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Abstract

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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Authors and contacts

Corresponding author:Su Xiao-Long,suxl@sxu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 11834010, 62005149, 11804001, 11974227), the Fund for Shanxi “1331 Project” Key Subjects Construction, China, and the Fundamental Research Program of Shanxi Province, China (Grant Nos. 20210302121002, 20210302122002, 201901D211164).

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Cited By

DownLoad: Full-Size Img PowerPoint

	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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Catalog

Vol. 71, Issue 16 - 2022-08-20

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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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