arXiv subjects

Daoyi Dong

Publications and source records attributed to Daoyi Dong.

At least 145 records · Page 8Linked to original sources

arXiv2016

Learning robust control for generating universal quantum gates

Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results show that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gates.

quant-ph↗

arXiv2016

Robust manipulation of superconducting qubits in the presence of fluctuations

Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, the existence of defects, fluctuations, and inaccuracies is unavoidable for practical superconducting quantum circuits. In this paper, a sampling-based learning control (SLC) method is used to guide the design of control fields for manipulating superconducting quantum systems. Numerical results for one-qubit systems and coupled two-qubit systems show that the "smart" fields learned using the SLC method can achieve robust manipulation of superconducting qubits, even in the presence of large fluctuations and inaccuracies.

quant-ph↗

arXiv2016

Performance Analysis and Coherent Guaranteed Cost Control for Uncertain Quantum Systems Using Small Gain and Popov Methods

This paper extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear quantum system and is subject to quadratic perturbations in the system Hamiltonian. Based on these two methods, coherent guaranteed cost controllers are designed for a given quantum system to achieve improved control performance. An illustrative example also shows that the quantum Popov approach can obtain less conservative results than the quantum small gain approach for the same uncertain quantum system.

eess.SY↗

arXiv2016

Exact Analysis of the Response of Quantum Systems to Two Photons Using a QSDE Approach

We introduce the quantum stochastic differential equation (QSDE) approach to exactly analyze of the response of quantum systems to a continuous-mode two-photon input. The QSDE description of the two-photon process allows us to integrate the input-output analysis with the quantum network theory, and so the analytical computability of the output state of a general quantum system can be addressed within this framework. We show that the time-domain two-photon output states can be exactly calculated for a large class of quantum systems including passive linear networks, optomechanical oscillators and two-level emitter in waveguide systems. In particular, we propose to utilize the results for the exact simulation of the stimulated emission as well as the study of the scattering of two-mode photon wave packets.

quant-ph↗

arXiv2016

Realization of mutually unbiased bases for a qubit with only one wave plate: Theory and experiment

We consider the problem of implementing mutually unbiased bases (MUB) for a polarization qubit with only one wave plate, the minimum number of wave plates. We show that one wave plate is sufficient to realize two MUB as long as its phase shift (modulo $360^\circ$) ranges between $45^\circ$ and $315^\circ$. {It can realize} three MUB (a complete set of MUB for a qubit) if the phase shift of the wave plate is within $[111.5^\circ, 141.7^\circ]$ or its symmetric range with respect to 180$^\circ$. The systematic error of the realized MUB using a third-wave plate (TWP) with $120^\circ$ phase is calculated to be a half of that using the combination of a quarter-wave plate (QWP) and a half-wave plate (HWP). As experimental applications, TWPs are used in single-qubit and two-qubit quantum state tomography experiments and the results show a systematic error reduction by $50\%$. This technique not only saves one wave plate but also reduces the systematic error, which can be applied to quantum state tomography and other applications involving MUB. The proposed TWP may become a useful instrument in optical experiments, replacing multiple elements like QWP and HWP.

quant-ph↗

arXiv2016

Fault Tolerant Filtering and Fault Detection for Quantum Systems Driven By Fields in Single Photon States

The purpose of this paper is to solve a fault tolerant filtering and fault detection problem for a class of open quantum systems driven by a continuous-mode bosonic input field in single photon states when the systems are subject to stochastic faults. Optimal estimates of both the system observables and the fault process are simultaneously calculated and characterized by a set of coupled recursive quantum stochastic differential equations.

quant-ph↗

arXiv2015

Fault Tolerant Quantum Filtering and Fault Detection for Quantum Systems

This paper aims to determine the fault tolerant quantum filter and fault detection equation for a class of open quantum systems coupled to a laser field that is subject to stochastic faults. In order to analyze this class of open quantum systems, we propose a quantum-classical Bayesian inference method based on the definition of a so-called quantum-classical conditional expectation. It is shown that the proposed Bayesian inference approach provides a convenient tool to simultaneously derive the fault tolerant quantum filter and the fault detection equation for this class of open quantum systems. An example of two-level open quantum systems subject to Poisson-type faults is presented to illustrate the proposed method. These results have the potential to lead to a new fault tolerant control theory for quantum systems.

math-ph↗

arXiv2015

Rapid Lyapunov control of finite-dimensional quantum systems

Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang-bang Lyapunov control can speed up the control process, but cannot guarantee convergence to a target state. This paper proposes two classes of new Lyapunov control methods that can achieve rapidly convergent control for quantum states. One class is switching Lyapunov control where the control law is designed by switching between bang-bang Lyapunov control and standard Lyapunov control. The other class is approximate bang-bang Lyapunov control where we propose two special control functions which are continuously differentiable and yet have a bang-bang type property. Related stability results are given and a construction method for the degrees of freedom in the Lyapunov function is presented to guarantee rapid convergence to a target eigenstate being isolated in the invariant set. Several numerical examples demonstrate that the proposed methods can achieve improved performance for rapid state control of quantum systems.

