Enhancing Virtual Distillation with Circuit Cutting for Quantum Error Mitigation

Abstract: Virtual distillation is a technique that aims to mitigate errors in noisy quantum computers. It works by preparing multiple copies of a noisy quantum state, bridging them through a circuit, and conducting measurements. As the number of copies increases, this process allows for the estimation of the expectation value with respect to a state that approaches the ideal pure state rapidly. However, virtual distillation faces a challenge in realistic scenarios: preparing multiple copies of a quantum state and bridging them through a circuit in a noisy quantum computer will significantly increase the circuit size and introduce excessive noise, which will degrade the performance of virtual distillation. To overcome this challenge, we propose an error mitigation strategy that uses circuit-cutting technology to cut the entire circuit into fragments. With this approach, the fragments responsible for generating the noisy quantum state can be executed on a noisy quantum device, while the remaining fragments are efficiently simulated on a noiseless classical simulator. By running each fragment circuit separately on quantum and classical devices and recombining their results, we can reduce the noise accumulation and enhance the effectiveness of the virtual distillation technique. Our strategy has good scalability in terms of both runtime and computational resources. We demonstrate our strategy's effectiveness through noisy simulation and experiments on a real quantum device.