Efficient simulation of parametrized quantum circuits under non-unital noise through Pauli backpropagation

TL;DR

This paper extends Pauli backpropagation algorithms to efficiently simulate parametrized quantum circuits affected by realistic non-unital noise, such as amplitude damping, enhancing classical simulation capabilities for near-term quantum devices.

Contribution

It adapts and proves the efficiency of Pauli backpropagation for non-unital noise models, a significant step beyond previous depolarizing noise assumptions.

Findings

Pauli backpropagation remains efficient under non-unital noise.

The analysis uses refined combinatorial techniques.

Simulation of realistic noise models is now theoretically supported.

Abstract

As quantum devices continue to grow in size but remain affected by noise, it is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient classical simulation algorithms possible. Among the most promising approaches are Pauli backpropagation algorithms, which have already demonstrated their ability to efficiently simulate certain classes of parameterized quantum circuits-a leading contender for near-term quantum advantage-under random circuit assumptions and depolarizing noise. However, their efficiency was not previously established for more realistic non-unital noise models, such as amplitude damping, that better capture noise on existing hardware. Here, we close this gap by adapting Pauli backpropagation to non-unital noise, proving that it remains efficient even under these more challenging conditions. Our proof leverages a refined combinatorial analysis to handle the complexities introduced by non-unital channels, thus strengthening Pauli backpropagation as a powerful tool for simulating near-term quantum devices.