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 epsilon(L) of the encoded logical qubit to values much below the error rate epsilon(phys) of the physical qubits-fitting the expected power law scaling epsilon(L)proportional to epsilon((d+1)/2)(phys), 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.