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Physical Review Applied

Time-Domain-Multiplexed Measurement-Based Quantum Operations with 25-MHz Clock Frequency

Warit Asavanant, Baramee Charoensombutamon, Shota Yokoyama, Takeru Ebihara, Tomohiro Nakamura, Rafael N. Alexander, Mamoru Endo, Jun–ichi Yoshikawa, Nicolas C. Menicucci, Hidehiro Yonezawa, Akira Furusawa

Published Sep 2, 2021• 75 citations
Publisher

Abstract

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.

DOI
10.1103/physrevapplied.16.034005

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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.
Among various approaches toward quantum computation, measurement-based quantum computation (MBQC) multiplexed in time domain is currently a promising method for addressing the need for scalability. MBQC requires two components: cluster states and programmable measurements. With time-domain multiplexing, the former has been realized on an ultra-large-scale. The latter, however, has remained unrealized, leaving the large-scale cluster states unused. In this work, we make such a measurement system and use it to demonstrate basic quantum operations multiplexed in the time domain with 25 MHz clock frequency. We verify transformations of the input states and their nonclassicalities for single-step quantum operations and also observe multi-step quantum operations up to one hundred steps.
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.
A large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating a large-scale CV cluster state multiplexed in a time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to a three-dimensional (3D) CV cluster state by combining two time-delay nondegenerate optical parametric amplification systems with beam-splitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines, the partite number of each array can be very large (million), and the scale of the 3D cluster state can be ultra-large. In addition, the concrete quantum computing schemes of applying the generated 1D and 3D cluster states are also demonstrated. Our schemes may pave the way for fault-tolerant and topologically protected MBQC in hybrid domains, by further combining with efficient coding and quantum error correction.
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.
Measurement-based quantum computation with continuous variables in an optical setup shows great promise toward implementation of large-scale quantum computation, where the time-domain multiplexing approach enables us to generate the large-scale cluster state used to perform measurement-based quantum computation. To make effective use of the advantage of the time-domain multiplexing approach, in this paper, we propose the method to generate the large-scale three-dimensional cluster state which is a platform for topologically protected measurement-based quantum computation. Our method combines a time-domain multiplexing approach with a divide-and-conquer approach and has two advantages for implementing large-scale quantum computation. First, the squeezing level for verification of the entanglement of the three-dimensional cluster states is experimentally feasible. The second advantage is the robustness against analog errors derived from the finite squeezing of continuous variables during topologically protected measurement-based quantum computation. Therefore, our method is a promising approach to implement large-scale quantum computation with continuous variables.
Quantum computers, leveraging the principles of quantum mechanics, hold the potential to surpass classical computers in numerous applications, with implications across various domains. Besides the well-known gate model, Measurement-based Quantum Computation (MBQC) is another promising computational approach to achieve universal quantum computation. In MBQC, large ensembles of qubits are prepared in a highly entangled cluster state, forming the basis for executing quantum computations through sequential measurements. Cluster states are realized using both continuous variables (CV) and discrete variables (DV) techniques. In the CV-based methods, Frequency Domain Multiplexing (FDM), Time Domain Multiplexing (TDM), Spatial Domain Multiplexing (SDM), and hybrid schemes are employed. This paper thoroughly discusses and compares these approaches, elucidating their strengths and limitations. Additionally, the generation of photonic cluster states in DV is explored and some recent results are reported. Some recent state-of-the-art advancements in photonic and superconducting qubits entanglement, which can potentially serve as cluster states, are also presented. Finally, we highlight the approach that exhibits the most promising characteristics for achieving efficient cluster state realization in the context of MBQC.