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arXiv:2210.17120 · Nature Communications

Nonlinear feedforward enabling quantum computation

A. Sakaguchi, Shunya Konno, Fumiya Hanamura, Warit Asavanant, Kan Takase, Hisashi Ogawa, Petr Marek, Radim Filip, Jun–ichi Yoshikawa, Elanor H. Huntington, Hidehiro Yonezawa, Akira Furusawa

Published Jul 12, 2023• 41 citations
arXivHTMLPDF

Abstract

Measurement-based quantum computation with optical time-domain multiplexing is a promising method to realize a quantum computer from the viewpoint of scalability. Fault tolerance and universality are also realizable by preparing appropriate resource quantum states and electro-optical feedforward that is altered based on measurement results. While linear feedforward has been realized and become a common experimental technique, nonlinear feedforward was unrealized until now. In this paper, we demonstrate that a fast and flexible nonlinear feedforward realizes the essential measurement required for fault-tolerant and universal quantum computation. Using non-Gaussian ancillary states, we observed 10% reduction of the measurement excess noise relative to classical vacuum ancilla.

DOI
10.1038/s41467-023-39195-w

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Measurement-based quantum computation with optical time-domain multiplexing is a promising method to realize a quantum computer from the viewpoint of scalability. Fault tolerance and universality are also realizable by preparing appropriate resource quantum states and electro-optical feedforward that is altered based on measurement results. While linear feedforward has been realized and become a common experimental technique, nonlinear feedforward was unrealized until now. In this paper, we demonstrate that a fast and flexible nonlinear feedforward realizes the essential measurement required for fault-tolerant and universal quantum computation. Using non-Gaussian ancillary states, we observed 10% reduction of the measurement excess noise relative to classical vacuum ancilla.
Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $\ensuremath{\pi}$) to boost photonic quantum computing and significantly reduce its resources' overhead. The key element in our scheme is a nonlinear router that preferentially directs photonic wavepackets to different output ports depending on their intensity. As a relevant example, we analyze the nonlinearity provided by Rydberg blockade in atomic ensembles, in which the trade-off between the nonlinearity and the accompanying loss is well understood. We present protocols for efficient Bell measurement and GHZ-state preparation---both key elements in the construction of cluster states, as well as for the cnot gate and quantum factorization. Given the large number of entangling operations involved in fault-tolerant MBQC, the increase in success probability provided by our protocols already at moderate nonlinearities can result in a significant reduction in the required resources.
Quantum non-Gaussian gate is a missing piece to the realization of continuous-variable universal quantum operations in an optical system. In a measurement-based implementation of the cubic phase gate, a lowest-order non-Gaussian gate, non-Gaussian ancillary states that have a property we call nonlinear squeezing are required. This property, however, has never been experimentally verified. In this paper, we generate a superposition between a vacuum state and a single-photon state whose nonlinear squeezing is maximized by the optimization of the superposition coefficients. The nonlinear squeezing is observed via real-time quadrature measurements, meaning that the generated states are compatible with real-time feedforward and are suitable as ancillary states for the cubic phase gate in the time domain. Moreover, by increasing the number of photons, it is expected that nonlinear squeezing can be further improved. The idea presented here can be readily extended to higher-order phase gates [P. Marek et al., Phys. Rev. A 97, 022329 (2018)]. As such, this work presents an important step to extend continuous-variable quantum information processing from Gaussian regime to non-Gaussian regime.
In a continuous-variable optical system, the Gottesman-Kitaev-Preskill (GKP) qubit is a promising candidate for fault-tolerant quantum computation. To implement non-Clifford operations on GKP qubits, non-Gaussian operations are required. In this context, the implementation of a cubic phase gate by combining nonlinear feedforward with ancillary states has been widely researched. Recently, however, it was pointed out that the cubic phase gate is not the most suitable for non-Clifford operations on GKP qubits. In this paper, we show that we can achieve linear optical implementation of non-Clifford operations on GKP qubits with high fidelity by applying the nonlinear feedforward originally developed for the cubic phase gate and using a GKP-encoded ancillary state. Our paper shows the versatility of the nonlinear feedforward technique---important for optical implementation of the fault-tolerant continuous-variable quantum computation.
Universal quantum computing requires an architecture that supports both linear circuits and, crucially, strong nonlinear resources. For quantum photonic systems, integrating such nonlinearities with scalable linear circuitry has been a major bottleneck, leaving most optical experiments without nonlinear operations and, consequently, incapable of achieving universality. Here, we report an extensible photonic computer that supports a universal gate set by seamlessly combining fully programmable, scalable linear optical networks with integrated nonlinear modules. This platform enables a broad range of quantum computing and simulation tasks. We demonstrate the quasi-deterministic generation of optical Gottesman-Kitaev-Preskill states, which are essential resources for bosonic error correction, yet had previously been realized only probabilistically. Furthermore, we simulate complex many-body quantum dynamics, exemplified by the Bose-Hubbard model. Such quantum simulation tasks have long been considered beyond the reach of photonic hardware limited to linear operations. These capabilities, enabled by our extensible architecture, establish a viable route towards photonic quantum simulation and fault-tolerant quantum computing.
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.