Efficient classical simulation and benchmarking of quantum processes in the Weyl basis

Abstract

One of the crucial steps in building a scalable quantum computer is to identify the noise sources which lead to errors in the process of quantum evolution. Different implementations come with multiple hardware-dependent sources of noise and decoherence making the problem of their detection manyfoldly more complex. We develop a randomized benchmarking algorithm which uses Weyl unitaries to efficiently identify and learn a mixture of error models which occur during the computation. We provide an efficiently computable estimate of the overhead required to compute expectation values on outputs of the noisy circuit relying only on locality of the interactions and no further assumptions on the circuit structure. The overhead decreases with the noise rate and this enables us to compute analytic noise bounds that imply efficient classical simulability. We apply our methods to ansatz circuits that appear in the Variational Quantum Eigensolver and establish an upper bound on classical simulation complexity as a function of noise, identifying regimes when they become classically efficiently simulatable.

References in corpus (5)

• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Non-negative Wigner functions in prime dimensions
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Statistical analysis of randomized benchmarking

Cited by in corpus (6)

• Matchgate benchmarking: Scalable benchmarking of a continuous family of many-qubit gates
• Exponentially tighter bounds on limitations of quantum error mitigation
• Improved simulation of quantum circuits dominated by free fermionic operations
• Faster Born probability estimation via gate merging and frame optimisation
• Detection of entanglement for multipartite quantum states
• Benchmarking non-Clifford gates using only Pauli twirling group