         each group holds at most K +, and its other members −

A group with a member at 0 fails either check.

A reader MUST refuse, with one plain sentence and the line:

2.2. Constraints

A variable named in a constraint takes only + and −. Its cost is its own where the program gives one, which is below 0; else the program’s cost C where that is below 0; else −1, the least that keeps it out of 0 in every state of lowest energy (§1).

With x = (1 + s)/2 for each such variable (1 for +, 0 for −), the constraints lower to couplings and fields, exactly:

statementcouplingseach variable’s field gainsenergy, on states of + and −
exactly K over g variables−1 on every pair2K − g½(Σ s − (2K − g))² and a constant: 2(K′ − K)², K′ the + it holds
atmost 1 over g variables−1 on every pair−(g − 1)4 Σ_{i<j} x_i x_j and a constant: 2K′(K′ − 1)

So a group that holds what its constraint says costs nothing, and one that does not costs 2 for an exactly one step off (8 for two steps), and 4 for an atmost 1 holding two +. A constraint’s fields are added to the variable’s own (field, lean), all of them after every line is read. A pin’s size (the first version’s §2.1) is D + B + C + 1, with B the largest |b_i| once the constraints’ fields are added and C the largest cost in size.

A constraint is a term of the energy, not a rule a run is held to: its weight is fixed by its couplings, so another term on the same variables, a field larger than its step or a coupling beside it, can outvote it, and then the lowest states do not solve the problem. The worked examples hold that every lowest state solves theirs (§6), and a program whose own check fails on a lowest state is failed, as in the first version (its §3.1).

3. The answer

The first version’s (its §3), with:

A classical emulator of the settling model of a planned energy-based processor, running on your machine. Energies are computed exactly. The joule line prices a run at temperature 0 at the settle rate measured on an FPGA board running this project’s open reference design, with a published figure for one integer add beside it for scale, and leaves a run above temperature 0 unpriced, saying why. No photonic hardware, custom chip or quantum effect is involved in this run.

4. The kernels

4.1. wai.quantum.landscape2/settle

The first version’s settle (its §4.1), each cell at its own cost: a cell moves to the state of lowest energy −h_i·s + c_i·|s|, and at a tie to 0, then to +. That is

+1  when  h_i >  max(c_i, −1)
−1  when  h_i < −max(c_i, 0)
 0  otherwise

Where c_i ≥ 0 it is the first version’s move exactly. Where c_i < 0 the cell never rests at 0: it takes the sign of its field, and + at a field of 0, where + and − tie. Everything is whole-number arithmetic, and a settle kernel MUST give the reference’s bits.

4.2. wai.quantum.landscape2/sample

The first version’s sampling kernel (its §4.2), each cell’s cut points at its own cost: the formula is the same, and holds at a cost of either sign; the order of cells, the schedule, the draws and the exponential are the first version’s, and a sweep at 0 is §4.1’s move.

4.3. How the joules are stated

joules is an object. A run at temperature 0 (a settle or a quench) is priced; a run above it (a sample) is unpriced. A host:

The settle rate, about 0.88 pJ per accumulate. This project’s open FPGA member, wai/wai-quantum-landscape-fpga (its README, What it measured, and measurements/2026-11-06/):

what ranthe member’s engine in its T0 mode (the settle sweep, one sweep a clock), rtl version 2, the EMIO build, on one KV260 board at 100 MHz
the joba dense 64-cell recall, every pair coupled, settled 12.5 million times a second: 1.831 × 10¹¹ accumulates a second (emio-checks/throughput-emio.txt)
the reading162.0 mW over ten passes, run minus halt on one bitstream, the order randomised, the board’s input power read by its own sensor (emio-classes/t0-recall.dat)
the rate162.0 mW ÷ 1.831 × 10¹¹ /s = 0.885 pJ an accumulate, 13.0 nJ a settle; given as about 0.88
committed firstthe prediction, 160 mW (130 to 200), before the campaign (PREDICTION.txt)
checks that passedthe same job at 50 MHz drew 0.494 of it; two later builds of the same engine read 158.3 and 166.7 mW
what it does not showone board, one meter, one build; the sensor reads the whole board, its regulators included; one of the campaign’s two null controls failed at about 8 mW, so the instrument’s floor is not shown below that (this reading is twenty times it); no other board has repeated it
left outthe board’s own draw, about 3.14 W halted, at every clock: a small job prices low, and the answer says by how much, from at least one clock a sweep

Above temperature 0, no rate. On the same member, sampling drew 11.0 mW, within that instrument’s floor, and is not relied on (its README says so). The first build of the same design (measurements/2026-11-05/) drew 0.20 and 0.32 nJ a cell draw on one engine and on four, two figures 2.0 standard deviations apart, from draws of its own rather than the reference’s. The first version’s sampling rate was read on a design that updates every cell at once, which does not sample this model (the first version’s §4.2). None of these is a rate for this kernel, so a run above temperature 0 is unpriced.

For scale, beside a priced figure only: a published 2014 figure for one 8-bit integer add in 45 nm logic, about 0.03 pJ, class Estimator, which models no processor.

