Polynomial-Time Approximation of Zero-Free Partition Functions
Zero-free based algorithms are a major technique for deterministic approximate counting. In Barvinok’s original framework [Barvinok, 2017], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free partition functions. Patel and Regts [Patel and Regts, 2017] later gave a refinement of Barvinok’s framework, which gave a polynomial-time algorithm for a class of zero-free graph polynomials that can be expressed as counting induced subgraphs in bounded-degree graphs.
In this paper, we give a polynomial-time algorithm for estimating classical and quantum partition functions specified by local Hamiltonians with bounded maximum degree, assuming a zero-free property for the temperature. Consequently, when the inverse temperature is close enough to zero by a constant gap, we have a polynomial-time approximation algorithm for all such partition functions. Our result is based on a new abstract framework that extends and generalizes the approach of Patel and Regts.
partition function
zero-freeness
local Hamiltonian
Theory of computation~Design and analysis of algorithms
108:1-108:20
Track A: Algorithms, Complexity and Games
This research was supported by National Natural Science Foundation of China (Grant No. 61972191) and the Program for Innovative Talents and Entrepreneur in Jiangsu and Anhui Initiative in Quantum Information Technologies Grant No. AHY150100.
https://arxiv.org/abs/2201.12772
Penghui
Yao
Penghui Yao
State Key Laboratory for Novel Software Technology, Nanjing University, China
Yitong
Yin
Yitong Yin
State Key Laboratory for Novel Software Technology, Nanjing University, China
Xinyuan
Zhang
Xinyuan Zhang
State Key Laboratory for Novel Software Technology, Nanjing University, China
10.4230/LIPIcs.ICALP.2022.108
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Penghui Yao, Yitong Yin, and Xinyuan Zhang
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