Estimating Gibbs partition function with quantumClifford sampling

Abstract

The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum-classical algorithm to estimate the partition function, utilising a novel Clifford sampling technique. Note that previous works on quantum estimation of partition functions require $\mathcal{O}(1/\epsilon \sqrt{\Delta })$-depth quantum circuits~\cite{Arunachalam2020Gibbs, Ashley2015Gibbs}, where $\Delta$ is the minimum spectral gap of stochastic matrices and $\epsilon$ is the multiplicative error. Our algorithm requires only a shallow $\mathcal{O}(1)$-depth quantum circuit, repeated $\mathcal{O}(1/{\epsilon }^2)$ times, to provide a comparable $\epsilon$ approximation. Shallow-depth quantum circuits are considered vitally important for currently available NISQ (Noisy Intermediate-Scale Quantum) devices.

References in corpus (3)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• Hybrid quantum-classical algorithms and quantum error mitigation
• The Clifford group fails gracefully to be a unitary 4-design

Cited by in corpus (3)

• Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers
• Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit
• Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states