The form:

priced:   { "kind": "priced", "class": "ModelBased", "describes", "line", "rate_pj_per_accumulate": 0.88,
            "rate_source", "evidence": [paths], "pj", "published_add": {…}, "left_out": {…}, "why": null, "metered" }
unpriced: { "kind": "unpriced", "class": null, "describes", "line", "rate_pj_per_accumulate": null,
            "rate_source": null, "evidence": [paths], "pj": null, "published_add": null, "left_out": null,
            "why", "metered" }

metered is the first version’s (its §4.4): a member’s reading beside the statement, or null. A sweep’s row gives priced_per_run and left_out_per_run as the first version’s do for a priced run, and "not priced" for an unpriced one.

5. Members

A member says which versions of the protocol it runs (Member::protocols; the first alone where it says nothing). A host gives no workload of this version to a member that does not run it, and passes over such a member for a job of this version, saying so under refusals, however it was reached: placed, or asked for by name.

This version holds no member to a declared capacity: the first version’s vectors generated from a capacity, and its statistical battery, are not defined here. So a member that declares a capacity is given no job of this version, and no kernel of this version is statistical. A member’s kernel is graded:

paritygranted when
referenceto the host’s own reference kernels, and to nothing else
bit-exactit gives every settle vector of this version’s set (for the settle kernel), or every chains vector in one call each (for the sampling kernel), exactly
uncertifiedanything else

The host audits a kernel graded bit-exact as the first version’s §7.3 says.

What runs this version today. The CPU reference alone. The GPU members (WebGPU, CUDA, Metal) and the FPGA member read one cost for every cell: they run the first version’s kernels only, are certified on the first version’s set only, and are passed over for a job of this version. The FPGA member’s grade names the set it is earned on: the first version’s, as frozen on 2026-11-10 (§7). Nothing here claims any of them runs this version.

5.4. Verifying an answer

A job is of this version when its result’s protocol or schema is wai.quantum.landscape/2. A verifier holds it to the first version’s rules (its §5.4), with:

Rule 13, a provider’s job, is the first version’s: a job of this version that ran on a provider carries the same provider, job and cost (quantum-providers §11.3).

A verifier that holds this text’s reader reads the program with it, and states whether the answer’s energy and plan are the program’s (landscape.recomputed), as the first version’s §5.4 says.

6. Conformance

quantum-conformance/landscape/v2/vectors.json is written by wai-quantum landscape vectors --protocol 2, and a test holds the file to the code and to its digest (§7). Its exponential, schedule and draws are the first version’s, which that version’s set pins.

The sampling kernel of this version is also held to its joint law over every state, on two landscapes of this version among the eight of the first version’s §7.4 (informative; quantum-conformance/landscape/stage0/).

The worked examples, at their own plans (each solve restarts=8 steps=40, the first version’s plan for its examples, but the settled one):

examplevariablesevery arrangement checkedlowestat lowest, solving it100 seeds
colour-four: two triangles sharing a side, three colours12531,441−356 of 6100 solved
colour-five-ring: an odd ring, three colours1514,348,907−4030 of 30100 solved
colour-six: the first version’s six regions, three colours18too many(§2.2)the 12 colourings100 solved
colour-four-all-touching: four regions, three colours12531,441−360 of 24100 failed, as it must
assign-3x3919,683−216 of 6100 solved
assign-4x41643,046,721−4824 of 24100 solved
assign-5x525too many(§2.2)the 120 assignments100 solved
two-in-each-row-and-column: exactly 2 in each row and column of 4×41643,046,721−3290 of 90100 solved
four-queens: at most one in each row, column and diagonal, each queen worth 11643,046,721−842 of 2100 solved
assign-3x3-settled: the 3×3 assignment at temperature 0919,683−216 of 6100 failed: it never comes to rest

Where every arrangement is too many to check, the lowest energy is still known: on states of + and −, the energy above an answer that passes the check is the constraints’ penalty (§2.2), 0 exactly where the check passes, and a state that holds a 0 is lowered by one move (§1); a test holds both on random states. These are a few small instances, run on the reference at one plan each; they say that these landscapes express their problems and that this plan reached their lowest states, and nothing of larger instances or of any device’s time.

7. Versioning, and the rule for the vectors

The protocol’s name carries its version. Within /2: fields may be added to an answer, never removed or given another meaning; the kernels’ bits, the replay digest and the conformance set do not change. The set is frozen: the code pins its BLAKE3 digest (conformance2::VECTORS_2_BLAKE3), a test fails on any difference, and a change of any kind, an entry changed, removed or added, is a new version of the protocol with kernels of its own. Every grade names the set it was earned on.

The first version’s set is held the same way from 2026-11-10 (conformance2::VECTORS_1_BLAKE3, the BLAKE3 of quantum-conformance/landscape/vectors.json as it stood on main that day; its sha256 1da13d2570eb5b1367d3017b465e1b6a199429210def0c4300dbc403413e3a8e). The first version’s §9 says how that set changed before then, and why.

The words of a sentence and a host’s label are not part of the protocol. §4.3’s rule is: a host MAY price at a rate of its own, with its evidence in this repository named, and never below what this project’s own hardware measured for the same work.

8. What does not run on this version