Neural network decoder for topological color codes with circuit level noise

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 ϵL of the encoded logical qubit to values much below the error rate ϵphys of the physical qubits—fitting the expected power law scaling ϵ L ∝ ϵ 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.