Classical simulation of a quantum circuit with noisy magic inputs

TL;DR

This paper investigates how noise in magic states affects the classical simulability of quantum circuits, identifying conditions under which noisy magic enables efficient classical simulation, thus impacting quantum advantage.

Contribution

It introduces a resource-centric noise model and develops an approximate classical sampling algorithm with explicit noise-dependent efficiency conditions.

Findings

Noise on magic states can make quantum circuits classically simulable

The paper provides explicit thresholds for efficient simulation under noise

Applicable to qubit Clifford and fermionic matchgate circuits

Abstract

Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources changes the classical simulability of quantum circuits and when it induces a transition from classically intractable behavior to efficient classical simulation. We adopt a resource-centric noise model in which only the injected magic components are noisy, while the baseline states, operations, and measurements belong to an efficiently simulable family. Within this setting, we develop an approximate classical sampling algorithm with controlled error and prove explicit noise-dependent conditions under which the algorithm runs in polynomial time. Our framework applies to both qubit circuits with Clifford baselines and fermionic circuits with matchgate baselines, covering representative noise channels such as dephasing and particle loss. We complement the analysis with numerical estimates of the simulation cost, providing concrete thresholds and runtime scaling across practically relevant parameter regimes.