Partitioned Quantum Subspace Expansion

TL;DR

This paper introduces an iterative generalization of the quantum subspace expansion algorithm that improves numerical stability and is suitable for near-term quantum hardware by balancing quantum resources and classical processing.

Contribution

It proposes a variance-based criterion for selecting iterative sequences, enhancing stability without increasing quantum circuit depth.

Findings

Iterative approach improves numerical stability over single-step methods.

Good sequences identified show resilience to finite sampling noise.

Method maintains quantum resource requirements similar to existing approaches.

Abstract

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We propose a variance-based criterion for determining a good iterative sequence and provide numerical evidence that these good sequences display improved numerical stability over a single step in the presence of finite sampling noise. Implementing the generalisation requires additional classical processing with a polynomial overhead in the subspace dimension. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware. Our work suggests that the numerical instability limiting the accuracy of this approach can be substantially alleviated in a parameter-free way.