Canonical Partition Function on a Quantum Computer through Trotter Interpolation

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 $\tilde{O}({\hat{I}}^2\log 1/\hat{I}\mu )$. Our approach saves $\log (\hat{I}“)$ ancilla qubits compared with the qubitization-based methods for Hamiltonian with $\hat{I}“$ 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.

9 pages, 3 figures