arXiv subjects

Re-Bing Wu

Publications and source records attributed to Re-Bing Wu.

At least 55 records · Page 3Linked to original sources

arXiv2016

Searching for an optimal control in the presence of saddles on the quantum mechanical observable landscape

The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable expectation value, the landscape has been shown to lack local optima if three assumptions are satisfied: (i) the quantum system is controllable, (ii) the Jacobian of the map from the control field to the evolution operator is full-rank, and (iii) the control field is not constrained. In the case of the observable objective, this favorable analysis shows that the associated landscape also contains saddles, i.e., critical points that are not local suboptimal extrema. In this paper, we investigate whether the presence of these saddles affects the trajectories of gradient-based searches for an optimal control. We show through simulations that both the detailed topology of the control landscape and the parameters of the system Hamiltonian influence whether the searches are attracted to a saddle. For some circumstances with a special initial state and target observable, optimizations may approach a saddle very closely, reducing the efficiency of the gradient algorithm. Encounters with such attractive saddles are found to be quite rare. Neither the presence of a large number of saddles on the control landscape nor a large number of system states increase the likelihood that a search will closely approach a saddle. Even for applications that encounter a saddle, well-designed gradient searches with carefully chosen algorithmic parameters will readily locate optimal controls.

quant-ph↗

arXiv2016

Inherently trap-free convex landscapes for full quantum optimal control

We present a comprehensive analysis of the landscape for full quantum-quantum control associated with the expectation value of an arbitrary observable of one quantum system controlled by another quantum system. It is shown that such full quantum-quantum control landscapes are convex, and hence devoid of local suboptima and saddle points that may exist in landscapes for quantum systems controlled by time-dependent classical fields. There is no controllability requirement for the full quantum-quantum landscape to be trap-free, although the forms of Hamiltonians, the flexibility in choosing initial state of the controller, as well as the control duration, can infulence the reachable optimal value on the landscape. All level sets of the full quantum-quantum landscape are connected convex sets. Finally, we show that the optimal solution of the full quantum-quantum control landscape can be readily determined numerically, which is demonstrated using the Jaynes-Cummings model depicting a two-level atom interacting with a quantized radiation field.

quant-ph↗

arXiv2016

Minimum-Time Selective Control of Homonuclear Spins

In NMR (Nuclear Magnetic Resonance) quantum computation, the selective control of multiple homonuclear spins is usually slow because their resonance frequencies are very close to each other. To quickly implement controls against decoherence effects, this paper presents an efficient numerical algorithm fordesigning minimum-time local transformations in two homonuclear spins. We obtain an accurate minimum-time estimation via geometric analysis on the two-timescale decomposition of the dynamics. Such estimation narrows down the range of search for the minimum-time control with a gradient-type optimization algorithm. Numerical simulations show that this method can remarkably reduce the search efforts, especially when the frequency difference is very small and the control field is high. Its effectiveness is further demonstrated by NMR experiments with two homunuclear carbon spins in a trichloroethylene (C2H1Cl3) sample system.

quant-ph↗

arXiv2015

Non-Markovian coherent feedback control of quantum dot systems

This paper presents a non-Markovian coherent feedback scheme to control single quantum dot systems. The feedback loop is closed via a quantum tunneling junction between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived for describing the dynamics of the quantum dot. To deal with the nonlinear memory function in the Langevin equation, we analyze the Green's function-based root locus, from which we show that the decoherence of the quantum dot can be suppressed via increasing the feedback coupling strength. This effectiveness of decoherence suppression induced by non-Markovian coherent feedback is verified by an example of single quantum dot systems.

