QuBEC: Boosting Equivalence Checking for Quantum Circuits with QEC Embedding

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.