QRP: quantum reliability polynomial for stochastic reliability analysis of reversible circuits

The rapid growth of quantum computing is due to its ability to solve problems that cannot be solved using traditional computers. However, the inherent noise and other errors of quantum systems make them prone to failures, so fault tolerance is crucial. The rapid accumulation of errors can seriously affect the robustness of complex calculations. Techniques need to be developed to reduce these effects and enable reliable quantum computing. In this article, we adapt and extend the reliability polynomial, originally introduced by Moore and Shannon, for quantum circuits and gates. We introduce the Quantum Reliability Polynomial (QRP), a novel metric for evaluating the reliability of quantum gates and reversible circuits based on their complex properties. The QRP offers a powerful method for quantifying the fault tolerance of reversible gates under various random failures and stochastic fault models. We exploit the sensitivity of the QRP by carefully calculating its coefficients and associated probabilities for different fault models. This comprehensive analysis covers different circuit topologies and enables a comparative assessment of their reliability and effectiveness. Our results demonstrate the QRP potential as an effective tool for assessing the reliability of reversible quantum circuits and gates. Furthermore, they highlight the ongoing need to further develop this area of research to develop more reliable and efficient quantum computing systems.