Dynamical Gaussian state transfer with quantum-error-correcting architecture

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 to a great extent. In this paper, we consider the transfer of a Gaussian state of light to a linear medium memory such as an opto-mechanical 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.

Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information

“…II-B. Also the conjugate noise operator is given byP = M 2Ŵ ; these matrices satisfy the conditions (16). The controller is a classical system that processes the measurement result y(t) and produces the control signal u(t).…”

“…NowQ = M 1Ŵ2 is the unavoidable shot noise andP := M 2Ŵ2 is the BA noise, where the matrices satisfy Eq. (16). Note that the noise term of the closed-loop system (43) can be expressed by noise term of Eq.…”

“…In fact, the above-described cooling problem can be formulated as a quantum Linear Quadratic Gaussian (LQG) feedback control problem and explicitly solved [1,10,11,12,13]. Also the theory has been applied to various control problems in quantum information science such as error correction [14,15,16]. Notably, experiment of MF control is now within the reach of current technologies [17,18,19,20].…”

Noise suppression of on-chip mechanical resonators by chaotic coherent feedback

“…The cavity B is used for storing the quantum state in the membrane. The coupling between the cavity mode and the mechanical mode is assumed to be linear under the strong-driving regime [18,19]. Thus, the Hamiltonian of the total system can be written as…”

“…One of the most interesting problems for optomechanical systems is to explore the quantum aspects of mechanical motion [12][13][14][15], which is important not only for fundamental studies of quantum mechanics, but also for further applications, such as the detection of gravitational waves [16,17], and quantum memorise [18,19]. However, these quantum effects will be damaged by environmental noises.…”