Neural network decoder for topological color codes with circuit level noise

Abstract

A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment --- without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate ${\epsilon }_{\mathrm{L}}$ of the encoded logical qubit to values much below the error rate ${\epsilon }_{\mathrm{phys}}$ of the physical qubits --- fitting the expected power law scaling ${\epsilon }_{\mathrm{L}}\propto {\epsilon }_{\mathrm{phys}}^{(d+1)/2}$, with $d$ the code distance. The neural network incorporates the information from "flag qubits" to avoid reduction in the effective code distance caused by the circuit. As a test, we apply the neural network decoder to a density-matrix based simulation of a superconducting quantum computer, demonstrating that the logical qubit has a longer life-time than the constituting physical qubits with near-term experimental parameters.

10 pages, 9 figures; V2: updated text and figures

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