toroidal-noise

Quantum noise channels with density matrix simulation. Includes toroidal dephasing suppression via the spectral gap of cycle graph Laplacians.

Channels

Channel	Parameters	Kraus operators
`dephasing(gamma)`	`gamma` in [0,1]	2
`amplitude_damping(gamma)`	`gamma` in [0,1]	2
`depolarizing(p)`	`p` in [0,1]	4 (I, X, Y, Z)
`toroidal_dephasing(gamma, n, alpha)`	`gamma` in [0,1], `n >= 2`, `alpha > 0`	2

Toroidal dephasing

The effective dephasing probability is suppressed by the spectral gap of the cycle graph C_n:

gamma_eff = gamma * lambda_1 / (lambda_1 + alpha)

where lambda_1 = 2 - 2*cos(2*pi/n). Larger grids produce smaller spectral gaps and stronger noise suppression.

Usage

use toroidal_noise::{
    apply_channel, apply_unitary, toroidal_dephasing,
    HADAMARD, RHO_ZERO,
};

// Start with |+> state
let rho = apply_unitary(&RHO_ZERO, &HADAMARD);

// Apply toroidal dephasing (12x12 grid, alpha=1.0)
let rho_out = apply_channel(&rho, &toroidal_dephasing(0.5, 12, 1.0));

// Off-diagonal coherence is preserved better than plain dephasing
assert!(rho_out[0][1].norm() > 0.0);

Reference

S. Cormier, "Toroidal Logit Bias," Zenodo, 2026. DOI: 10.5281/zenodo.18516477

License