Estimating Gibbs partition function with quantum Clifford sampling

Abstract The partition function is an essential quantity in statistical mechanics, and its accurate computation a key component of any analysis quantum system phenomenon. However, for interacting many-body systems, calculation generally involves summing over exponential number terms can thus quickly grow to be intractable. Accurately efficiently estimating the corresponding Hamiltonian then becomes solving problems. In this paper we develop hybrid quantumclassical algorithm estimate function, utilising novel Clifford sampling technique. Note that previous works on estimation functions require O(1/ε√∆)-depth circuits [17, 23], where ∆ minimum spectral gap stochastic matrices ε multiplicative error. Our requires only shallow O(1)-depth circuit, repeated O(n/ε2) times, provide comparable approximation. Shallow-depth are considered vitally important currently available NISQ (Noisy Intermediate-Scale Quantum) devices.