Quantum algorithms for Gibbs sampling and hitting-time estimation
Journal Article
·
· Quantum Information & Computation
- Univ. of New Mexico, Albuquerque, NM (United States). Center for Quantum Information and Control; New Mexico Consortium, Los Alamos, NM (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.
- Research Organization:
- Los Alamos National Laboratory (LANL)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- Contributing Organization:
- New Mexico Consortium, Los Alamos, NM (United States)
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1360697
- Report Number(s):
- LA-UR-16-21218
- Journal Information:
- Quantum Information & Computation, Journal Name: Quantum Information & Computation Journal Issue: 1-2 Vol. 17; ISSN 1533-7146
- Publisher:
- Rinton PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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