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arXiv:1509.00484 · Physical Review A

One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator

Rafael N. Alexander, Pei Wang, Niranjan Sridhar, Moran Chen, Olivier Pfister, Nicolas C. Menicucci

Published Sep 27, 2016• 65 citations
arXivHTMLPDF

Abstract

One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but nonuniversal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\ifmmode\times\else\texttimes\fi{}{10}^{3}$ frequencies) $\ifmmode\times\else\texttimes\fi{}$ (unlimited number of temporal modes) into a computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this entanglement resource.

DOI
10.1103/physreva.94.032327

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One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but nonuniversal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to (3\ifmmode×\else\texttimes\fi1033\ifmmode\times\else\texttimes\fi{}{10}^{3}3\ifmmode×\else\texttimes\fi103 frequencies) \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi (unlimited number of temporal modes) into a computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this entanglement resource.
One-way quantum computing uses single-qubit projective measurements performed on a cluster state (a highly entangled state of multiple qubits) in order to enact quantum gates. The model is promising due to its potential scalability; the cluster state may be produced at the beginning of the computation and operated on over time. Continuous variables (CV) offer another potential benefit in the form of deterministic entanglement generation. This determinism can lead to robust cluster states and scalable quantum computation. Recent demonstrations of CV cluster states have made great strides on the path to scalability, utilizing either time or frequency multiplexing in optical parametric oscillators (OPO), both above and below threshold. The techniques relied on a combination of entangling operators and beam-splitter transformations. Here we show that an analogous transformation exists for amplifiers with Gaussian inputs states operating on multiple spatial modes. By judicious selection of local oscillators, the spatial mode distribution is analogous to the optical frequency comb consisting of axial modes in an OPO cavity. We outline an experimental system that generates cluster states across the spatial frequency comb, which can also scale the amount of quantum noise reduction to potentially larger than in other systems.
Enabling large-scale and high-speed quantum computation is a key to practical quantum computation. Continuous-variable approach in optical systems offer advantages in scalability and speed by leveraging their temporal degree of freedom and inherent large carrier frequency. In this paper, we investigate the generation and manipulation of quantum entanglement through a time-domain multiplexing approach. By employing time-domain multiplexing, we generate a two-dimensional cluster state—a universal resource for large-scale quantum computation—and perform quantum operations in the time domain with cluster state. Additionally, our ongoing research focuses on the generation and measurement of broadband optical quantum entanglement through an optical parametric oscillator, which holds potential as a foundation for high-speed quantum computing surpassing limitations of existing systems. By further engineering the quantum entanglement, we have also theoretically formulated a practical teleportation-based architectures for quantum computation in time domain. These advancements form the groundwork for the development of practical optical quantum computation.
Continuous-variable optical quantum computation has seen much progress in recent years. In particular, cluster states---the universal resource for measurement-based quantum computation---have been realized in a scalable fashion using the time-domain multiplexing method. To utilize the cluster states in actual quantum computation, the measurement bases need to be programmed according to the desired computation. In addition, as the information is encoded in time in the time-domain multiplexing method, the measurement bases must be dynamically changed in time to fully utilize the large-scale cluster states. Here we report demonstrations of quantum operations using time-domain-multiplexed cluster states with a clock frequency of 25 MHz. This is achieved by our combining the cluster-state-generation setup with the setup to change the measurement basis in the time domain. We also formulate a method to evaluate and verify continuous-variable operations where the quantum entanglements in the cluster states are utilized. Therefore, we demonstrate the implementation of quantum operations on scalable continuous-variable cluster-state architectures. The results in this work are compatible with the developing nonlinear feedforward and non-Gaussian state generation technology, which brings the realization of the large-scale fault-tolerant universal optical quantum computer closer to reality.
One-way quantum computation is a promising scheme for realizing large-scale quantum computation, where computation is done via measurements on a universal multi-mode entangled resource called cluster state. The capability of this method is determined by the size and the dimension of the cluster state; the size is roughly equivalent to the number of input modes times number of operation steps, while the dimension determines universality and fault tolerance of the computation. To achieve universality, two-dimensional cluster state is required. Among many approaches, time-domain multiplexing using optical system [1, 2] is a promising method where quantum state is encoded in a temporal wave packet. Although universality is still lacking, one-million-mode one-dimensional cluster state has been demonstrated with this approach [3].
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Quantum computing promises exponential speedup for particular computational tasks, such as integer factoring, which bears importance for encryption technology, and quantum simulation, which holds vast scientific potential. Comparing with the traditional circuit-based quantum computers, one-way quantum computers are experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. In this thesis, I first review the fundamental theory of one-way quantum computing and its experimental implementation using the quantum optical frequency comb. After that, I present two novel schemes for generating ultra-scalable cluster states with rich structures that can be used for universal quantum computing.