Quantum Circuit Optimization for the Fault-Tolerance Era: Do We Have to Start from Scratch?

Abstract: Quantum computing has made significant advancements in the last years in both hardware and software. Unfortunately, the currently available Noisy Intermediate-Scale Quantum (NISQ) hardware is still heavily affected by noise. Many optimization techniques have been developed to reduce the negative effects thereof, which, however, only works up to a certain point. Therefore, scaling quantum applications from currently considered small research examples to industrial applications requires error-correction techniques to execute quantum circuits in a fault-tolerant fashion and enter the Fault-Tolerant Quantum Computing (FTQC) era. These error-correction techniques introduce dramatic qubit overheads, leading to the requirement of tens of thousands of qubits already for toy-sized examples. Hence, quantum circuit optimization that reduces qubit overheads when shifting from the NISQ to the FTQC era is essential. This raises the question, whether we need to start from scratch, or whether current state-of-the-art optimization techniques can be used as a basis for this. To approach this question, this work investigates the effects of different optimization passes on a representative selection of quantum circuits. Since hardly any tools to automatically design and evaluate FTQC quantum circuits exist yet, we utilize resource estimation to compare the (potential) benefits gained by applying NISQ quantum circuit optimization to estimated FTQC resource requirements. The results indicate that, indeed, the estimated resource requirements for FTQC can be improved by applying NISQ quantum circuit optimization techniques. At the same time, more detailed investigations show what techniques lead to more benefits for FTQC compared to others, providing guidelines for the transfer of NISQ optimization techniques to the FTQC era.