DC: Depth Control on Quantum Classical Circuit

As the application range of Near-term Intermediate-scale Quantum (NISQ) systems expands, the primary hurdle that emerges is the assurance of circuit reliability. Various facets of quantum computing, from circuit design to multi-qubit mapping strategies, have aimed at bolstering reliability through assorted optimizations. Quantum classical circuits, a key type of quantum circuits, have been previously studied with the aim of enhancing reliability by reusing ancilla-qubits and employing a variety of strategies to optimize the size and depth of the circuit. However, even the most sophisticated optimization strategies may not yield reliable results for large-scale circuits. Classical Quantum Circuit Depth Control (DC), proposed and evaluated in this paper, seeks to confront this critical issue. The DC approach breaks a given classical circuit into segments, and limits its depth, thereby ensuring reliable output and reduced mapping costs for real quantum hardware. In addition, DC can deliver reliable output for quantum classical circuits of any depth on any NISQ system. Our trials with DC indicate that it consistently renders reliable output for quantum classical circuits that previously showed minimal or no reliability in output. Importantly, DC ensures the attainment of the expected output with a Probability of Successful Trial (PST) greater than 50\% for baseline circuits that otherwise yield no reliable output. DC achieves, on average, an 11x PST improvement compared to the non-segmented baseline, while guaranteeing the correct output with a significant lead over the second most common result. Furthermore, by reducing the number of gates per segment under DC, all mapping/routing optimizations can be completed in polynomial time, as confirmed by our theoretical analysis. This accomplishment was previously out of reach with mapping/routing techniques, which required exponential time.