Robust ultra-shallow shadows

TL;DR

This paper introduces a noise-robust shadow estimation method for shallow quantum circuits that improves measurement accuracy and efficiency in noisy quantum computing environments, demonstrated through simulations and IBM device experiments.

Contribution

The authors develop a practical protocol for noise mitigation in shadow estimation applicable to low-depth circuits, using tensor-network tools for efficient data analysis.

Findings

Robust ultra-shallow shadows outperform unmitigated shadows as circuit depth increases.

The method achieves about tenfold improvement in fidelity estimation precision.

Optimal circuit depth depends on the noise level, balancing measurement bias and variance.

Abstract

We present a robust shadow estimation protocol for wide classes of low-depth measurement circuits that mitigates noise as long as the effective measurement map including noise is locally unitarily invariant. This is in practice an excellent approximation, encompassing for instance the case of ideal single-qubit Clifford gates composing the first circuit layer of an otherwise arbitrary circuit architecture and even non-Markovian, gate-dependent noise in the rest of the circuit. We argue that for weakly-correlated local noise, the measurement channel has an efficient matrix-product representation, and show how to estimate this directly from experimental data using tensor-network tools, eliminating the need for analytical or numeric calculations. We illustrate the relevance of our method with both numerics and proof-of-principle experiments on an IBM Quantum device. Numerically, we show that unmitigated shallow shadows with noisy circuits become more biased as the depth increases. In contrast, using the same number of samples, robust ultra-shallow shadows become more precise with increasing depth for relevant parameter regimes. The gain in sample efficiency is still limited by the noise per gate, resulting in an optimal circuit depth per noise level. Experimentally, we observe improved precision in two simple fidelity estimation tasks using five-qubit circuits with up to two layers of entangling gates, by about an order of magnitude. Under the practical constraints of current and near-term noisy quantum devices, our method maximally realizes the potential of shadow estimation with global rotations and identifies its fundamental limitations in the presence of noise.