quant-ph↗

arXiv2015

Limits of optimal control yields achievable with quantum controllers

In quantum optimal control theory, kinematic bounds are the minimum and maximum values of the control objective achievable for any physically realizable system dynamics. For a given initial state of the system, these bounds depend on the nature and state of the controller. We consider a general situation where the controlled quantum system is coupled to both an external classical field (referred to as a classical controller) and an auxiliary quantum system (referred to as a quantum controller). In this general situation, the kinematic bound is between the classical kinematic bound (CKB), corresponding to the case when only the classical controller is available, and the quantum kinematic bound (QKB), corresponding to the ultimate physical limit of the objective's value. Specifically, when the control objective is the expectation value of a quantum observable (a Hermitian operator on the system's Hilbert space), the QKBs are the minimum and maximum eigenvalues of this operator. We present, both qualitatively and quantitatively, the necessary and sufficient conditions for surpassing the CKB and reaching the QKB, through the use of a quantum controller. The general conditions are illustrated by examples in which the system and controller are initially in thermal states. The obtained results provide a basis for the design of quantum controllers capable of maximizing the control yield and reaching the ultimate physical limit.

quant-ph↗

arXiv2015

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

We propose a method to decouple the nanomechanical resonator in optomechanical systems from the environmental noise by introducing a chaotic coherent feedback loop. We find that the chaotic controller in the feedback loop can modulate the dynamics of the controlled optomechanical system and induce a broadband response of the mechanical mode. This broadband response of the mechanical mode will cut off the coupling between the mechanical mode and the environment and thus suppress the environmental noise of the mechanical modes. As an application, we use the protected optomechanical system to act as a quantum memory. It's shown that the noise-decoupled optomechanical quantum memory is efficient for storing information transferred from coherent or squeezed light.

quant-ph↗

arXiv2015

Experimental exploration over a quantum control landscape through nuclear magnetic resonance

The growing successes in performing quantum control experiments motivated the development of control landscape analysis as a basis to explain these findings.When a quantum system is controlled by an electromagnetic field, the observable as a functional of the control field forms a landscape. Theoretical analyses have revealed many properties of control landscapes, especially regarding their slopes, curvatures, and topologies. A full experimental assessment of the landscape predictions is important for future consideration of controlling quantum phenomena. Nuclear magnetic resonance (NMR) is exploited here as an ideal laboratory setting for quantitative testing of the landscape principles. The experiments are performed on a simple two-level proton system in a H$_2$O-D$_2$O sample. We report a variety of NMR experiments roving over the control landscape based on estimation of the gradient and Hessian, including ascent or descent of the landscape, level set exploration, and an assessment of the theoretical predictions on the structure of the Hessian. The experimental results are fully consistent with the theoretical predictions. The procedures employed in this study provide the basis for future multispin control landscape exploration where additional features are predicted to exist.

quant-ph↗

arXiv2015

Searching for quantum optimal controls under severe constraints

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.

quant-ph↗

arXiv2014

Signal Flows in Non-Markovian Linear Quantum Feedback Networks

Enabled by rapidly developing quantum technologies, it is possible to network quantum systems at a much larger scale in the near future. To deal with non-Markovian dynamics that is prevalent in solid-state devices, we propose a general transfer function based framework for modeling linear quantum networks, in which signal flow graphs are applied to characterize the network topology by flow of quantum signals. We define a noncommutative ring $\mathbb{D}$ and use its elements to construct Hamiltonians, transformations and transfer functions for both active and passive systems. The signal flow graph obtained for direct and indirect coherent quantum feedback systems clearly show the feedback loop via bidirectional signal flows. Importantly, the transfer function from input to output field is derived for non-Markovian quantum systems with colored inputs, from which the Markovian input-output relation can be easily obtained as a limiting case. Moreover, the transfer function possesses a symmetry structure that is analogous to the well-know scattering transformation in \sd picture. Finally, we show that these transfer functions can be integrated to build complex feedback networks via interconnections, serial products and feedback, which may include either direct or indirect coherent feedback loops, and transfer functions between quantum signal nodes can be calculated by the Riegle's matrix gain rule. The theory paves the way for modeling, analyzing and synthesizing non-Markovian linear quantum feedback networks in the frequency-domain.

