7.2 Benchmark and validation protocol
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7.2.1 Fair comparison
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A packet simulator and a full simulator should use the same precision, gate parameters, initial state, observable, and arithmetic path wherever possible. Report compilation separately from repeated application.
7.2.2 Required metrics
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A complete benchmark should report:
full and reduced dimensions,
packet-discovery and compilation time,
one-shot runtime,
repeated-application runtime,
peak memory,
reconstruction or observable error,
symmetry leakage,
hardware and software versions,
number of repetitions over which compilation is amortized.
7.2.3 Algebraic and numerical validation paths
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For manageable \(n\), embed a random packet state into the full space, apply identical gates in both representations, and compare final states. The included numerical validation program performs this check for structurally invariant fixed-weight circuits using complex floating-point arithmetic, with reconstruction tolerance \(2\cdot10^{-12}\). The separate rational validation uses exact fractions and rational orthogonal gates. Exact subspace invariance is a property of the model, while near-machine-precision agreement is numerical evidence about this implementation.
7.2.4 Scaling studies
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A scaling plot should include both fine packets and coarse packets. Fixed weight two demonstrates polynomial dimension. Parity demonstrates a constant-factor packet. Half filling demonstrates an exponential packet with a polynomial memory reduction factor. These controls prevent overinterpreting a speedup as a complexity collapse.
7.2.5 Leakage tests
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Deliberately append a gate that breaks the proposed symmetry and verify that the simulator detects nonzero leakage. The archived tests break exact weight, parity, and weight modulo four, producing retained probabilities below one. A simulator that reports zero error after a symmetry-breaking gate without enlarging its representation is incorrect.
7.2.6 Reproducibility contract
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The release preserves:
the benchmark JSON data,
the Python figure generator,
packet and gate utilities,
exact rational checks and separately labeled numerical validation tests,
LaTeX source,
deterministic build commands,
checksums of final artifacts.
Recorded computation
The release validation reproduces fixed-weight basis dimensions, residue partitions, symmetric/bosonic/fermionic dimension formulas, hypercube quotient symmetry, and full-vs-packet state reconstruction near machine precision.