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量子计算机在解决某些复杂问题方面具有经典计算机无法比拟的优势. 实现大规模量子计算需建立具有通用性、可扩展性和容错性的硬件平台. 连续变量光学系统具有独特的优势, 是实现大规模量子计算的一种可行途径, 近年来受到了广泛关注. 基于测量的连续变量量子计算通过对大规模高斯簇态(cluster态)的测量和测量结果的前馈来实现计算, 为实现量子计算提供了一条可行的途径. 量子纠错是量子计算和量子通信中保护量子信息的重要环节. 本文简要介绍了基于cluster态的单向量子计算、基于光学薛定谔猫态的量子计算和连续变量量子纠错的基本原理和研究进展, 并讨论了连续变量量子计算面临的问题和挑战.Quantum computation presents incomparable advantages over classical computer in solving some complex problems. To realize large-scale quantum computation, it is required to establish a hardware platform that is universal, scalable and fault tolerant. Continuous-variable optical system, which has unique advantages, is a feasible way to realize large-scale quantum computation and has attracted much attention in recent years. Measurement-based continuous-variable quantum computation realizes the computation by performing the measurement and feedforward of measurement results in large-scale Gaussian cluster states, and it provides an efficient method to realize quantum computation. Quantum error correction is an important part in quantum computation and quantum communication to protect quantum information. This review briefly introduces the basic principles and research advances in one-way quantum computation based on cluster states, quantum computation based on optical Schrödinger cat states and quantum error correction with continuous variables, and discusses the problems and challenges that the continuous-variable quantum computation is facing.
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Keywords:
- quantum computation/
- continuous variables/
- cluster states/
- Schrödinger cat states/
- quantum error correction
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离散变量 (qubits) 连续变量 (qumodes) 计算基矢 $ \{{ |0 \rangle }_{\mathrm{L}}, { |1 \rangle }_{\mathrm{L}} \} $ $ \{{{ |s \rangle }_{x}\}}_{\mathrm{s}\in \mathbb{R}} $ 共轭基矢 $ \big\{{{ |\pm \rangle }_{\mathrm{L}}=( |0 \rangle }_{\mathrm{L}}\pm { |1 \rangle }_{\mathrm{L}})/\sqrt{2} \big \} $ ${ \bigg\{ { |t \rangle }_{p}=\dfrac{1}{\sqrt{2\mathrm{\pi } } } \displaystyle\int_{-\infty }^{\infty }\mathrm{d}s{\mathrm{e} }^{\mathrm{i}st}{ |s \rangle }_{x} \bigg\} }_{t\in \mathbb{R} }$ 编码 $ { |\psi \rangle =\alpha |0 \rangle }_{\mathrm{L}}+\beta { |1 \rangle }_{\mathrm{L}} $$ ({ |\alpha |}^{2}+{ |\beta |}^{2}=1 $) $|\psi \rangle = \displaystyle\int_{-\infty }^{\infty }\mathrm{d}s\psi (s ){ |s \rangle }_{x} \bigg(\displaystyle\int_{-\infty }^{\infty }\mathrm{d}s{ |\psi (s ) |}^{2}=1 \bigg)$ 探测方式 光子探测 平衡零拍探测 量子逻辑门 Bit-flip: $ {\widehat{X} |0 \rangle }_{\mathrm{L}}={ |1 \rangle }_{\mathrm{L}}, {\widehat{X} |1 \rangle }_{\mathrm{L}}={ |0 \rangle }_{\mathrm{L}} $ x方向平移: $ \widehat{X} (v ){ |s \rangle }_{x}={ |s+v \rangle }_{x} $ Phase-flip: $ {\widehat{Z} |0 \rangle }_{\mathrm{L}}={ |0 \rangle }_{\mathrm{L}}, {\widehat{Z} |1 \rangle }_{\mathrm{L}}={- |1 \rangle }_{\mathrm{L}} $ p方向平移: $ \widehat{Z} (u ){ |t \rangle }_{p}={ |t+u \rangle }_{p} $ Hadamard门:$ {\widehat{H} |0 \rangle }_{\mathrm{L}}={ |+ \rangle }_{\mathrm{L}}, {\widehat{H} |1 \rangle }_{\mathrm{L}}={ |- \rangle }_{\mathrm{L}} $ 傅立叶变换: $\widehat{R} ( {\mathrm{\pi } }/{2} ){ |s \rangle }_{x}={ |s \rangle }_{p}, \widehat{R} ( {\mathrm{\pi } }/{2} ){ |t \rangle }_{p}={ |-t \rangle }_{x}$ 可控非门: $ {\widehat{CX} |0 \rangle }_{\mathrm{L}}{ |0 (1 ) \rangle }_{\mathrm{L}}={ |0 \rangle }_{\mathrm{L}}{ |0 (1 ) \rangle }_{\mathrm{L}} $ 可控X门: $ {\widehat{CX} |{s}_{1} \rangle }_{{q}_{1}}{ |{s}_{2} \rangle }_{{q}_{2}}={ |{s}_{1} \rangle }_{{q}_{1}}{ |{s}_{2}+{s}_{1} \rangle }_{{q}_{2}} $ $ {\widehat{CX} |1 \rangle }_{\mathrm{L}}{ |0 (1 ) \rangle }_{\mathrm{L}}={ |1 \rangle }_{\mathrm{L}}{ |1 (0 ) \rangle }_{\mathrm{L}} $ $ {\widehat{CX} |{t}_{1} \rangle }_{{p}_{1}}{ |{t}_{2} \rangle }_{{p}_{2}}={ |{t}_{1}-{t}_{2} \rangle }_{{p}_{1}}{ |{t}_{2} \rangle }_{{p}_{2}} $ 
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