Continuous-variable Gaussian analog of cluster states

Zhang, Jing; Braunstein, Samuel L.

doi:10.1103/physreva.73.032318

Cited by 241 publications

(277 citation statements)

References 26 publications

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“…The interest in the realization of a full QND gate grew only recently, mainly in the context of continuous-variable (CV) quantum information processing [4]. In particular, the QND sum gate is (up to local phase rotations) the canonical entangling gate for building up Gaussian cluster states [5], a sufficient resource for universal quantum computation [6]. Other applications of the sum gate are CV quantum error correction [7] and CV coherent communication [8].…”

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confidence: 99%

Demonstration of a Quantum Nondemolition Sum Gate

et al. 2008

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The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light fields. We experimentally demonstrate a QND sum gate, employing the scheme by R. The analogue of a two-qubit C-NOT gate, when continuous quantum variables are considered, is the so-called sum gate. It represents the canonical version of a twomode entangling gate for universal quantum computation in the regime of continuous variables [1]. When applied to two optical, bosonic modes, as opposed to a simple beam splitter transformation, the sum gate is even capable of entangling two modes each initially in a coherent state, i.e., a close-to-classical state.Apart from representing a universal two-mode gate, the sum gate also describes a quantum nondemolition (QND) interaction. The concept of a QND measurement has been known for almost 30 years. Initially, it was proposed to allow for better accuracies in the detection of gravitational waves [2]. A QND measurement is a projection measurement onto the basis of a QND observable which is basically a constant of motion. The QND measurement should preserve the measured observable, but still gain sufficient information about its value; the back action is confined to the conjugate observable.Various demonstrations of QND or backaction evading measurements have been reported [3]. The interest in the realization of a full QND gate grew only recently, mainly in the context of continuous-variable (CV) quantum information processing [4]. In particular, the QND sum gate is (up to local phase rotations) the canonical entangling gate for building up Gaussian cluster states [5], a sufficient resource for universal quantum computation [6]. Other applications of the sum gate are CV quantum error correction [7] and CV coherent communication [8].Here we report on the experimental demonstration of a full QND sum gate. The gate leads to quantum correlations in both conjugate variables, consistent with an entangled state, and allowing for a QND measurement of either variable with signal and probe interchanged. While previous works focused on fulfilling the criteria for a QND measurement [9] of one fixed variable, here we satisfy the QND criteria for two non-commuting observables, verifying entanglement at the same time. As our implementation is very efficient and controllable, the current scheme can be used to process arbitrary optical quantum states, including fragile non-Gaussian states. Similar to the measurement-based implementation of single-mode squeezing gates [10,11], realization of the QND gate only requires two offline squeezed ancilla modes [10,12].Let us write the QND-gate Hamiltonian asĤ QND = x 1p2 , with a suitable choice of the absolute phase for each mode. Herex/2 andp/2 are the real and imaginary parts of each mode's annihilation operator,â = (x + ip)/2, and the ...

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Demonstration of a Quantum Nondemolition Sum Gate

et al. 2008

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“…In parallel, quantum variables with a continuous spectrum, have attracted a lot of interest and appear to yield very promising perspectives concerning both experimental realizations and general theoretical insights [5,6], due to relative simplicity and high efficiency in the generation, manipulation, and detection of continuous variable (CV) state. CV cluster and graph states have been proposed [7], which can be generated by squeezed state and linear optics [7,8,9], and demonstrated experimentally for the four-mode cluster state [10,11]. The one-way CV quantum computation was also proposed with the CV cluster state [12].…”

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Graphical description of local Gaussian operations for continuous-variable weighted graph states

