String Abstractions for Qubit Mapping

TL;DR

This paper introduces a novel string-based qubit mapping technique for quantum circuit compilation, which improves performance metrics by optimizing initial qubit placement based on substring analysis and usage frequency.

Contribution

The paper proposes a new qubit mapping approach using string abstractions, enhancing existing compilation methods by reducing circuit depth and gate count.

Findings

Achieves 13-17% average improvement over baseline methods.

Reduces circuit depth by up to 32%.

Decreases gate volume by up to 63%.

Abstract

One of the key compilation steps in Quantum Computing (QC) is to determine an initial logical to physical mapping of the qubits used in a quantum circuit. The impact of the starting qubit layout can vastly affect later scheduling and placement decisions of QASM operations, yielding higher values on critical performance metrics (gate count and circuit depth) as a result of quantum compilers introducing SWAP operations to meet the underlying physical neighboring and connectivity constraints of the quantum device. In this paper we introduce a novel qubit mapping approach, string-based qubit mapping. The key insight is to prioritize the mapping of logical qubits that appear in longest repeating non-overlapping substrings of qubit pairs accessed. This mapping method is complemented by allocating qubits according to their global frequency usage. We evaluate and compare our new mapping scheme against two quantum compilers (QISKIT and TKET) and two device topologies, the IBM Manhattan (65 qubits) and the IBM Kolkata (27 qubits). Our results demonstrate that combining both mapping mechanisms often achieve better results than either one individually, allowing us to best QISKIT and TKET baselines, yielding between 13% and 17% average improvement in several group sizes, up to 32% circuit depth reduction and 63% gate volume improvement.