MITS: A Quantum Sorcerer Stone For Designing Surface Codes

Abstract: In the evolving landscape of quantum computing, determining the most efficient parameters for Quantum Error Correction (QEC) is paramount. Various quantum computers possess varied types and amounts of physical noise. Traditionally, simulators operate in a forward paradigm, taking parameters such as distance, rounds, and physical error to output a logical error rate. However, usage of maximum distance and rounds of the surface code might waste resources. An approach that relies on trial and error to fine-tune QEC code parameters using simulation tools like STIM can be exceedingly time-consuming. Additionally, daily fluctuations in quantum error rates can alter the ideal QEC settings needed. As a result, there is a crucial need for an automated solution that can rapidly determine the appropriate QEC parameters tailored to the current conditions. To bridge this gap, we present MITS, a tool designed to reverse-engineer the well-known simulator STIM for designing QEC codes. MITS accepts the specific noise model of a quantum computer and a target logical error rate as input and outputs the optimal surface code rounds and code distances. This guarantees minimal qubit and gate usage, harmonizing the desired logical error rate with the existing hardware limitations on qubit numbers and gate fidelity. We explored and compared multiple heuristics and machine learning models for training/designing MITS and concluded that XGBoost and Random Forest regression were most effective, with Pearson correlation coefficients of 0.98 and 0.96 respectively.