Zhang

2008

Phys. Rev. A

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The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit graph states. The novel property of the CV weighted graph states is shown, which can be expressed by the stabilizer formalism. It is distinctively different from the qubit weighted graph states, which can not be expressed by the stabilizer formalism. The corresponding graph rule, stated in purely graph theoretical terms, is described, which completely characterizes the evolution of CV weighted graph states under this LC operation. This LC operation may be applied repeatedly on a CV weighted graph state, which can generate the infinite LC equivalent graph states of this graph state. This work is an important step to characterize the LC equivalence class of CV weighted graph states.Graph states [1, 2] -or equivalently called stabilizer states, are special instances of multiparty quantum sates that are of interest in a number of domains in quantum information theory and quantum computation. Graph states can be defined in terms of the stabilizer formalism, which is a group-theoretic framework originally designed to construct broad classes of quantum error-correcting codes -the stabilizer codes [3]. In addition to their role in quantum error-correction, graph states have been used in a number of interesting applications, where the measure-based model of quantum computation known as the one-way quantum computer is certainly among the most prominent [4].Most of the concepts of quantum information and computation have been initially developed for discrete quantum variables, in particular two-level or spin-1 2 quantum variables (qubits). In parallel, quantum variables with a continuous spectrum, have attracted a lot of interest and appear to yield very promising perspectives concerning both experimental realizations and general theoretical insights [5,6], due to relative simplicity and high efficiency in the generation, manipulation, and detection of continuous variable (CV) state. CV cluster and graph states have been proposed [7], which can be generated by squeezed state and linear optics [7,8,9], and demonstrated experimentally for the four-mode cluster state [10,11]. The one-way CV quantum computation was also proposed with the CV cluster state [12]. Moreover, the protocol of CV anyonic statistics implemented with CV graph states is proposed [13].It is well known that many graph states exhibit a high degree of genuine multi-party entanglement [14], and that this entanglement is a key ingredient responsible for the successful use of these states in various applications. Therefore, a detailed study of the entanglement properties of graph states is of natural interest. The study of the nonlocal properties of graph states naturally leads to an investigation of the action of local unitary (LU) operations on graph states, and a classification of graph sates under LU equivalence. Especial...

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“…The year 1999 saw the first important attempt at developing a CV model of quantum computing [27]. Seven years later, the cluster state version [28] of CVs [29,30], accelerated the field due to experimental interest. The result were proof-of-principle demonstrations [31][32][33][34], which culminated in a time domain one-million-node cluster [35,36] and a 60-node frequency domain cluster [37].…”

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Quantum Machine Learning over Infinite Dimensions

et al. 2017

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Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the finite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practical, infinite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that can lead to exponential speed-ups in situations where classical algorithms scale polynomially. Finally, we also map out an experimental implementation which can be used as a blueprint for future photonic demonstrations.Introduction -We are now in the age of big data [1]. An unprecedented era in history where the storing, managing and manipulation of information is no longer effective using previously techniques. To compensate for this, one important approach in manipulating such large data sets and extracting worthwhile inferences, is by utilizing machine learning techniques. Machine learning [2,3] involves using specially tailored 'learning algorithms' to make important predictions in fields as varied as finance, business, fraud detection, and counter terrorism. Tasks in machine learning can involve either supervised or unsupervised learning and can solve such problems as pattern and speech recognition, classification, and clustering. Interestingly enough, the overwhelming rush of big data in the last decade has also been responsible for the recent advances in the closely related field of artificial intelligence [4].Another important field in information processing which has also seen a significant increase in interest in the last decade is that of quantum computing [5]. Quantum computers are expected to be able to perform certain computations much faster than any classical computer. In fact, quantum algorithms have been developed which are exponentially faster than their classical counterparts [6,7]. Recently, a new subfield within quantum information has emerged combining ideas from quantum computing with artificial intelligence to form quantum machine learning [8].These discrete-variable schemes have observed a performance that scales logarithmically in the vector dimension, such as supervised and unsupervised learning [9], support vector machine [10], cluster assignment [11] and others [12][13][14][15][16][17][18]. Initial proof-of-principle experimental demonstrations have also been performed [19][20][21][22]. It was mentioned in [23], that certain caveats apply to quantum machine learning. However, since then these caveats (relating to sparsity, condition number, epsilon precision, quantum output), have been closed or applications found where they are not a concern, cf. [8,10,18,24].

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Continuous-variable Gaussian analog of cluster states

Cited by 241 publications

References 26 publications

Demonstration of a Quantum Nondemolition Sum Gate

Demonstration of a Quantum Nondemolition Sum Gate

Graphical description of local Gaussian operations for continuous-variable weighted graph states

Quantum Machine Learning over Infinite Dimensions

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