Virtual distillation with noise dilution

TL;DR

This paper demonstrates that distributing noise sources evenly across a quantum circuit enhances error mitigation in virtual distillation, especially under loss and Pauli noise, with practical implications for noisy intermediate-scale quantum computing.

Contribution

It introduces the concept of noise dilution across circuit layers to improve virtual distillation error mitigation, supported by analytical and numerical evidence.

Findings

Splitting peripheral noise improves mitigation performance.

Second-order distillation suffices for near-optimal results.

Uniform noise distribution benefits shallow quantum circuits.

Abstract

Virtual distillation is an error-mitigation technique that reduces quantum-computation errors without assuming the noise type. In scenarios where the user of a quantum circuit is required to additionally employ peripherals, such as delay lines, that introduce excess noise, we find that the error-mitigation performance can be improved if the peripheral, whenever possible, is split across the entire circuit; that is, when the noise channel is uniformly distributed in layers within the circuit. We show that under the multiqubit loss and Pauli noise channels respectively, for a given overall error rate, the average mitigation performance improves monotonically as the noisy peripheral is split~(diluted) into more layers, with each layer sandwiched between subcircuits that are sufficiently deep to behave as two-designs. For both channels, analytical and numerical evidence show that second-order distillation is generally sufficient for (near-)optimal mitigation. We propose an application of these findings in designing a quantum-computing cluster that houses realistic noisy intermediate-scale quantum circuits that may be shallow in depth, where measurement detectors are limited and delay lines are necessary to queue output qubits from multiple circuits.