quant-ph↗

arXiv2014

Quantum feedback: theory, experiments, and applications

The control of individual quantum systems is now a reality in a variety of physical settings. Feedback control is an important class of control methods because of its ability to reduce the effects of noise. In this review we give an introductory overview of the various ways in which feedback may be implemented in quantum systems, the theoretical methods that are currently used to treat it, the experiments in which it has been demonstrated to-date, and its applications. In the last few years there has been rapid experimental progress in the ability to realize quantum measurement and control of mesoscopic systems. We expect that the next few years will see further rapid advances in the precision and sophistication of feedback control protocols realized in the laboratory.

quant-ph↗

arXiv2014

Nonlinear quantum input-output analysis using Volterra series

Quantum input-output theory plays a very important role for analyzing the dynamics of quantum systems, especially large-scale quantum networks. As an extension of the input-output formalism of Gardiner and Collet, we develop a new approach based on the quantum version of the Volterra series which can be used to analyze nonlinear quantum input-output dynamics. By this approach, we can ignore the internal dynamics of the quantum input-output system and represent the system dynamics by a series of kernel functions. This approach has the great advantage of modelling weak-nonlinear quantum networks. In our approach, the number of parameters, represented by the kernel functions, used to describe the input-output response of a weak-nonlinear quantum network, increases linearly with the scale of the quantum network, not exponentially as usual. Additionally, our approach can be used to formulate the quantum network with both nonlinear and nonconservative components, e.g., quantum amplifiers, which cannot be modelled by the existing methods, such as the Hudson-Parthasarathy model and the quantum transfer function model. We apply our general method to several examples, including Kerr cavities, optomechanical transducers, and a particular coherent feedback system with a nonlinear component and a quantum amplifier in the feedback loop. This approach provides a powerful way to the modelling and control of nonlinear quantum networks.

quant-ph↗

arXiv2014

Searching for quantum optimal controls in the presence of singular critical points

Quantum optimal control has enjoyed wide success for a variety of theoretical and experimental objectives. These favorable results have been attributed to advantageous properties of the corresponding control landscapes, which are free from local optima if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is full rank, and (3) the control field is not constrained. This paper explores how gradient searches for globally optimal control fields are affected by deviations from assumption (2). In some quantum control problems, so-called singular critical points, at which the Jacobian is rank-deficient, may exist on the landscape. Using optimal control simulations, we show that search failure is only observed when a singular critical point is also a second-order trap, which occurs if the control problem meets additional conditions involving the system Hamiltonian and/or the control objective. All known second-order traps occur at constant control fields, and we also show that they only affect searches that originate very close to them. As a result, even when such traps exist on the control landscape, they are unlikely to affect well-designed gradient optimizations under realistic searching conditions.

quant-ph↗

arXiv2013

Feedback-induced nonlinearity and superconducting on-chip quantum optics

Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired by the recent progress of quantum feedback experiments, especially those in mesoscopic circuits, we prove that superconducting circuit QED systems, shunted with a coherent feedback loop, can change the dynamics of a superconducting transmission line resonator, i.e., a linear quantum cavity, and lead to strong on-chip nonlinear optical phenomena. We find that bistability can occur under the semiclassical approximation, and photon anti-bunching can be shown in the quantum regime. Our study presents new perspectives for engineering nonlinear quantum dynamics on a chip.

quant-ph↗

arXiv2013

Quantum internet using code division multiple access

A crucial open problem in large-scale quantum networks is how to efficiently transmit quantum data among many pairs of users via a common data-transmission medium. We propose a solution by developing a quantum code division multiple access (q-CDMA) approach in which quantum information is chaotically encoded to spread its spectral content, and then decoded via chaos synchronization to separate different sender-receiver pairs. In comparison to other existing approaches, such as frequency division multiple access (FDMA), the proposed q-CDMA can greatly increase the information rates per channel used, especially for very noisy quantum channels.

