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arXiv:1112.0254 · Physical Review A

Dynamical Gaussian state transfer with quantum-error-correcting architecture

Go Tajimi, Naoki Yamamoto

Published Feb 3, 2012• 6 citations
arXivHTMLPDF

Abstract

Transferring a quantum state of a light field to a memory is of particular importance. However, this transfer is usually hampered because the memory system is subjected to some noise and this can limit the performance of the state transfer greatly. In this paper, we consider the transfer of a Gaussian state of light to a linear medium memory such as an optomechanical oscillator and propose a dynamical feedback controller that suppresses the noise in the memory system. To protect an unknown state, the feedback scheme employs the specific configuration of the quantum error correction; that is, a three-mode Gaussian state having appropriate syndromes is taken as the input. Correspondingly, the memory consists of three independent linear systems. The syndrome errors are estimated continuously in time through the measurement of the output field, and the results are then fed back to control the system. Because the input is Gaussian and the systems are all linear, it is possible to formulate the problem using the framework of the celebrated classical Kalman filtering and linear quadratic Gaussian control. A numerical simulation demonstrates the effectiveness of the control scheme.

DOI
10.1103/physreva.85.022303

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Transferring a quantum state of a light field to a memory is of particular importance. However, this transfer is usually hampered because the memory system is subjected to some noise and this can limit the performance of the state transfer greatly. In this paper, we consider the transfer of a Gaussian state of light to a linear medium memory such as an optomechanical oscillator and propose a dynamical feedback controller that suppresses the noise in the memory system. To protect an unknown state, the feedback scheme employs the specific configuration of the quantum error correction; that is, a three-mode Gaussian state having appropriate syndromes is taken as the input. Correspondingly, the memory consists of three independent linear systems. The syndrome errors are estimated continuously in time through the measurement of the output field, and the results are then fed back to control the system. Because the input is Gaussian and the systems are all linear, it is possible to formulate the problem using the framework of the celebrated classical Kalman filtering and linear quadratic Gaussian control. A numerical simulation demonstrates the effectiveness of the control scheme.
The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. In this paper, we propose an analogous method utilizing entanglement for the purpose of feedback control. The system considered is a general linear dynamical quantum system, where the control goal can be systematically formulated as a linear quadratic Gaussian control problem based on the quantum Kalman filtering method; in this setting, an entangled input probe field is effectively used to reduce the estimation error and accordingly the control cost function. In particular, we show that, in the problem of cooling an opto-mechanical oscillator, the entanglement-assisted feedback control can lower the stationary occupation number of the oscillator below the limit attainable by the controller with a coherent probe field and furthermore beats the controller with an optimized squeezed probe field.
The purpose of this work is to develop a systematic approach towards synchronisation of two micro-mechanical oscillators inside one optical cavity using feedback control. We first obtain the linear quantum stochastic state space model for the optomechanical system considered in this paper. Then we design a measurement-based optimal controller, aimed at achieving complete quantum synchronisation of the two mechanical oscillators with different natural frequencies, in the linear quadratic Gaussian setting. In addition, simulation results are provided, which show how system parameters impact on the control effect. These findings shed light on the synchronised network of oscillators that can be used for memory and quantum state transfer.
In many optical and atomic systems it is now possible to monitor an individual quantum system with high signal to noise and feed back by altering the system dynamics in real time. This motivates further development of quantum mechanical descriptions of feedback control. We discuss recent work on closed loop control of open quantum systems, focusing on general linear systems for which the statistics of the problem are Gaussian. Such systems may be realized with linear optics, parametric amplifiers and homodyne detection. This problem allows a direct comparison with the classical linear, quadratic cost, Gaussian noise (LQG) optimal control problem. This highlights the key distinction between the quantum and classical theories for linear systems: that increased measurement sensitivity may run counter to the control objectives since it increases the backaction noise. While in an idealized classical control problem it is always preferable to obtain a better sensor, quantum mechanical problems generically have an optimal sensitivity since quantum mechanical measurements irreducibly disturb the system. The general theory will be illustrated by reference to specific simple examples.
Abstract A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stage of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single photon while maintaining the perfect state transfer. The key idea is twofold; (i) the control signal is allowed to vary continuously in time to introduce an additional degree of freedom, and then (ii) an optimal control problem is formulated to design a simple-formed input pulse and the corresponding control signal. Numerical simulations are conducted for Λ-type atomic media and networked atomic ensembles, to show the effectiveness of the proposed method.
We give a concrete description of a controlled quantum stochastic dynamical model corresponding to a quantum system (a cavity mode) undergoing continual quadrature measurements, with a PID controller acting on the filtered estimate for the mode operator. The control has three feedback paths: P (proportional), I (integral) and D (derivative) of the error signal. Central use is made of the input and output pictures when constructing the model: these unitarily equivalent pictures are presented in the paper, and used to transfer concepts relating to the controlled internal dynamics to those relating to measurement output, and vice versa. The approach shows the general principle for investigating mathematically and physically consistent models in which standard control theoretic methods are to be extended to the quantum setting.
This paper is concerned with a quantum memory system for storing quantum information in the form of its initial dynamic variables in the presence of environmental noise. In order to compensate for the deviation from the initial conditions, the classical parameters of the system Hamiltonian are affected by the actuator output of a measurement-based classical controller. The latter uses an observation process produced by a measuring apparatus from the quantum output field of the memory system. The underlying system is modelled as an open quantum harmonic oscillator whose Heisenberg evolution is governed by linear Hudson-Parthasarathy quantum stochastic differential equations. The controller is organised as a classical linear time-varying system, so that the resulting closed-loop system has quantum and classical dynamic variables. We apply linear-quadratic-Gaussian control and fixed-point smoothing at the level of the first two moments and consider controllers with a separation structure which involve a continuously updated estimate for the initial quantum variables. The initial-point smoother is used for actuator signal formation so as to minimise the sum of a mean-square deviation of the quantum memory system variables at a given time horizon from their initial values and an integral quadratic penalty on the control signal.