Program-Synthesis-Driven Autodesign of Universal Unitary Operators

Area of Science:

• Photonic Networks
• Quantum Computing
• Artificial Intelligence

Background:

• Unitary matrix decomposition is crucial for photonic network design.
• Existing methods like Reck and Clements architectures have limitations.
• AI-driven approaches offer potential for discovering more efficient decomposition strategies.

Purpose of the Study:

• To demonstrate AI-driven program synthesis for autonomous discovery of unitary matrix decomposition strategies.
• To develop a system capable of generating minimal Mach-Zehnder interferometer (MZI) decompositions.
• To explore dimension-agnostic and structure-specific optimization rules for photonic networks.

Main Methods:

• Extending DreamCoder to handle complex-valued linear algebra for program synthesis.
• Generating decomposition programs for unitary matrices.
• Evaluating discovered strategies for minimal MZI count and generalizability across matrix dimensions.
• Analyzing performance for specific matrix types like Householder and sparse matrices.

Main Results:

• AI synthesized novel decomposition programs achieving the minimal N(N-1)/2 MZIs.
• Discovered dimension-agnostic invariants that generalize strategies from 5x5 to 64x64 matrices.
• Identified matrix-specific optimizations, e.g., a dimension-independent rule for Householder matrices requiring only 2N-3 MZIs.
• Achieved up to 38% fewer MZIs than the theoretical bound for sparse matrices.

Conclusions:

• Autonomous program synthesis is a scalable paradigm for discovering universal unitary operators and optimizing photonic networks.
• The AI system discovers both universal decomposition rules and matrix-specific optimizations without prior knowledge of matrix properties.
• These findings offer significant practical hardware benefits for scalable photonic implementations.