Canonical Partition Function on a Quantum Computer through Trotter Interpolation

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.