A quantum information approach to statistical mechanics

Abstract

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proofs of these two results are based on a mapping from partition functions to quantum states and to quantum circuits, respectively. Finally, we show how classical spin models can be used to describe certain fluctuating lattices appearing in models of discrete quantum gravity.

9 pages, 9 figures

References in corpus (10)

• Criticality, the area law, and the computational power of PEPS
• A Quantum Approach to Classical Statistical Mechanics
• On measurement-based quantum computation with the toric code states
• Completeness of the classical 2D Ising model and universal quantum computation
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Statistical Mechanical Models and Topological Color Codes
• On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
• Unifying all classical spin models in a Lattice Gauge Theory
• Measurement-based quantum computation and undecidable logic
• Classical spin systems and the quantum stabilizer formalism: general mappings and applications

Cited by in corpus (6)

• Simple universal models capture all classical spin physics
• Phase transition in a noisy Kitaev toric code model
• Analytical percolation theory for topological color codes under qubit loss
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture
• Systematic study of the completeness of two-dimensional classical ${\varphi }^4$ theory
• The grammar of the Ising model: A new complexity hierarchy