We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols (for example Ahn et. al, PRA, 65, 042301 (2001)), is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit-flips. We also consider implementation in a solid-state quantum computation architecture and estimate the maximal error rate which could be corrected with current technology.
We study the dynamics of two identical atoms resonantly coupled to a single-mode cavity under practical feedback control, and focus on the detection inefficiency. The entanglement is induced to vanish in finite time by the inefficiency of detection. Counterintuitively, the asymptotic entanglement and quantum discord can be increased by the inefficiency of detection. The noise of detection triggers control field to create entanglement and discord when no photon are emitted from the atoms. Furthermore, sudden change happens to the dynamics of entanglement.
Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find out the highest achievable precision with given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter we show that the sequential feedback scheme has a 3-fold improvement over the parall…
We develop a general framework to describe interferometric coherent feedback loops and prove that, under any such scheme, the steady-state squeezing of a bosonic mode subject to a rotating wave coupling with a white noise environment and to any quadratic Hamiltonian must abide by a noise-dependent bound that reduces to the 3dB limit at zero temperature. Such a finding is contrasted, at fixed dynamical parameters, with the performance of homodyne continuous monitoring of the output modes. The latter allows one to beat coherent feedback and the 3dB limit under certain dynamical conditions, which…
The protection of quantum states is challenging for non-orthogonal states especially in the presence of noises. The recent research breakthrough shows that this difficulty can be overcome by feedback control with weak measurements. However, the state-protection schemes proposed recently work optimally only for special quantum states. In this paper, {by applying different weak measurements, we extend the idea of the state-protection scheme to protect general states.} We calculate numerically the optimal parameters and discuss the performance of the scheme. Comparison between this extended schem…
We model the cooling of open optical and optomechanical resonators via optical feedback in the Linear Quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process non-commuting output field quadratures simultaneously without loss of fidelity, and may provide im…
Utilizing the continuous frequency mode quantization scheme, we study from first principle the efficiency of a feedback scheme that can generate maximally entangled states of two atoms in an optical cavity through their interactions with a single input photon. The spectral function of the photon emitted from the cavity, which will be used as the input of the next round in the feedback process, is obtained analytically. We find that the spectral function of the photon is modified in each round and deviates from the original one. The efficiency of the feedback scheme consequently deteriorates gr…
A feedback scheme for preparation of photon number states in a microwave cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity field provides information on its actual state. The control consists in injecting into the cavity mode a microwave pulse adjusted to maximize the population of the desired target photon number. In the ideal case (perfect cavity and measures), we present the feedback scheme and its detailed convergence proof through stochastic Lyapunov techniques based on super-martingales and other probabilistic arguments. Quantum Monte-Carlo simulations performed …
We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the Linear Quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the cohere…
We perform a comprehensive study of stability of a pumped atom laser in the presence of pumping, damping and outcoupling. We also introduce a realistic feedback scheme to improve stability by extracting energy from the condensate and determine its effectiveness. We find that while the feedback scheme is highly efficient in reducing condensate fluctuations, it usually does not alter the stability class of a particular set of pumping, damping and outcoupling parameters.
We propose a scheme for performing quantum simulations with atoms in cavities based on a photon detection feedback loop that requires only linear optical elements. Atoms can be stored individually without the need of directly interacting with one another. The scheme is able to simulate any time evolution that can be written as a sum of two-qubit Hamiltonians, .e.g., any next neighbor interaction on a lattice. It can also be made robust against photon losses.
We propose a simple feedback-control scheme for adiabatic quantum computation with superconducting flux qubits. The proposed method makes use of existing on-chip hardware to monitor the ground-state curvature, which is then used to control the computation speed to maximize the success probability. We show that this scheme can provide a polynomial speed-up in performance and that it is possible to choose a suitable set of feedback-control parameters for an arbitrary problem Hamiltonian.
Enviroment - caused dissipation disrupts the hamiltonian evolution of all quantum systems not fully isolated from any bath. We propose and examine a feedback-control scheme to eliminate such dissipation, by tracking the free hamiltonian evolution. We determine a driving-field that maximizes the projection of the actual molecular system onto the freely propagated one. The evolution of a model two level system in a dephasing bath is followed, and the driving field that overcomes the decoherence is calculated. An implementation of the scheme in the laboratory using feedback control is suggested.
We present a detailed study to show the possibility of approaching the quantum ground-state of a hybrid optomechanical quantum device formed by a Bose-Einstein condensate (BEC) confined inside a high-finesse optical cavity with an oscillatory end mirror. Cooling is achieved using two experimentally realizable schemes: back-action cooling and cold damping quantum feedback cooling. In both the schemes, we found that increasing the two body atom-atom interaction brings the mechanical oscillator to its quantum ground state. It has been observed that back-action cooling is more effective in the goo…
Circuit QED is a promising solid-state quantum computing architecture. It also has excellent potential as a platform for quantum control -- especially quantum feedback control -- experiments. However, the current scheme for measurement in circuit QED is low efficiency and has low signal-to-noise ratio for single shot measurements. The low quality of this measurement makes the implementation of feedback difficult, and here we propose two schemes for measurement in circuit QED architectures that can significantly improve signal-to-noise, and potentially achieve quantum limited measurement. Such …
We introduce an efficient, quasideterministic scheme to generate maximally entangled states of two atomic ensembles. The scheme is based on quantum nondemolition measurements of total atomic populations and on adiabatic quantum feedback conditioned by the measurements outputs. The high efficiency of the scheme is tested and confirmed numerically for ideal photodetection as well as in the presence of losses.
Circuit cavity quantum electrodynamics (QED) is proving to be a powerful platform to implement quantum feedback control schemes due to the ability to control superconducting qubits and microwaves in a circuit. Here, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit $W$ state in the superconducting circuit QED system. The control scheme is based on continuous joint Zeno measurements of multiple qubits in a dispersive regime, which enables us not only to infer the state of the qubits for further information processin…
We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and in particular a single-electron transistor. We provide a general scheme to stabilize pure states in the quantum system and employ an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the soluti…
We determine a general upper bound for the steady-state entanglement achievable by continuous feedback for systems of any number of bosonic degrees of freedom. We apply such a bound to the specific case of parametric interactions - the most common practical way to generate entanglement in quantum optics - and single out optimal feedback strategies that achieve the maximal entanglement. We also consider the case of feedback schemes entirely restricted to local operations and compare their performance to the optimal, generally nonlocal, schemes.
