A quantum-quantum Metropolis algorithm

The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method t...

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Veröffentlicht in:Proceedings of the National Academy of Sciences - PNAS Jg. 109; H. 3; S. 754
Hauptverfasser: Yung, Man-Hong, Aspuru-Guzik, Alán
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States 17.01.2012
Schlagworte:
Algorithms
Computer Simulation
Markov Chains
Quantum Theory
ISSN:1091-6490, 1091-6490
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Zusammenfassung:The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overcome by quantum computers. Here, we present a quantum algorithm which fully generalizes the classical Metropolis algorithm to the quantum domain. The meaning of quantum generalization is twofold: The proposed algorithm is not only applicable to both classical and quantum systems, but also offers a quantum speedup relative to the classical counterpart. Furthermore, unlike the classical method of quantum Monte Carlo, this quantum algorithm does not suffer from the negative-sign problem associated with fermionic systems. Applications of this algorithm include the study of low-temperature properties of quantum systems, such as the Hubbard model, and preparing the thermal states of sizable molecules to simulate, for example, chemical reactions at an arbitrary temperature.
Bibliographie:ObjectType-Article-1
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ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.1111758109