QuBEC: Boosting Equivalence Checking for Quantum Circuits with QEC Embedding

TL;DR

This paper introduces QuBEC, a decision diagram-based method for quantum circuit equivalence checking that significantly reduces verification time and resource usage, especially for circuits with quantum error correction, thereby facilitating scalable quantum computing.

Contribution

The paper presents a novel verification approach that improves efficiency and scalability in quantum circuit equivalence checking by incorporating quantum error correction into the decision diagram framework.

Findings

Verification time reduced by up to 271.49 times

Decision diagram nodes reduced by up to 798.31 times

Enables faster, more efficient quantum circuit verification

Abstract

Quantum computing has proven to be capable of accelerating many algorithms by performing tasks that classical computers cannot. Currently, Noisy Intermediate Scale Quantum (NISQ) machines struggle from scalability and noise issues to render a commercial quantum computer. However, the physical and software improvements of a quantum computer can efficiently control quantum gate noise. As the complexity of quantum algorithms and implementation increases, software control of quantum circuits may lead to a more intricate design. Consequently, the verification of quantum circuits becomes crucial in ensuring the correctness of the compilation, along with other processes, including quantum error correction and assertions, that can increase the fidelity of quantum circuits. In this paper, we propose a Decision Diagram-based quantum equivalence checking approach, QuBEC, that requires less latency compared to existing techniques, while accounting for circuits with quantum error correction redundancy. Our proposed methodology reduces verification time on certain benchmark circuits by up to $271.49 \times$, while the number of Decision Diagram nodes required is reduced by up to $798.31 \times$, compared to state-of-the-art strategies. The proposed QuBEC framework can contribute to the advancement of quantum computing by enabling faster and more efficient verification of quantum circuits, paving the way for the development of larger and more complex quantum algorithms.