MITS: A Quantum Sorcerer Stone For Designing Surface Codes

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. To bridge this gap, we present MITS, a tool designed to reverse-engineer the well-known simulator STIM for designing QEC codes. By curating a comprehensive dataset from STIM using valid physical errors, MITS is equipped to ascertain the optimal surface code parameters for a given quantum computer's noise model. 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 this task and concluded that XGBoost and Random Forest regression to be most effective, with Pearson correlation coefficients of 0.98 and 0.96 respectively. MITS employs these models to reliably and swiftly achieve the target error rates.