Differentiable Logical Programming for Quantum Circuit Discovery and Optimization

TL;DR

This paper presents a neuro-symbolic, differentiable logic programming framework for quantum circuit design, enabling autonomous discovery and hardware-aware optimization using gradient-based methods.

Contribution

It introduces a novel continuous logic formulation for quantum circuit discovery, bridging logic and quantum evolution, and demonstrates adaptive optimization on real quantum hardware.

Findings

Successfully discovered a 4-qubit Quantum Fourier Transform from a candidate gate scaffold.

Achieved hardware-aware adaptation on IBM Fez, reducing error rates by up to 46.7%.

Addressed barren plateau issues through biased initialization.

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 hardware-aware adaptation experiments on the 156-qubit IBM Fez processor, where the method autonomously adapted to both gradual noise drift (24.2~pp over static baseline) and catastrophic hardware failure (46.7~pp post-failure improvement), using only measurement-driven gradient updates with no hardwired bias or prior path preference