Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low and high) ML-based decoding scheme, where the first level corrects errors on physical qubits and the second one corrects any existing logical errors, for different noise models. Our results show that our proposed decoding method achieves ∼ 10× and ∼ 2× higher values of pseudo-threshold and threshold respectively, than for MWPM. We show that usage of more sophisticated ML models with higher training/testing time, do not provide significant improvement in the decoder performance. Finally, data generation for training the ML decoder requires significant overhead hence lower volume of training data is desirable. We have shown that our decoder maintains a good performance with the train-test-ratio as low as 40 : 60.
While a Quantum Approximate Optimization Algorithm (QAOA) is intended to provide a quantum advantage in finding approximate solutions to combinatorial optimization problems, noise in the system is a hurdle in exploiting its full potential. Several error mitigation techniques have been studied to lessen the effect of noise on this algorithm. Recently, Majumdar et al. proposed a Depth First Search (DFS) based method to reduce n − 1 CNOT gates in the ansatz design of QAOA for finding Max-Cut in a graph G = (V, E), |V | = n. However, this method tends to increase the depth of the circuit, making it more prone to relaxation error. The depth of the circuit is proportional to the height of the DFS tree, which can be n − 1 in the worst case. In this paper, we propose an O(∆ • n 2 ) greedy heuristic algorithm, where ∆ is the maximum degree of the graph, that finds a spanning tree of lower height, thus reducing the overall depth of the circuit while still retaining the n − 1 reduction in the number of CNOT gates needed in the ansatz. We numerically show that this algorithm achieves 10 times increase in the probability of success for each iteration of QAOA for Max-Cut. We further show that although the average depth of the circuit produced by this heuristic algorithm still grows linearly with n, our algorithm reduces the slope of the linear increase from 1 to 0.11.
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose, although how an ML decoder will behave in a more realistic asymmetric noise model has not been studied. In this article we (i) establish a methodology to formulate the surface code decoding problem as an ML classification problem, and (ii) propose a two-level (low and high) ML-based decoding scheme, where the first (low) level corrects errors on physical qubits and the second (high) level corrects any existing logical errors, for various noise models. Our results show that our proposed decoding method achieves ∼ 10× and ∼ 2× higher values of pseudo-threshold and threshold respectively, than for those with MWPM. We also empirically establish that usage of more sophisticated ML models with higher training/testing time, do not provide significant improvement in the decoder performance.
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