Abstract
We present a hybrid quantum-classical algorithm to simulate thermal states of classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one at a time. We identified a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Grover-like or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for two-dimensional Ising models with magnetic field on a square lattice, compared with the previously known Zalka's algorithm.
Highlights
Simulation of a finite-temperature physical system with a controllable quantum device is one of the most important goals of quantum simulation [1, 2]
We present a hybrid quantum-classical algorithm to simulate thermal states of classical Hamiltonians on a quantum computer
Classical Markov-Chain Monte Carlo (MCMC) algorithms are powerful tools for sampling Gibbs distributions. They are efficient provided that the gap ∆ of the transition matrix is non-vanishing; the running time typically scales as τ ∼ O (1/∆)
Summary
Simulation of a finite-temperature physical system with a controllable quantum device is one of the most important goals of quantum simulation [1, 2]. This approach is a generalization of the state preparation method by Lidar and Biham [9], and Zalka [10].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
