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

Abstract

We present a 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 the surface code, and the potential for Surface-17 to perform beyond the break-even point of quantum memory. However, Surface-49 is required to surpass the break-even point of computation at state-of-the-art qubit relaxation times and readout speeds.Quantum computing: current experiments break scalability barrierQuantum computing hardware has reached low enough error rates for any computation to be performed given a large enough system. A collaboration between Delft University of Technology and Leiden University have simulated the performance of state-of-the-art superconducting qubits in a small quantum circuit designed to protect information from otherwise catastrophic errors. Such a circuit requires the underlying device to perform above a ‘fault-tolerant’ threshold before it can be scaled to a full quantum computer. The team determined that not only should current technology break this barrier, but also that this quantum circuit should already store information better than its individual components. This work provides performance targets and guidance on design choices for experiments currently in development across the world.