Improving Hardware Requirements for Fault-Tolerant Quantum Computing by Optimizing Error Budget Distributions

Abstract: Despite significant progress in quantum computing in recent years, executing quantum circuits for practical problems remains challenging due to error-prone quantum hardware. Hence, quantum error correction becomes essential but induces significant overheads in qubits and execution time, often by orders of magnitude. Obviously, these overheads must be reduced. Since many quantum applications can tolerate some noise, end users can provide a maximum tolerated error, the error budget, to be considered during compilation and execution. This error budget, or, more precisely, its distribution, can be a key factor in achieving the overhead reduction. Conceptually, an error-corrected quantum circuit can be divided into different parts that each have a specific purpose. Errors can happen in any of these parts and their errors sum up to the mentioned error budget, but how to distribute it among them actually constitutes a degree of freedom. This work is based on the idea that some of the circuit parts can compensate for errors more efficiently than others. Consequently, these parts should contribute more to satisfy the total error budget than the parts where it is more costly. However, this poses the challenge of finding optimal distributions. We address this challenge not only by providing general guidelines on distributing the error budget, but also a method that automatically determines resource-efficient distributions for arbitrary circuits by training a machine learning model on an accumulated dataset. The approach is evaluated by analyzing the machine learning model's predictions on so far unseen data, reducing the estimated space-time costs for more than 75% of the considered quantum circuits, with an average reduction of 15.6%, including cases without improvement, and a maximum reduction of 77.7%.