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Metriq SCPN Benchmark Schema Proposal

Date: 2026-05-07

Status

Prepared for future upstream discussion. Not submitted upstream and not accepted by Metriq-Gym.

This document defines the benchmark shape that would make an scpn-quantum-control Metriq result scientifically valid. It is not a Metriq result, not a score, and not a benchmark acceptance notice.

Proposed Benchmark Name

Kuramoto--XY parity leakage

Scientific Purpose

Measure how accurately a backend preserves a simple, symmetry-defined observable of a heterogeneous Kuramoto--XY circuit family. The ideal nearest-neighbour XY circuit conserves excitation-number parity, so its parity-survival reference is exactly 1 at every depth. The proposed measurement is a symmetry-leakage diagnostic, not a test of full-state fidelity or a nontrivial ideal parity-decay curve.

The benchmark targets a concrete NISQ question:

Given the same Kuramoto--XY Hamiltonian, initial state, Trotter step, and
measurement basis, how closely does the observed parity-survival curve
match the exact small-system reference curve?

This makes the benchmark a hardware-fidelity and reproducibility test, not a quantum-advantage claim.

Required Input Fields

Field Type Required Meaning
benchmark_name string yes Must be Kuramoto-XY parity leakage.
n_qubits integer yes Number of oscillators/qubits. The locally exercised proposal is 4; 6 and 8 require separate resource and simulator checks before inclusion.
depths list[int] yes Trotter depths to evaluate.
shots integer yes Shots per circuit.
initial_states list[string] yes Computational-basis states in qubit-0-first convention.
coupling_profile string yes Initial schema: exp_decay_0p45_0p3.
t_step float yes Trotter step; default 0.3.
reference_mode string yes exact_statevector for n <= 8.
transpilation_policy string yes Backend/default transpilation policy identifier.

Circuit Definition

For n qubits and Trotter depth d, prepare each listed initial state and apply:

H_XY = sum_i omega_i Z_i + sum_(i,i+1) K_(i,i+1) (X_i X_(i+1) + Y_i Y_(i+1))

with:

omega_i = linspace(0.8, 1.2, n)
K_(i,i+1) = 0.45 * exp(-0.3)
t_step = 0.3

The initial schema should use nearest-neighbour Trotter layers first, because that keeps the benchmark practical on sparse gate hardware and matches the current SCPN hardware artefact family.

Primary Observable

Parity survival:

P_same_parity =
    sum_{bitstrings with popcount parity equal to initial popcount parity}
        observed_probability(bitstring)

Primary Score

The proposed score is one minus the clipped mean absolute parity error:

score = 1 - clip(mean_depth_state(|P_observed - P_exact|) / tolerance, 0, 1)

Provisional score tolerance, subject to maintainer review:

tolerance = 0.05

Interpretation:

  • 1.0 means the measured parity-survival curve matches the exact reference within negligible error;
  • 0.0 means the mean parity-survival error is at least the tolerance;
  • intermediate values report bounded hardware fidelity for this circuit family.

Required Secondary Metrics

Every result should also report:

  • exact-state retention error;
  • transpiled depth per circuit;
  • two-qubit gate count per circuit;
  • readout-baseline parity-flip estimate if calibration circuits are run;
  • backend name and simulator/hardware flag;
  • timestamp and provider metadata available from the benchmark runner;
  • raw counts or a reproducible pointer to raw counts;
  • SHA-256 hash of the result payload.
{
  "benchmark_name": "Kuramoto-XY parity leakage",
  "n_qubits": 4,
  "depths": [2, 4, 6, 8, 10],
  "shots": 2048,
  "initial_states": ["0011", "0001"],
  "coupling_profile": "exp_decay_0p45_0p3",
  "t_step": 0.3,
  "reference_mode": "exact_statevector",
  "transpilation_policy": "provider_default"
}

Acceptance Gates for an Upstream Schema

Before this should be submitted as an upstream Metriq-Gym benchmark, the following local gates should pass:

  • deterministic reference values for n=4 are generated from committed code;
  • local simulator execution produces a score near 1.0 within shot noise;
  • the JSON result schema can represent raw counts, score, resources, and reference metadata;
  • the benchmark can be run without SCPN-private artefacts or credentials;
  • documentation clearly states that this is a parity-leakage fidelity benchmark, not a quantum-advantage benchmark.

Non-Claim Boundary

This proposed schema must not be used to claim:

  • broad quantum advantage;
  • DLA-parity-only causality;
  • universal decoherence protection;
  • clinical, biological, or consciousness-related conclusions;
  • hardware superiority outside the measured circuit family.

Upstream Draft Text

I would like to propose a Metriq-Gym benchmark for heterogeneous
Kuramoto--XY parity leakage. The first workload prepares fixed n=4
nearest-neighbour Kuramoto--XY Trotter circuits, measures computational-basis
counts, and reports the fraction of shots leaving the prepared parity sector.
The ideal parity-survival reference is exactly one at every depth. The goal
is a bounded symmetry-leakage diagnostic for this circuit family, not a
full-state fidelity or quantum-advantage claim.

The related scpn-quantum-control campaign has committed n=4 exact-reference
code and public hardware raw-count artefacts. A standalone Metriq-Gym
implementation and accepted schema do not yet exist. Such an implementation
should report raw counts, exact references, depth, two-qubit gates, backend
metadata, and SHA-256 payload hashes.