Feynman's Entangled Paths to Optimized Circuit Design

TL;DR

This paper introduces a novel quantum circuit optimization approach inspired by Feynman's path formalism, focusing on entanglement evolution to guide the search for optimal circuit configurations.

Contribution

It proposes a new perspective using path integrals and entanglement as guiding principles for quantum circuit optimization, which is a largely unexplored area.

Findings

Path-entanglement sum minimization may identify optimal state paths.

The approach can potentially accelerate circuit optimization by reducing search space.

Certain target states may not benefit from this optimization method.

Abstract

We motivate an intuitive way to think about quantum circuit optimization problem inspired by Feynman's path formalism. While the use of path integrals in quantum circuits remains largely underdeveloped due to the lack of definition of the action functional for such systems. However this feynman's path perspective leads us to consider about how entanglement evolution throughout the circuit can serve as a guiding principle for optimizing circuit design. We conjecture that an optimal state-path is highly likely to belong to a family of paths with the minimum possible path-entanglement sum. This could enhance the efficiency of circuit optimization problems by narrowing the state-path search space, leading to faster convergence and reliable output. Further, we discuss that for some special target states this conjecture may not provide significant insights to the circuit optimization problem and argue that such cases constitute only a small subset of the target sets encountered by a circuit optimization algorithm.