Measurement-based Feedback Control Research Articles

State initialization of a hot spin qubit in a double quantum dot by measurement-based quantum feedback control

A measurement-based quantum feedback protocol is developed for spin-state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting cavity. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be preset. Being able to preset the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts toward scaling up the number of qubits in quantum computers.

Comparison of quantum state protection against decoherence via weak measurement, a survey

One of the crucial tasks in quantum systems is to reduce the effects of decoherence due to the unavoidable interactions between a system and its environment. Many protection schemes have been proposed recently, among them the weak measurement quantum measurement reversal (WMQMR), weak measurement-based quantum feedback control (QFBC) and quantum feedforward control (QFFC) are reviewed in this paper. By considering weak measurement, the aim is to find a balance between information gain and disturbance of the system caused by the measurement. We classify different types of measurement and give the definition of noise sources and their effects on the state of the system. Finally, we compare and analyze the performance of the discussed protection schemes for different noise sources by numerical simulations.

Strategy of state transfer for open quantum systems by no-knowledge feedback control: Via reverse engineering

It has long been interest to control the transfer of population between specified quantum states and protect the coherence of the system at the same time. In this paper, we investigate a scheme to improve the strategy of state transfer for open quantum systems using no-knowledge measurement-based feedback control and reverse engineering. In order to ensure that the system can process information effectively, we first design the control pulse in advance from the perspective of population and coherence and then verify it through numerical simulations. The research results show that, based on the designed control pulse, we can indeed drive the system from any initial state to the desired target state, and the coherence of the system can be effectively protected during the state transition.

Robust control of quantum systems by quantum systems

Quantum systems can be controlled by other quantum systems in a reversible way, without any information leaking to the outside of the system-controller compound. Such coherent quantum control is deterministic, is less noisy than measurement-based feedback control, and has potential applications in a variety of quantum technologies, including quantum computation, quantum communication and quantum metrology. Here we introduce a coherent feedback protocol, consisting of a sequence of identical interactions with controlling quantum systems, that steers a quantum system from an arbitrary initial state towards a target state. We determine the broad class of such coherent feedback channels that achieve convergence to the target state, and then stabilise as well as protect it against noise. Our results imply that also weak system-controller interactions can counter noise if they occur with suitably high frequency. We provide an example of a control scheme that does not require knowledge of the target state encoded in the controllers, which could be the result of a quantum computation. It thus provides a mechanism for autonomous, purely quantum closed-loop control.

Optimal measurement-based feedback control on noisy quantum systems

A quantum system will both lose and gain excitation through interaction with the environment in a non-zero temperature environment. In this paper, we investigate how a feedback control scheme utilizing weak measurement stabilizes a quantum state which suffers from an environment with finite temperature. Our study has shown that compared with the conventional ‘do-nothing’ and ‘Helstrom’ schemes, this method is much more useful for suppressing decoherence in a generalized amplitude damping (GAD) noise channel. Additionally, for a quantum state, we give the expression of optimum measurement strength, correction angle and the general analytic expression for the optimum fidelity. Additionally, the maximum value of the fidelity improvement can be achieved by controlling the measurement strength, correction angle and the special initial state of the system. More importantly, we find that this approach can not only be helpful for suppressing decoherence in the GAD channel, but can also play a significant role in the amplitude damping noise channel. This phenomenon reveals that in non-zero temperature noise channels, the feedback control scheme via weak measurement can be better for stabilizing a quantum state.

Sub-Kelvin Feedback Cooling and Heating Dynamics of an Optically Levitated Librator.

Rotational optomechanics strives to gain quantum control over mechanical rotors by harnessing the interaction of light and matter. We optically trap a dielectric nanodumbbell in a linearly polarized laser field, where the dumbbell represents a nanomechanical librator. Using measurement-based parametric feedback control in high vacuum, we cool this librator from room temperature to 240mK and investigate its heating dynamics when released from feedback. We exclude collisions with residual gas molecules as well as classical laser noise as sources of heating. Our findings indicate that we observe the torque fluctuations arising from the zero-point fluctuations of the electromagnetic field.

Quantum control of a nanoparticle optically levitated in cryogenic free space.

Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1-3. Quantum control of mechanical motion has been achieved by engineering the radiation-pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4-7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10-15grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.

