Variational quantum algorithms for thermal states preparation

Abstract

The quantum simulation of thermal equilibrium states is a promising near-term application of quantum computation, with applicability in fields such as quantum chemistry. This dissertation investigates Gibbs state preparation of the free fermion Hamiltonian using a variational quantum algorithm (VQA). While the Grover-Rudolph algorithm can prepare an arbitrary distribution of 2n probabilities using 2n − 1 circuit parameters, it does not achieve quantum advantage, since it offers no exponential speed-up over classical methods. This work is motivated by the circuit optimisation problem: can the properties of the free fermion Hamiltonian be used to design a more efficient Ansatz for this problem with a reduced number of gate parameters? By investigating the properties of the Gibbs states for small numbers of qubits, results were found suggesting that the Gibbs states of the free fermion Hamiltonian can be generated with only n single-qubit gates, without requiring any entangling gates. This optimised single-qubit gate circuit was used as the Ansatz in a VQA for Gibbs state preparation, and the calculated and target probability distributions were compared for different system sizes and temperatures using the VQA cost function as well as various distance measures. The VQA results show that the single-qubit Ansatz is expressible enough for up to n = 5 qubits, reducing the circuit complexity for this problem.