1. Advanced Mean Field Methods in Quantum Probabilistic Inference
Kazuyuki Tanaka
Graduate School of Information Sciences,
Tohoku University
URL:
July, 2007
STATPHYS23 (Genova, Italy)

2. Probability Distribution and Density Matrix
Probability Distribution: Summation over all the 2N possible configurations
Density Matrix: Diagonalization
of 2Nx2N matrix
Computational Complexity of Exponential Order O(eN)
July, 2007
STATPHYS23 (Genova, Italy)

3. Conventional Belief Propagation
Fundamental Structure of
Conventional Belief Propagation
We cannot factorize it in the similar way. 1 2 3
July, 2007
STATPHYS23 (Genova, Italy)

4. Density Matrix and Reduced Density Matrixj i
Reducibility
Condition
July, 2007
STATPHYS23 (Genova, Italy)

5. Reduced Density Matrix and Effective Fields
All effective field
are matrices j i
July, 2007
STATPHYS23 (Genova, Italy)

6. Belief Propagation for Quantum Statistical Systems
Propagating Rule of Effective Fields j i
Output
July, 2007
STATPHYS23 (Genova, Italy)

7. Graphical Model for Probabilistic Inference
Undirected Graph
Directed Graph
July, 2007
STATPHYS23 (Genova, Italy)

8. A Quantum-Statistical Extension of Probabilistic Inference
July, 2007
STATPHYS23 (Genova, Italy)

9. Numerical Results for Quantum Belief Propagation
Exact
Undirected Graph
Quantum Belief Propagation
July, 2007
STATPHYS23 (Genova, Italy)

10. Linear Response Theory
July, 2007
STATPHYS23 (Genova, Italy)

11. Numerical Results for Canonical Correlations
Exact
Undirected Graph
Quantum Belief Propagation
July, 2007
STATPHYS23 (Genova, Italy)

12. STATPHYS23 (Genova, Italy)
Summary
An Extension to Quantum Belief Propagation
It is based on Quantum CVM (Morita, JPSJ1957)
Future Problem
Statistical-Mechanical Approaches to Quantum Statistical Inferences
July, 2007
STATPHYS23 (Genova, Italy)