Reducing the CNOT count for Clifford+T circuits on NISQ architectures

TL;DR

This paper presents a new method for reducing CNOT gate count in Clifford+T quantum circuits on NISQ devices by using circuit slicing and Steiner trees, leading to fewer errors and more reliable quantum computations.

Contribution

The authors introduce a novel circuit slicing and Steiner tree-based approach to significantly lower CNOT counts in constrained quantum architectures, outperforming existing transpilers.

Findings

Reduced CNOT count compared to Qiskit and TKET

Effective on various benchmark and random circuits

Potential for more reliable NISQ quantum computations

Abstract

While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit operations, such as CNOT, to "connected" qubits. SWAP gates can be used to place the logical qubits on admissible physical qubits, but they entail a significant increase in CNOT-count. In this paper we consider the problem of reducing the CNOT-count in Clifford+T circuits on connectivity constrained architectures, like noisy intermediate-scale quantum (NISQ) computing devices. We "slice" the circuit at the position of Hadamard gates and "build" the intermediate {CNOT,T} sub-circuits using Steiner trees, significantly improving on previous methods. We compared the performance of our algorithms while mapping different benchmark and random circuits to some well-known architectures such as 9-qubit square grid, 16-qubit square grid, Rigetti 16-qubit Aspen, 16-qubit IBM QX5 and 20-qubit IBM Tokyo. Our methods give less CNOT-count compared to Qiskit and TKET transpiler as well as using SWAP gates. Assuming most of the errors in a NISQ circuit implementation are due to CNOT errors, then our method would allow circuits with few times more CNOT gates be reliably implemented than the previous methods would permit.