Exploring finite temperature properties of materials with quantum computers

Abstract

Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.

Mixed State Variational Quantum Eigensolver for the Estimation of Expectation Values at Finite Temperature

“…Our interest is focused in particular on the estimation of thermal averages, i.e., the expectation value of observables for a system at equilibrium at finite temperature. Many quantum algorithms for thermal average estimation have been proposed in literature [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. As we discuss in more detail in Sec.…”