TY - JOUR

T1 - Estimating Gibbs partition function with quantum Clifford sampling

AU - Wu, Yusen

AU - Wang, Jingbo B.

PY - 2022/4

Y1 - 2022/4

N2 - The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. 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 quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require O(1/ µ ") -depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112-22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δis the minimum spectral gap of stochastic matrices and µ is the multiplicative error. Our algorithm requires only a shallow O(1) -depth quantum circuit, repeated O(n/ µ2) times, to provide a comparable µ approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.

AB - The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. 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 quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require O(1/ µ ") -depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112-22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δis the minimum spectral gap of stochastic matrices and µ is the multiplicative error. Our algorithm requires only a shallow O(1) -depth quantum circuit, repeated O(n/ µ2) times, to provide a comparable µ approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.

KW - NISQ

KW - partition function

KW - quantum Clifford sampling

KW - shallow-circuit quantum algorithm

UR - http://www.scopus.com/inward/record.url?scp=85126032159&partnerID=8YFLogxK

U2 - 10.1088/2058-9565/ac47f0

DO - 10.1088/2058-9565/ac47f0

M3 - Article

AN - SCOPUS:85126032159

VL - 7

JO - Quantum Science and Technology

JF - Quantum Science and Technology

SN - 2058-9565

IS - 2

M1 - 025006

ER -