MITS: A Quantum Sorcerer Stone For Designing Surface Codes

TL;DR

This paper tackles the challenge of selecting optimal surface-code parameters under hardware-specific noise by introducing MITS, an inverse-modeling framework that uses STIM-generated data to predict the minimal code distance $d$ and rounds $r$ needed to achieve a target logical error rate $TLER$. It builds a large STIM-based dataset (about $8.64k$ experiments) across four error channels and employs a two-stage predictive model where $d$ is predicted with XGBoost and $r$ with Random Forest, applying rounding rules to ensure practical, robust parameter choices. The results show near-perfect Pearson correlations ($\approx$0.986 for $d$ and $\approx$0.967 for $r$ in raw form; $\approx$0.968 and $\approx$0.964 after rounding) and demonstrate that MITS can reduce simulation time from hours to approximately $11\pm3$ milliseconds per prediction, while reliably achieving the target $TLER$. The approach offers a practical, hardware-aware pathway to optimize surface-code implementations, enabling faster calibration and more efficient quantum error correction in real devices, with code available on public repositories.

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.

Figures (6)

• Figure 1: Rotated surface codes: interactions, structures, and overheads.ⓐ Z-stabilizers interact with four data qubits. ⓑ X-stabilizers interact with the same qubits. ⓒ A distance $5$ rotated surface code forms a $5 \times 5$ lattice, with grey-blobs as data qubits and yellow/blue surfaces representing Z/X-stabilizers. ⓓ A distance $3$ code across $2$ rounds highlights the $3 \times 3$ lattice's repetition over time. ⓔ Increased distances raise qubit counts, and more rounds lead to greater gate numbers. With rounds being threefold the distance, the overhead of high distance and rounds is evident.
• Figure 2: Logical error rate heat map analysis. With increasing distance, the logical error rate shows an anticipated reduction. Yet, there is a nuanced relationship with rounds: the error rate fluctuates initially, reaches a 'sweet spot' where distance seems to counterbalance the errors from rounds sufficiently, and subsequently increases again, potentially from heat relaxation risks.
• Figure 3: The developmental and operational blueprint of MITS.①STIM Simulation: Using STIM to estimate logical error rates from physical attributes, distance, and rounds. ②Data Compilation: Generated a dataset from $8.5k$ STIM experiments over weeks. ③Dataset Partition: Split into training and test subsets. ④Model Exploration: Evaluated various heuristic and ML models for optimal surface code parameters. ⑤Optimal Model Selection: Chose a two-step model using xgboost and random forest. ⑥User Input: Users specify physical error attributes and desired logical error rate. ⑦Output: MITS recommends optimal distance and rounds.
• Figure 4: Pearson Correlation of Heuristic vs. ML Models. The bar graph shows heuristic models outperformed by XGBoost and Random Forest in machine learning. Optimal are XGBoost for distance and Random Forest for rounds, both in bold.
• Figure 5: Comparative Analysis of Predicted vs. Optimal Distance and Rounds.ⓐ and ⓒ: Scatter plots comparing predicted and optimal distances, showing a trend towards rounding to the nearest odd number starting at three. ⓑ and ⓓ: Scatter plots of rounds, with raw values generally rounding up to the nearest integer, showing minimal variance. Dotted diagonals indicate perfect predictions. ⓔ and ⓕ: Box plots contrasting original, predicted, and rounded values. Distances show deviations upon rounding, while rounds remain consistent across all measures.