Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers

Abstract

The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-team quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, and these could be costly performed on the near-term quantum computers. Here, we propose an efficient scheme to calculate the Gibbs function with the imaginary time evolution. To calculate the Gibbs function of $N$ qubits, only $2N$ qubits are required in our scheme. After preparing Gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, and this allows us to calculate the Gibbs partition function.

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Cited by in corpus (2)

• Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
• 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