Recursive Methods for Synthesizing Permutations on Limited-Connectivity Quantum Computers

TL;DR

This paper introduces recursive algorithms for efficiently synthesizing qubit permutations on quantum computers with limited connectivity, optimizing circuit size and depth, and demonstrating their effectiveness on Quantum Volume circuits.

Contribution

It presents a novel recursive synthesis approach combining scalable heuristics with exact methods for limited-connectivity quantum circuits.

Findings

Algorithms scale favorably with system size

Achieve near-optimal circuit performance in many cases

Disprove a conjecture about permutation complexity on paths

Abstract

We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic with a non-scalable, yet exact, synthesis. Our algorithms are applicable to generic connectivity constraints, scale favorably, and achieve close-to-optimal performance in many cases. We demonstrate the utility of these algorithms by optimizing the compilation of Quantum Volume circuits, and to disprove an old conjecture on reversals being the hardest permutation on a path.