Large-scale implementation of quantum subspace expansion with classical shadows

TL;DR

This paper demonstrates a large-scale implementation of quantum subspace expansion using classical shadows, enabling efficient spectral calculations on quantum processors with improved accuracy and reduced measurement overhead.

Contribution

It introduces a reformulation of QSE as a constrained optimization problem and showcases the first large-scale experimental use of classical shadows in quantum spectral analysis.

Findings

Accurate ground state energy recovery for a spin model with 80 qubits.

Mitigation of local order parameters across large system sizes.

Implementation of over 30,000 measurement basis randomizations per circuit.

Abstract

Quantum subspace expansion (QSE) offers promising avenues to perform spectral calculations on quantum processors but comes with a large measurement overhead. Informationally complete (IC) measurements, such as classical shadows, were recently proposed to overcome this bottleneck. Here, we report the first large-scale implementation of QSE with IC measurements. In particular, we probe the quantum phase transition of a spin model with three-body interactions, for which we observe accurate ground state energy recovery and mitigation of local order parameters across system sizes of up to 80 qubits. We achieve this by reformulating QSE as a constrained optimization problem, obtaining rigorous statistical error estimates and avoiding numerical ill-conditioning. With over $3 \times 10^4$ measurement basis randomizations per circuit and the evaluation of $O(10^{14})$ Pauli traces, this represents one of the most significant experimental realizations of classical shadows to date.