Differentiable Logical Programming for Quantum Circuit Discovery and Optimization

2026-02-09

AI Summary

This work addresses the challenge of designing high-fidelity quantum circuits, which often suffer from limited generality and suboptimal performance. The authors propose modeling the design problem as differentiable logic programming, uniquely integrating continuous logic with quantum unitary evolution. They develop an optimization framework based on T-norm fuzzy logic and geodesic interpolation, augmented with bias-aware initialization to mitigate barren plateaus. The approach enables users to specify custom differentiable logical axioms—such as correctness, simplicity, and robustness—and automatically discovers a 4-qubit quantum Fourier transform (QFT) circuit from a space of 21 candidate gates. Validated on the IBM Torino processor for local routing tasks, the method achieves a 59.3-percentage-point fidelity improvement over baselines and demonstrates resilience to hardware faults.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Designing high-fidelity quantum circuits remains challenging, and current paradigms often depend on heuristic, fixed-ansatz structures or rule-based compilers that can be suboptimal or lack generality. We introduce a neuro-symbolic framework that reframes quantum circuit design as a differentiable logic programming problem. Our model represents a scaffold of potential quantum gates and parameterized operations as a set of learnable, continuous ``truth values''or ``switches,''$s \in [0, 1]^N$. These switches are optimized via standard gradient descent to satisfy a user-defined set of differentiable, logical axioms (e.g., correctness, simplicity, robustness). We provide a theoretical formulation bridging continuous logic (via T-norms) and unitary evolution (via geodesic interpolation), while addressing the barren plateau problem through biased initialization. We illustrate the approach on tasks including discovery of a 4-qubit Quantum Fourier Transform (QFT) from a scaffold of 21 candidate gates. We also report a hardware-aware adaptation experiment on the 133-qubit IBM Torino processor, where the method improved fidelity by 59.3 percentage points in a localized routing task while adapting to hardware failures.

Problem

• quantum circuit design
• high-fidelity
• suboptimal ansatz
• rule-based compilers
• generality

Innovation

• differentiable logic programming
• neuro-symbolic quantum design
• continuous truth values
• barren plateau mitigation
• hardware-aware circuit optimization