Preparing thermal states of quantum systems by dimension reduction

Area of Science:

• Quantum Computing
• Quantum Many-Body Physics
• Statistical Mechanics

Background:

• Preparing thermal Gibbs states is crucial for simulating quantum systems.
• Existing methods often suffer from significant memory overhead or long computation times.
• Understanding thermalization in quantum systems is a fundamental challenge.

Purpose of the Study:

• To introduce a novel quantum algorithm for preparing thermal Gibbs states.
• To achieve efficient state preparation with minimal memory requirements.
• To improve the time complexity of thermalization algorithms for quantum systems.

Main Methods:

• Development of a quantum algorithm tailored for one-dimensional quantum systems.
• Analysis of the algorithm's time complexity, dependent on system size (N), Hamiltonian norm (‖h‖), and temperature (T).
• Comparison of the proposed algorithm's performance against existing state-of-the-art methods.

Main Results:

• The algorithm prepares thermal Gibbs states on a quantum computer without memory overhead.
• Achieved a time complexity dominated by N(‖h‖/T), which is significantly faster than alternatives.
• Demonstrated improved scaling for higher-dimensional systems, reducing time complexity dependence on system dimension.

Conclusions:

• The presented algorithm offers a highly efficient and memory-optimal solution for preparing thermal Gibbs states.
• The time complexity scaling suggests near-optimality for quantum thermalization.
• The algorithm provides a valuable tool for advancing quantum simulations and understanding thermalization in quantum many-body systems.