Virtual Distillation for Quantum Error Mitigation

Abstract

Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuringMcopies of a noisy stateρ. This enables us to estimate expectation values with respect to a state with dramatically reduced errorρM/Tr(ρM)without explicitly preparing it, hence the name “virtual distillation.” AsMincreases, this state approaches the closest pure state toρexponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of ρ). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.

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Plain Language Summary

State-of-the-art quantum computers are capable of rivaling or exceeding classical supercomputers for specifically designed tasks. However, the noisy nature of these devices makes it difficult to find a quantum advantage for any practical purpose, such as the simulation of natural phenomena. To help address this, we develop a technique for suppressing noise by using multiple copies of a quantum computation.

In the absence of noise, a quantum computation should always yield the same quantum state. Therefore, exchanging two copies of this final state should not have any effect. This symmetry is violated when errors affect the two copies differently. Our technique uses measurements of these violations to cancel out certain kinds of noise. The technique is realizable on near-term devices with substantially lower overhead than traditional quantum error correction.

Applying our technique to calculations performed on real quantum hardware will improve the results of those calculations, taking a step toward the dream of using a quantum computer to answer questions beyond the reach of classical computation. The results of these experiments will also help shed new light on the details of the noise present in today’s devices.