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arXiv:1507.08782 · Physical Review A

Implementation of a quantum cubic gate by an adaptive non-Gaussian measurement

Kazunori Miyata, Hisashi Ogawa, Petr Marek, Radim Filip, Hidehiro Yonezawa, Jun–ichi Yoshikawa, Akira Furusawa

Published Feb 1, 2016• 125 citations
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Abstract

We present a concept of non-Gaussian measurement composed of a non-Gaussian ancillary state, linear optics, and adaptive heterodyne measurement, and on the basis of this we also propose a simple scheme of implementing a quantum cubic gate on a traveling light beam. In analysis of the cubic gate in the Heisenberg representation, we find that nonlinearity of the gate is independent from nonclassicality; the nonlinearity is generated solely by a classical nonlinear adaptive control in a measurement-and-feedforward process, while the nonclassicality is attached by the non-Gaussian ancilla that suppresses excess noise in the output. By exploiting the noise term as a figure of merit, we consider the optimum non-Gaussian ancilla that can be prepared within reach of current technologies and discuss performance of the gate. It is a crucial step towards experimental implementation of the quantum cubic gate.

DOI
10.1103/physreva.93.022301

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We present a concept of non-Gaussian measurement composed of a non-Gaussian ancillary state, linear optics, and adaptive heterodyne measurement, and on the basis of this we also propose a simple scheme of implementing a quantum cubic gate on a traveling light beam. In analysis of the cubic gate in the Heisenberg representation, we find that nonlinearity of the gate is independent from nonclassicality; the nonlinearity is generated solely by a classical nonlinear adaptive control in a measurement-and-feedforward process, while the nonclassicality is attached by the non-Gaussian ancilla that suppresses excess noise in the output. By exploiting the noise term as a figure of merit, we consider the optimum non-Gaussian ancilla that can be prepared within reach of current technologies and discuss performance of the gate. It is a crucial step towards experimental implementation of the quantum cubic gate.
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.
We investigate non-Gaussian states of light as ancillary inputs for generating nonlinear transformations required for quantum computing with continuous variables. We consider a recent proposal for preparing a cubic phase state, find the exact form of the prepared state and perform a detailed comparison to the ideal cubic phase state. We thereby identify the main challenges to preparing an ideal cubic phase state and describe the gates implemented with the non-ideal prepared state. We also find the general form of operations that can be implemented with ancilla Fock states, together with Gaussian input states, linear optics, squeezing transformations, and homodyne detection with feed forward, and discuss the feasibility of continuous variable quantum computing using ancilla Fock states.
Non-Gaussian quantum gates are essential components for optical quantum information processing. However, the efficient implementation of practically important multimode higher-order non-Gaussian gates has not been comprehensively studied. We propose a measurement-based method to directly implement general, multimode, and higher-order non-Gaussian gates using only fixed non-Gaussian ancillary states and adaptive linear optics. Compared to existing methods, our method allows for a more resource-efficient and experimentally feasible implementation of multimode gates that are important for various applications in optical quantum technology, such as the two-mode cubic quantum nondemolition gate or the three-mode continuous-variable Toffoli gate, and their higher-order extensions. Our results will expedite the progress toward fault-tolerant universal quantum computing with light. Published by the American Physical Society 2024
We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian, and we find that the cubic phase gate error decreases inverse quartically with the amount of quadrature squeezing, even in the presence of linear loss. We also show how our scheme can be adapted to deterministically generate a nonclassical approximate cubic phase state with high fidelity using a ratio of native nonlinearity to linear loss of only 10^{-4}, indicating that our approach may be experimentally viable in the near term even on all-optical platforms, e.g., using quantum solitons in pulsed nonlinear nanophotonics.
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.
Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.