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 ò L of the encoded logical qubit to values much below the error rate ò phys of the physical qubits-fitting the expected power law scaling   µ + ( ) d L phys 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.

Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits

“…We point out that in [36], information from flag qubit measurement outcomes were used in a neural network decoder to decode topological color codes resulting in improved thresholds. However the scheme is not scalable as it requires an exponential increase in training data as a function of the code distance.…”

Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes

“…In this article, we use this strategy for the decoding of quantum LDPC codes. Neural-networkbased decoders for quantum error-correcting codes have attracted great interest recently, particularly in the context of topological codes [16][17][18][19][20][21][22][23][24][25][26][27]. But near optimal (or very fast suboptimal) decoding algorithms are already proposed for these codes [28][29][30][31], which exploit their regular lattice structure.…”

Neural ensemble decoding for topological quantum error-correcting codes

“…Finally, we briefly compare our framework to existing neural decoders for topological codes. One of the common approaches that neural decoders use involves training a neural network to correct failures of a given decoder [18,33,34]. Note that when the decoding algorithm produces a recovery operator R( s) on error E corresponding to the error syndrome s, applying the recovery operation on the error is equivalent to applying a logical operator L( s) to the stabilizers G( s) of the original code state [9,10].…”