# Noise Resilience of Variational Quantum Compiling

## TL;DR

This paper demonstrates that variational quantum compiling algorithms are surprisingly resilient to various types of noise, maintaining correct gate sequences despite incoherent noise during cost evaluation.

## Contribution

The paper provides rigorous proofs and numerical evidence showing noise resilience in variational quantum compiling, a property not previously established.

## Key findings

- Optimal parameters unaffected by measurement noise
- Resilience observed in numerical simulations with IBM's noisy simulator
- Potential generalization to other VHQCAs like VQE

## Abstract

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary $U$ is compiled into a short-depth gate sequence $V$. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence $V$ (i.e., the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.