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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Time-Domain Multiplexed Two-Dimensional Cluster State for Large-Scale Universal Multi-Input One-Way Quantum Computation

Warit Asavanant, Hidehiro Yonezawa, Akira Furusawa, Yu Shiozawa, Baramee Charoensombutamon, H. Emura, Shota Yokoyama, Rafael N. Alexander, Nicolas C. Menicucci, Shuntaro Takeda, Jun–ichi Yoshikawa

Published Jun 1, 2019• 0 citations
Publisher

Abstract

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].

DOI
10.1109/cleoe-eqec.2019.8873387

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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].
Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states-based on bosonic modes rather than qubits-have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.
Optical systems have been long considered to be appropriate for tasks in quantum communications but not quantum computation. This is because the optical systems are “flying qubits” that need actual physical circuits to implement quantum computation, limiting their scalability. In this chapter, we explain a methodology that does not only overcome this limitation but is also one of the currently most promising methods in terms of scalability: time-domain quantum computation. In this method, quantum states are encoded in a localized temporal wave packet. These wave packets can be multiplexed in time, allowing the generation of large-scale cluster states and multi-step quantum operations using only minimal physical resources. We explain basic ideas of quantum computation in the time domain and show several experimental examples.
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.
Cluster states, a specific class of multi-partite entangled states, are of particular importance for quantum science, as such systems are equivalent to the realization of one-way (or measurement-based) quantum computers [1]. In this scheme, algorithms are implemented through high-fidelity measurements on the parties of the state [2]. While two-level (i.e. qubit) cluster states have been realized so far, increasing the number of particles to boost the computational resource comes at the price of significantly reduced coherence time and detection rates, as well as increased sensitivity to noise, restricting the realization of discrete cluster states to a record of eight qubits. In contrast, the demonstration of d-level (i.e. qudit) cluster states has the potential to i) increase quantum resources without modifying the number of particles; ii) enable the implementation of highly efficient computational protocols; iii) reduce the noise sensitivity of the states. Up till now, the realization of discrete d-level cluster states has not been shown in any quantum platform. We here demonstrate the realization of d-level cluster states, perform d-level one-way quantum processing operations on the states, and show that higher-dimensional forms of cluster states are more noise tolerant than lower dimensional realizations.
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.
Quantum optics is an extremely fruitful area of research in that it allows the probing of fundamental and basic science, as well as the opportunity to investigate potential applications that exploit these exotic phenomena. Entanglement is a uniquely quantum phenomenon that is a key feature of quantum mechanics. In this thesis we investigate the scalability of entangled states of light, as well as modest demonstrations of one-way quantum computations, based on a resource that exploits entanglement. Scalability has been a bottleneck of entanglement experiments since the first demonstrations began surfacing a few decades ago. In Part II of this thesis we investigate different methods of multiplexing quantum light modes in order to achieve a scalable architecture. 2 experiments are presented in spatial multiplexing, that lead to programmable linear optics networks that can produce up to 8 entangled modes. Building on this, and shifting domains we then demonstrate temporal multiplexing, where we entangle tens of thousands of quantum modes together in a highly entangled state called a cluster state. This is several orders of magnitude larger than any entangled state created to date, in any platform (be it atomic or electronic). The highly entangled cluster state is a universal resource for quantum computing, and we investigate a particular class of computations in Part III. We demonstrate that a cluster state consisting of only 4 highly entangled quantum modes is sufficient for universal 1-mode Gaussian quantum computing. Further, we demonstrate a tuneable entanglement gate that can be retrofitted to cluster states of arbitrary size or shape. Although the experiments in Part II and Part III are conceptually quite different, they employ very similar optical and electronic equipment. These experimental techniques as well as a survey of relevant quantum optics theory is presented in Part I.