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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Markov entropy decomposition: a variational dual for quantum belief propagation
David Poulin1, Matthew B Hastings
1Département de Physique, Université de Sherbrooke, Québec, J1K 2R1, Canada.
Physical Review Letters
|March 17, 2011
Summary
Researchers developed a new method to calculate the free energy of quantum many-body systems. This approach, based on convex optimization and quantum entropy, offers a robust theoretical foundation for quantum belief propagation and shows promise in complex system calculations.
Area of Science:
- Quantum Many-Body Physics
- Computational Physics
- Information Theory
Background:
- Accurate calculation of free energy in quantum many-body systems is crucial for understanding their thermodynamic properties.
- Existing methods often rely on approximations or computationally intensive techniques like quantum Monte Carlo.
- Variational upper bounds provide estimates but lack a complementary rigorous lower bound.
Purpose of the Study:
- To derive a rigorous lower bound for the free energy of quantum many-body systems at finite temperatures.
- To establish a theoretical foundation for quantum belief propagation methods.
- To provide a computationally tractable approach that complements existing variational upper bounds.
Main Methods:
- Utilized strong subadditivity of von Neumann entropy.
- Formulated the lower bound as a convex optimization problem with linear constraints.
- Relaxed the consistency condition of local density operators.
- Derived quantum belief propagation equations from the dual of the minimization problem.
Main Results:
- Successfully derived a novel lower bound for the free energy.
- The derived convex optimization problem is numerically tractable.
- Demonstrated good agreement between the lower bound calculations and quantum Monte Carlo results for a 2D spin-1/2 Heisenberg antiferromagnet.
- Established a theoretical basis for quantum belief propagation.
Conclusions:
- The developed lower bound offers a complementary tool to variational upper bounds for characterizing quantum many-body systems.
- The method provides a rigorous foundation for quantum belief propagation algorithms.
- The approach has potential applications in Hamiltonian complexity theory and generalizations of structure theorems.
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