Canonical Partition Function on a Quantum Computer through Trotter Interpolation

TL;DR

This paper introduces a Trotter interpolation-based algorithm for estimating Gibbs state observables on quantum computers, achieving lower computational costs and fewer ancilla qubits than existing methods, with validation on the SYK model.

Contribution

The paper presents a novel Trotter interpolation approach for Gibbs state estimation that reduces quantum computational cost and ancilla qubit requirements compared to prior techniques.

Findings

Achieves $ ilde{O}(eta ext{log}(1/ ext{epsilon}))$ cost for Gibbs state estimation.

Reduces ancilla qubits by $ ext{log}( ext{Gamma})$ compared to qubitization methods.

Validated performance on the SYK model benchmark.

Abstract

In this work, we present a Gibbs state observable estimation algorithm based on Trotter interpolation, which reaches a state-of-the-art quantum computational cost of $ \tilde{O}(\beta \log{1/\epsilon})$. Our approach saves $\log(\Gamma)$ ancilla qubits compared with the qubitization-based methods for Hamiltonian with $\Gamma$ stages. To provide a robust assessment of our approach, we benchmark our results against state-of-the-art methodology using the SYK model as a testbed. Our method provides an efficient alternative method for Gibbs-state accessing based on Trotterization in the context of quantum state preparation and estimation of thermal observables.