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Quantum Computation in Time Domain

Warit Asavanant, Akira Furusawa

Published Jan 25, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1063/9780735424074_004

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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 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].
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.
Achieving scalability is one of the most pressing tasks to realize practical quantum computer. In this regard, continuous-variable optical systems have shown many promising progresses such as generation of enormous cluster states, resources for measurement-based quantum computation, using minimal resources. In this talk, I will explain the concepts of continuous-variable quantum computation with the focuses on the quantum computation based on quantum teleportation. It turns out that the quantum teleportation protocol, a basic protocol that is equivalent to the identity operation, contains many essences of the quantum computation. I will discuss the recent experimental progresses with the main focuses on the time-domain multiplexing approach and how these progresses are paving the path toward large-scale fault-tolerant universal quantum computation.
Photonic quantum computing is one of the leading approaches to universal quantum computation. However, large-scale implementation of photonic quantum computing has been hindered by its intrinsic difficulties, such as probabilistic entangling gates for photonic qubits and lack of scalable ways to build photonic circuits. Here, we discuss how to overcome these limitations by taking advantage of two key ideas which have recently emerged. One is a hybrid qubit-continuous variable approach for realizing a deterministic universal gate set for photonic qubits. The other is the time-domain multiplexing technique to perform arbitrarily large-scale quantum computing without changing the configuration of photonic circuits. These ideas together will enable scalable implementation of universal photonic quantum computers in which hardware-efficient error correcting codes can be incorporated. Furthermore, all-optical implementation of such systems can increase the operational bandwidth beyond terahertz in principle, ultimately enabling large-scale fault-tolerant universal quantum computers with ultrahigh operation frequency.