Optimization of CNOT circuits on limited connectivity architecture

TL;DR

This paper develops optimization methods for CNOT circuits tailored to limited connectivity quantum architectures, achieving reduced size and depth, and demonstrating improved robustness and performance on real devices.

Contribution

The paper introduces new algorithms for optimizing CNOT circuits on limited connectivity architectures, with proven bounds and practical improvements over existing methods.

Findings

Optimized CNOT circuit size to O(n^2 / log δ) on connected graphs with minimum degree δ.

Achieved circuit size below 2n^2 for sparsely connected structures.

Experimental results show improved robustness and performance on IBMQ devices.

Abstract

A CNOT circuit is the key gadget for entangling qubits in quantum computing systems. However, the qubit connectivity of noisy intermediate-scale quantum (NISQ) devices is constrained by their {limited connectivity architecture}. To improve the performance of CNOT circuits on NISQ devices, we investigate the optimization of the size/depth of CNOT circuits under the limited connectivity architecture. We present a method that can optimize the size of any $n$-qubit CNOT circuit $O\left(\frac{n^2}{\log \delta}\right)$ on any connected graph with minimum degree $\delta$, and prove this bound is optimal for the regular graph. For the near-term sparsely connected structure, we additionally present a method that can optimize the size of any $n$-qubit CNOT circuit to below $2n^2$. The numerical experiment shows that our method performs better than state-of-the-art results. Specifically, we present an example to illustrate the applicability of our algorithm. For the grid structure, which is commonly used in current quantum devices, we demonstrate that the depth of any $n$-qubit CNOT circuit can be optimized to be linear in $n$ with certain ancillary qubits (ancillas). Experimental results indicate that this method has significant improvements compared with all of the existing methods. We additionally test our algorithms on the five-qubit IBMQ devices, and the experiments show that the measurement results of the optimized circuit with our algorithm are more robust to noise compared with the IBM mapping method.