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How to design a universal fault-tolerant quantum computation protocol with high fidelity and low resource consumption is a hot topic in the field of quantum computing research. By reducing the effective code distance, the design of a universal fault-tolerant gate set based on concatenation code has been proposed. The auxiliary state required by the error correction of code must be verified before it can be used, so as to avoid the errors spread from the auxiliary state to the data state. But the qubit consumption can be very large due to multiple verification processes for the ancillary block. In this work, we analyze the ancillary consumption of two different verification schemes used in the Steane's error correction process. We take the basic state preparation of a 25-qubit 2-level concatenation code as an example, adopt a simpler verification circuit in its error correction process, and design an efficient decoding strategy by using deep neural network algorithm. Numerical simulations are also performed to analyze our low qubit resource overhead error correction scheme. [ABSTRACT FROM AUTHOR]

We propose a non-transversal but pieceable fault tolerant conversion circuit that is used to convert encoded information between five-qubit code and seven-qubit CSS code. Since a syndrome extraction circuit requiring fewer ancillary qubit resources would facilitate the realization of large-scale quantum computations, we further adapt a flag-assisted fault tolerant syndrome measurement scheme to reduce the cost of ancillary preparation. Numerical simulations are also performed to further analyze the performance of our conversion method. [ABSTRACT FROM AUTHOR]

Abstract: Reversible logic plays an important role in the synthesis of circuits for quantum computing. In this paper, we introduce families of reversible gates based on the majority Boolean function (MBF) and we prove their properties in reversible circuit synthesis. These gates can be used to synthesize reversible circuits of minimum “scratchpad register width” for arbitrary reversible functions. We show that, given a MBF f with inputs, f can be implemented by a reversible logic gate with inputs and outputs, i.e., without any constant inputs. We also demonstrate new gates from this family with very efficient quantum realizations for majority-based applications. They can be used to synthesize any reversible function of the same width in conjunction with inverters and Feynman (2-qubit controlled-NOT) gates. The gate universality problem is formulated in terms of elementary group theory and solved using the algebraic software GAP. [Copyright &y& Elsevier]

Generative adversarial network (GAN) has shown profound power in machine learning. It inspires many researchers from other fields to create powerful tools for various tasks, including quantum state preparation, quantum circuit translation, and so on. It is known as classical techniques cannot efficiently simulate the quantum system, and the existing works haven't investigated the quantum version of maximum mean discrepancy as the metric in learning models and applied it to quantum data. In this paper, we propose a metric named quantum maximum mean discrepancy (qMMD), which can be used to measure the distance between quantum data in Hilbert space. Based on the qMMD, we then design a quantum generative adversarial model, named qMMD-GAN, under the hybrid quantum–classical methods. We also provide the construction of qMMD-GAN that can be easily implemented on a quantum device. We demonstrate the power of our qMMD-GAN by applying it to a crucial real-world application that is generating an unknown quantum state. Our numerical experiments show that qMMD-GAN has a competitive performance compared to existing results. We believe that the hybrid-based models will not only be applied to physics research but provide a new direction for improving classical data processing tasks. [ABSTRACT FROM AUTHOR]