Measurement-feedback control of the chiral photon emission from an atom chain into a nanofiber

We theoretically investigate measurement-based feedback control of a laser-driven one-dimensional atomic chain interfaced with a nanofiber. The interfacing leads to all-to-all interactions among the atomic emitters and induces chirality (i.e., the directional emission of photons into a preferred guided mode of the nanofiber). In the setting we consider, the measurement of guided light—conducted either by photon counting or through homodyne detection of the photocurrent quadratures—is fed back into the system through modulation of the driving laser field. We investigate how this feedback scheme allows control of the statistics of the photon counting and the quadratures of the light, as well as the many-body state of the atom chain. In particular, we identify regimes where both the photon counting rate and its fluctuations are dramatically enhanced. Moreover, we find that the action of homodyne detection feedback allows the alteration of the stationary state of the chain from a pure, dimer state, to a fully mixed one. Our results provide insights on how to control and engineer dynamics in light–matter networks realizable with state-of-the-art experimental setups.

Improving parameter precision of estimation by no-knowledge feedback control

We investigate a scheme to improve the precision of parameter estimation using no-knowledge measurement-based feedback control. The scheme shows that combination of no-knowledge measurement-based feedback control and quantum weak measurement is the optimal way to suppress decoherence. Our results indicate that compared with knowledge quantum feedback control, under the same weak measurement condition, the precision of parameter estimation can be improved more effectively with no knowledge quantum feedback control. Further, based on numerical simulation, we find that the feedback operator is chosen as [Formula: see text] (or both [Formula: see text] and [Formula: see text], which can protect quantum Fisher information (QFI) for a long time.

Simultaneous Feedback and Feedforward Control and Its Application to Realize a Random Walk on the Bloch Sphere in an Xmon-Superconducting-Qubit System

Measurement-based feedback control is central in quantum computing and precise quantum control. Here we realize a fast and flexible field-programmable-gate-array-based feedback control in a superconducting Xmon qubit system. The latency of room-temperature electronics is custom optimized to be as short as 140 ns. Projective measurement of a signal qubit produces a feedback tag to actuate a conditional pulse gate to the qubit. In a feed-forward process, the measurement-based feedback tag is brought to a different target qubit for a conditional control. In a two-qubit experiment, the feedback and feed-forward controls are simultaneously actuated in consecutive steps. A quantum number is then generated by the signal qubit, and a random walk of the target qubit is correspondingly triggered and realized on the Bloch sphere. Our experiment provides a conceptually simple and intuitive benchmark for the feedback control in a multi-qubit system. The feedback system can be further scaled up for more complex feedback control experiments.

Gradual partial-collapse theory for ideal nondemolition longitudinal readout of qubits in circuit QED

The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit-cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. This scheme becomes problematic in the case of strong coupling and/or strong measurement drive, owing to the so-called Purcell effect. A recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity, and {\it ideal QND} readout of qubit state. The aim of the present work is twofold: (i) In parallel to what has been done in the past years for the dispersive readout, we carry out the gradual partial-collapse theory for this recent scheme, in terms of both the quantum trajectory equation and quantum Bayesian approaches. The partial-collapse weak measurement theory is useful for such as the measurement-based feedback control and other quantum applications. (ii) In the physical aspect, we construct the joint qubit-plus-cavity entangled state under continuous measurement and present a comprehensive analysis for the quantum efficiency,qubit-state purity, and signal-to-noise ratio in the output currents. The combination of the joint state and the quantum Bayesian rule provides a generalized scheme of cavity reset associated with the longitudinal coupling, which can restore the qubit to a quantum pure state from entanglement with the cavity states, and thus benefits the successive partial-collapse measurements after qubit rotations.

Quantum estimation of detection efficiency with no-knowledge quantum feedback**Project supported by the National Natural Science Foundation of China (Grant No. 11747008) and the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2016GXNSFBA380227).

We investigate that no-knowledge measurement-based feedback control is utilized to obtain the estimation precision of the detection efficiency. We show that no-knowledge measurement is the optimal way to estimate the detection efficiency. The higher precision can be achieved for the lower or larger detection efficiency. It is found that no-knowledge feedback can be used to cancel decoherence. No-knowledge feedback with a high detection efficiency can perform well in estimating frequency and detection efficiency parameters simultaneously; simultaneous estimation is better than independent estimation given by the same probes.

