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Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer.
1Département de Physique, Université de Sherbrooke, Québec, Canada, J1K 2R1.
Physical Review Letters
|April 7, 2010
Summary
We developed a quantum algorithm for preparing thermal states in interacting quantum systems. This method provides a universal bound on thermalization time and efficiently calculates the partition function.
Area of Science:
- Quantum Computing
- Statistical Mechanics
- Quantum Many-Body Systems
Background:
- Understanding the thermal equilibrium states of quantum systems is crucial for various fields, including condensed matter physics and quantum information.
- Efficiently preparing these states and calculating thermodynamic properties like the partition function remains a significant challenge for classical and quantum computation.
Purpose of the Study:
- To introduce a novel quantum algorithm for the preparation of thermal Gibbs states of interacting quantum systems.
- To establish a universal upper bound for the thermalization time of quantum systems.
- To develop an efficient quantum algorithm for evaluating the partition function.
Main Methods:
- The study presents a quantum algorithm designed to prepare the thermal Gibbs state.
- The algorithm establishes a universal upper bound D(alpha) on thermalization time, dependent on system dimension (D) and a parameter (alpha) related to Helmholtz free energy density.
- A second algorithm is derived to compute the partition function.
Main Results:
- A quantum algorithm for preparing thermal Gibbs states is successfully presented.
- A universal upper bound on thermalization time, D(alpha), is established.
- An algorithm to evaluate the partition function is derived, with computational time scaling favorably with thermalization time and accuracy.
Conclusions:
- The developed quantum algorithm offers an efficient method for accessing thermal states of interacting quantum systems.
- The derived bounds and algorithms have implications for quantum simulation and the study of quantum thermodynamics.
- This work advances the capabilities of quantum computation in addressing fundamental problems in statistical mechanics.
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