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Does splitting a FIXED total measurement budget across more noise-scale
points actually help, or does the earlier "more points helps" finding
only look good because it secretly spent more measurements (more K per
point) than the 3-point baseline?
This is the fair comparison: same total number of Monte Carlo trajectories
across all configurations, just split differently -- 3 points x K=400
(1200 total) vs. 5 points x K=240 (1200 total) vs. 7 points x K=171
(~1200 total). Answers "what did we actually win, all else equal."
python experiments/matrix_healing_fixed_budget.py
"""
import os
import sys
import numpy as np
import jax.numpy as jnp
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
import dense_evolution as de
from dense_evolution.registry import NoiseModel
from dense_evolution.mitigation import (
uhlmann_fidelity, richardson_extrapolate, project_to_physical, zne_density_matrix,
)
N_QUBITS = 4
BASE_P = 0.05
SEEDS = (0, 1, 2, 3, 4)
NOISE_MODELS = ("depolarizing", "bitflip", "phaseflip", "amplitude_damping", "combined")
CONFIGS = {
"3pt K=400 (baseline, classic ZNE)": ((1.0, 2.0, 3.0), 400, "richardson"),
"5pt K=240 (deg2 lstsq)": ((1.0, 2.0, 3.0, 4.0, 5.0), 240, "lstsq2"),
"7pt K=171 (deg2 lstsq)": ((1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0), 171, "lstsq2"),
}
def ghz_sv(n):
sim = de.DenseSVSimulator(n)
ops = [("h", 0)] + [("cx", 0, i) for i in range(1, n)]
sim.run_circuit(ops)
return np.asarray(sim.get_statevector())
def noisy_rho(ideal_sv, model, p, k, rng):
dim = len(ideal_sv)
rho = np.zeros((dim, dim), dtype=np.complex128)
for _ in range(k):
sv = NoiseModel.apply_to_sv(ideal_sv.copy(), N_QUBITS, model, p, rng=rng)
rho += np.outer(sv, sv.conj())
rho /= k
return jnp.asarray(rho, dtype=jnp.complex128)
def run_one(ideal_sv, rho_ideal, model, scales, k, method, seed):
rng = np.random.default_rng(seed)
rho_at_scales = jnp.stack([noisy_rho(ideal_sv, model, BASE_P * s, k, rng) for s in scales])
raw = uhlmann_fidelity(rho_at_scales[0], rho_ideal)
if method == "richardson":
corrected_rho = project_to_physical(richardson_extrapolate(rho_at_scales, scales))
else:
corrected_rho = zne_density_matrix(rho_at_scales, scales, degree=2)
corrected = uhlmann_fidelity(corrected_rho, rho_ideal)
return raw, corrected
def main():
ideal_sv = ghz_sv(N_QUBITS)
rho_ideal = jnp.asarray(np.outer(ideal_sv, ideal_sv.conj()), dtype=jnp.complex128)
print(f"n_qubits={N_QUBITS}, base_p={BASE_P}, ~1200 total trajectories per run regardless of config\n")
summary = {}
for label, (scales, k, method) in CONFIGS.items():
actual_budget = k * len(scales)
all_deltas = []
for model in NOISE_MODELS:
deltas = []
for seed in SEEDS:
raw, corrected = run_one(ideal_sv, rho_ideal, model, scales, k, method, seed)
deltas.append(corrected - raw)
all_deltas.extend(deltas)
summary[label] = (np.array(all_deltas), actual_budget)
print(f"{'config':>36} {'actual_budget':>14} {'mean_delta':>12} {'std_delta':>10} {'wins/total':>12}")
print("-" * 90)
for label, (arr, budget) in summary.items():
print(f"{label:>36} {budget:>14} {arr.mean():>+12.4f} {arr.std():>10.4f} "
f"{int(np.sum(arr>0))}/{len(arr):>10}")
if __name__ == "__main__":
main()
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