# Density-matrix simulation of small surface codes under current and projected experimental noise

## TL;DR

This paper uses density-matrix simulations to evaluate the performance of small surface codes under realistic noise, showing they can achieve error rates below fault-tolerance thresholds and potentially surpass quantum memory and computation break-even points.

## Contribution

It provides a detailed simulation framework for surface codes with experimental noise parameters and explores optimization strategies and scalability to larger codes.

## Key findings

- Surface-17 achieves error rates below fault-tolerance thresholds.
- Feedback strategies improve quantum memory performance.
- Surface-49 could surpass the break-even point with current technology.

## Abstract

We present a full density-matrix simulation of the quantum memory and computing performance of the distance-3 logical qubit Surface-17, following a recently proposed quantum circuit and using experimental error parameters for transmon qubits in a planar circuit QED architecture. We use this simulation to optimize components of the QEC scheme (e.g., trading off stabilizer measurement infidelity for reduced cycle time) and to investigate the benefits of feedback harnessing the fundamental asymmetry of relaxation-dominated error in the constituent transmons. A lower-order approximate calculation extends these predictions to the distance-$5$ Surface-49. These results clearly indicate error rates below the fault-tolerance threshold of surface code, and the potential for Surface-17 to perform beyond the break-even point of quantum memory. At state-of-the-art qubit relaxation times and readout speeds, Surface-49 could surpass the break-even point of computation.