Exponential distillation of dominant eigenproperties

TL;DR

This paper introduces a hybrid quantum-classical algorithm for efficiently estimating observable expectation values in eigenstates, achieving exponential error suppression with potential applications in near-term quantum computing and classical simulations.

Contribution

The authors develop a novel exponential error suppression technique using random time evolution, enabling efficient eigenstate property estimation with rigorous guarantees.

Findings

Achieves exponential suppression of errors with a single quantum state copy.

Performance depends on the energy gap and scales similarly to phase estimation.

Demonstrates applicability in near-term quantum devices and classical tensor-network simulations.

Abstract

Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid quantum-classical algorithm that enables the estimation of an arbitrary observable expectation value in an eigenstate, given an initial state is supplied that has dominant overlap with the targeted eigenstate -- but may overlap with any other eigenstates. Our approach builds on and is conceptually similar to purification-based error mitigation techniques; however, it achieves exponential suppression of algorithmic errors using only a single copy of the quantum state. The key innovation is that random time evolution is applied in the quantum computer to create an average mixed quantum state, which is then virtually purified with exponential efficacy. We prove rigorous performance guarantees and conclude that the complexity of our approach depends directly on the energy gap in the problem Hamiltonian and remarkably, can be compared to phase estimation combined with amplitude estimation in terms of its scaling with respect to a target precision. We demonstrate in a broad range of numerical simulations the applicability of our framework in near-term and early fault-tolerant settings. Furthermore, we demonstrate in a 100-qubit example that direct classical simulation of our approach enables the prediction of ground and excited state properties of quantum systems using tensor-network techniques, which we recognize as a quantum-inspired classical approach.