quant-ph↗

arXiv2012

Spectral Analysis and Identification of Noises in Quantum Systems

In quantum information processing, knowledge of the noise in the system is crucial for high-precision manipulation and tomography of coherent quantum operations. Existing strategies for identifying this noise require the use of additional quantum devices or control pulses. We present a noise-identification method directly based on the system's non-Markovian response of an ensemble measurement to the noise. The noise spectrum is identified by reversing the response relationship in the frequency domain. For illustration, the method is applied to superconducting charge qubits, but it is equally applicable to any type of qubits. We find that the identification strategy recovers the well-known Fermi's golden rule under the lowest-order perturbation approximation, which corresponds to the Markovian limit when the measurement time is much longer than the noise correlation time. Beyond such approximation, it is possible to further improve the precision at the so-called optimal point by incorporating the transient response data in the non-Markovian regime. This method is verified with experimental data from coherent oscillations in a superconducting charge qubit.

quant-ph↗

arXiv2012

Non-Markovian quantum input-output networks

Quantum input-output response analysis is a useful method for modeling the dynamics of complex quantum networks, such as those for communication or quantum control via cascade connections. Non-Markovian effects have not yet been studied in such networks. Here we extend the Markovian input-output network formalism developed in optical systems to non-Markovian cascaded networks which can be used, e.g., to analyze the input-output response of mesoscopic quantum networks. We use this formalism to explore the behavior of superconducting qubit networks, where we examine the effect of finite cavity bandwidths. We also discuss its application to open- and closed-loop control networks, and show how these networks create effective Hamiltonians for the controlled system.

quant-ph↗

arXiv2012

Quantum Coherent Nonlinear Feedbacks with Applications to Quantum Optics on Chip

In the control of classical mechanical systems, the feedback has been successfully applied to the production of the desired nonlinear dynamics. However, how much this can be done is still an open problem in quantum mechanical systems. This paper proposes a scheme of generating strong nonlinear quantum effects via the recently developed coherent feedback techniques, which can be shown to outperform the measurement-based quantum feedback scheme that can only generate pseudo-nonlinear quantum effects. Such advancement is demonstrated by two application examples in quantum optics on chip. In the first example, we show that the nonlinear Kerr effect can be generated and amplified to be comparable with the linear effect in a transmission line resonator (TLR). In the second example, we show that by tuning the gains of the quantum amplifiers in a TLR coherent feedback network, non-Gaussian "light" (microwave field) can be generated and manipulated via the nonlinear effects which exhibits fully quantum sub-Poisson photoncount statistics and photon antibunching phenomenon. The scheme opens promising applications in demonstrating strong nonlinear quantum optics on chip, which is extremely weak and inflexible in traditional quantum optical devices.

quant-ph↗

arXiv2012

Suppressing nano-scale stick-slip motion by feedback

When a micro cantilever with a nano-scale tip is manipulated on a substrate with atomic-scale roughness, the periodic lateral frictional force and stochastic fluctuations may induce stick-slip motion of the cantilever tip, which greatly decreases the precision of the nano manipulation. This unwanted motion cannot be reduced by open-loop control especially when there exist parameter uncertainties in the system model, and thus needs to introduce feedback control. However, real-time feedback cannot be realized by the existing virtual reality virtual feedback techniques based on the position sensing capacity of the atomic force microscopy (AFM). To solve this problem, we propose a new method to design real-time feedback control based on the force sensing approach to compensate for the disturbances and thus reduce the stick-slip motion of the cantilever tip. Theoretical analysis and numerical simulations show that the controlled motion of the cantilever tip tracks the desired trajectory with much higher precision. Further investigation shows that our proposal is robust under various parameter uncertainties. Our study opens up new perspectives of real-time nano manipulation.

cond-mat.mes-hall↗