Enhancing quantum control by bootstrapping a quantum processor of 12 qubits

Accurate and efficient control of quantum systems is one of the central challenges for quantum information processing. Current state-of-the-art experiments rarely go beyond 10 qubits and in most cases demonstrate only limited control. Here we demonstrate control of a 12-qubit system, and show that the system can be employed as a quantum processor to optimize its own control sequence by using measurement-based feedback control (MQFC). The final product is a control sequence for a complex 12-qubit task: preparation of a 12-coherent state. The control sequence is about 10% more accurate than the one generated by the standard (classical) technique, showing that MQFC can correct for unknown imperfections. Apart from demonstrating a high level of control over a relatively large system, our results show that even at the 12-qubit level, a quantum processor can be a useful lab instrument. As an extension of our work, we propose a method for combining the MQFC technique with a twirling protocol, to optimize the control sequence that produces a desired Clifford gate.

Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

Quantum correlations between imprecision and back-action are a hallmark of continuous linear measurements. Here we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nano-optomechanical system. Back-action imparted by the meter laser, due to radiation pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement, and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e. feedback that suppresses measurement back-action, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to feedback back-action arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits of measurement-based feedback as a tool to manipulate quantum correlations.

Automated Direct Nucleation Control in Continuous Mixed Suspension Mixed Product Removal Cooling Crystallization

Automated direct nucleation control (ADNC) is a focused beam reflectance measurement-based feedback control approach that is used to produce large and uniform crystals in batch cooling crystallization. In this work, this feedback control approach is modified to work for continuous cooling crystallization processes, including single-stage and multistage mixed suspension mixed product removal crystallizers. The proposed continuous ADNC approach is observed to provide quick startup, high quality control of crystal size distribution, as well as automated and effective disturbance suppression.

Deterministic generation of symmetric multi‐qubit Dicke states: an application of quantum feedback control

In this study, the authors explore how to deterministically generate symmetric multi-qubit Dicke states such as symmetric W-states, from arbitrary initial states in a cavity quantum electrodynamics (QED) system with the aid of measurement-based quantum feedback control. The concrete implementation procedures of the feedback strategy, which is constructed in the form of only two constant modes, are presented in detail. In addition, the feasibility of the control scheme in preparing symmetric multi-qubit Dicke states is explicitly demonstrated by theoretical studies and numerical simulations.

Continuous joint measurement and entanglement of qubits in remote cavities

We present a first-principles theoretical analysis of the entanglement of two superconducting qubits in spatially separated microwave cavities by a sequential (cascaded) probe of the two cavities with a coherent mode, that provides a full characterization of both the continuous measurement induced dynamics and the entanglement generation. We use the SLH formalism to derive the full quantum master equation for the coupled qubits and cavities system, within the rotating wave and dispersive approximations, and conditioned equations for the cavity fields. We then develop effective stochastic master equations for the dynamics of the qubit system in both a polaronic reference frame and a reduced representation within the laboratory frame. We compare simulations with and analyze tradeoffs between these two representations, including the onset of a non-Markovian regime for simulations in the reduced representation. We provide conditions for ensuring persistence of entanglement and show that using shaped pulses enables these conditions to be met at all times under general experimental conditions. The resulting entanglement is shown to be robust with respect to measurement imperfections and loss channels. We also study the effects of qubit driving and relaxation dynamics during a weak measurement, as a prelude to modeling measurement-based feedback control in this cascaded system.

Quantum State Preparation and Protection by Measurement-Based Feedback Control Against Decoherence

We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered: phase damping and generalized amplitude damping. Based on quantum trajectory theory, we obtain an extended master equation for the dynamics of the reduced system in the presence of feedback control. For a qubit system we analytically solve this master equation and obtain the solution of the state vector dynamics. Then we propose an effective feedback control scheme for preparing an arbitrary quantum pure state. We also study how to protect two nonorthogonal states effectively, and find that projective measurement with unbiased basis is not optimal for this task, while weak measurement with biased basis could realize the best protection of two nonorthogonal states. Furthermore, the inefficiencies in the feedback process are also discussed.

Quantum feedback control of linear stochastic systems with feedback-loop time delays

In a quantum feedback control loop, one is often confronted with time delays that mainly originated from the transition delay of signals, which may cause the quantum feedback control system unstable. The purpose of this paper is to deal with a problem of quantum measurement-based feedback control subject to feedback-loop time delays. A quantum version of delay-independent stability criterion as well as an upper bound on a cost function is derived based on quantum Itō rules. We propose one numerical procedure for quantum feedback controller designs, which is then illustrated by an example.

Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information

To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.