Noise Resilience of Variational Quantum Compiling (1908.04416v2)

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.

• The paper establishes that optimal variational parameters remain robust under various incoherent noise models, ensuring reliable gate sequence recovery.
• The research utilizes rigorous theoretical proofs and IBM simulator experiments to validate noise resilience in compiling complex unitaries.
• These findings underscore the practical potential of variational quantum compiling for error mitigation in NISQ-era quantum computing.

Variational Quantum Compiling: An Exploration of Noise Resilience

This paper addresses the critical issue of noise resilience in the context of near-term quantum computing, focusing on Variational Hybrid Quantum-Classical Algorithms (VHQCAs). More specifically, the research explores Variational Quantum Compiling (VQC), a technique that optimizes short-depth gate sequences via variational methods to approximate target unitaries in the presence of noise. The paper introduces the concept of Optimal Parameter Resilience (OPR), revealing that the variational parameters that minimize the cost function remain unaffected by certain kinds of incoherent noise. This finding suggests a potentially impactful role for VQC, particularly in the immediate era where error-prone Noisy Intermediate-Scale Quantum (NISQ) devices are prevalent.

Theoretical Insights and Numerical Evidence

The paper's central theoretical contribution is the demonstration of OPR under various noise models that represent realistic conditions present in quantum devices today. The authors provide rigorous proofs that under numerous noise processes—including depolarizing noise, Pauli noise, and measurement noise—the parameters reaching the global optimum in VQC are unchanged. This implies that despite these noise sources, the optimal gate sequence can often be recovered with high fidelity.

Numerical simulations further corroborate these theoretical findings. Implementations of VQC were performed on IBM's noisy quantum simulator reflecting the Melbourne device's parameters. The paper successfully showed noise resilience in compiling a comprehensive set of unitaries including the three-qubit Quantum Fourier Transform, Toffoli gate, and W-state preparation. Even in the presence of realistic noise, the resulting variational parameters were capable of minimizing the noiseless cost functions to a degree often corresponding to the global minimum.

Implications for NISQ Era Computation

In practical terms, the implications of these findings are significant. As VHQCAs, and particularly VQC, become increasingly essential for quantum algorithm implementation on NISQ devices, understanding their noise resilience is vital. This OPR property could enable quantum computations that are both efficient and robust, even when the depth of circuits is compressed. Such resilience against noise ensures that VQC can be a powerful tool to mitigate errors, supporting the implementation of more elaborate quantum algorithms that would otherwise be infeasible.

Moreover, the delineation between coherent and incoherent noise types presents an opportunity for further exploration. While this paper explicitly focuses on incoherent noise, the implications of coherent errors on parameter optimization in VHQCAs remain an open question, indicating a pathway for future research.

Future Directions and Generalization

The paper also paves the way for generalizing these insights to other VHQCAs, such as the Variational Quantum Eigensolver. Demonstrating noise resilience across different algorithmic contexts could expand the utility and applicability of variational methods in quantum computing. Thus, this work not only makes a substantial contribution to current quantum compiling techniques but also lays groundwork for ongoing exploration into quantum error mitigation.

Overall, the research provides a thorough analysis of VQC in the presence of noise, bolstered by rigorous theoretical proofs and empirical validation. This exploration of noise resilience significantly contributes to advancing the field of quantum computing, specifically within the domain of noise management on NISQ devices.