quant-ph↗

arXiv2015

Recursively Adaptive Quantum State Tomography: Theory and Two-qubit Experiment

Adaptive techniques have important potential for wide applications in enhancing precision of quantum parameter estimation. We present a recursively adaptive quantum state tomography (RAQST) protocol for finite dimensional quantum systems and experimentally implement the adaptive tomography protocol on two-qubit systems. In this RAQST protocol, an adaptive measurement strategy and a recursive linear regression estimation algorithm are performed. Numerical results show that our RAQST protocol can outperform the tomography protocols using mutually unbiased bases (MUB) and the two-stage MUB adaptive strategy even with the simplest product measurements. When nonlocal measurements are available, our RAQST can beat the Gill-Massar bound for a wide range of quantum states with a modest number of copies. We use only the simplest product measurements to implement two-qubit tomography experiments. In the experiments, we use error-compensation techniques to tackle systematic error due to misalignments and imperfection of wave plates, and achieve about 100-fold reduction of the systematic error. The experimental results demonstrate that the improvement of RAQST over nonadaptive tomography is significant for states with a high level of purity. Our results also show that this recursively adaptive tomography method is particularly effective for the reconstruction of maximally entangled states, which are important resources in quantum information.

quant-ph↗

arXiv2015

Coherent Robust H-Infinity Control of Uncertain Linear Quantum Stochastic Systems

This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H-infinity controller so that the closed loop system is robustly stable and achieves a prescribed level of disturbance attenuation with all the admissible uncertainties. An illustrative example shows that for the given system, the method presented in this paper has improved performance over the existing quantum H-infinity control results without considering uncertainty.

eess.SY↗

arXiv2015

Guaranteed Cost Dynamic Coherent Control for Uncertain Linear Quantum Systems

This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved control performance, we propose two methods to design a coherent controller for the system. One is to formulate a static quantum controller by adding a controller Hamiltonian to the given system, and the other is to build a dynamic quantum controller which is directly coupled to the given system. Both controller design methods are given in terms of LMIs and a non-convex equality. Hence, a rank constrained LMI method is used as a numerical procedure. An illustrative example is given to demonstrate the proposed methods and also to make a performance comparison with different controller design methods. Results show that for the same uncertain quantum system, the dynamic quantum controller can offer an improvement in performance over the static quantum controller.

eess.SY↗

arXiv2015

Sampling-based Learning Control for Quantum Systems with Uncertainties

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with uncertainties. The SLC method includes two steps of "training" and "testing". In the training step, an augmented system is constructed using artificial samples generated by sampling uncertainty parameters according to a given distribution. A gradient flow based learning algorithm is developed to find the control for the augmented system. In the process of testing, a number of additional samples are tested to evaluate the control performance where these samples are obtained through sampling the uncertainty parameters according to a possible distribution. The SLC method is applied to three significant examples of quantum robust control including state preparation in a three-level quantum system, robust entanglement generation in a two-qubit superconducting circuit and quantum entanglement control in a two-atom system interacting with a quantized field in a cavity. Numerical results demonstrate the effectiveness of the SLC approach even when uncertainties are quite large, and show its potential for robust control design of quantum systems.

quant-ph↗

arXiv2015

Reaching a Quantum Consensus: Master Equations that Generate Symmetrization and Synchronization

In this paper, we propose and study a master-equation based approach to drive a quantum network with $n$ qubits to a consensus (symmetric) state introduced by Mazzarella et al. The state evolution of the quantum network is described by a Lindblad master equation with the Lindblad terms generated by continuous-time swapping operators, which also introduce an underlying interaction graph. We establish a graphical method that bridges the proposed quantum consensus scheme and classical consensus dynamics by studying an induced graph (with $2^{2n}$ nodes) of the quantum interaction graph (with $n$ qubits). A fundamental connection is then shown that quantum consensus over the quantum graph is equivalent to componentwise classical consensus over the induced graph, which allows various existing works on classical consensus to be applicable to the quantum setting. Some basic scaling and structural properties of the quantum induced graph are established via combinatorial analysis. Necessary and sufficient conditions for exponential and asymptotic quantum consensus are obtained, respectively, for switching quantum interaction graphs. As a quantum analogue of classical synchronization of coupled oscillators, quantum synchronization conditions are also presented, in which the reduced states of all qubits tend to a common trajectory.

quant-ph↗

arXiv2014

Real-time Information, Uncertainty and Quantum Feedback Control

Feedback is the core concept in cybernetics and its effective use has made great success in but not limited to the fields of engineering, biology, and computer science. When feedback is used to quantum systems, two major types of feedback control protocols including coherent feedback control (CFC) and measurement-based feedback control (MFC) have been developed. In this paper, we compare the two types of quantum feedback control protocols by focusing on the real-time information used in the feedback loop and the capability in dealing with parameter uncertainty. An equivalent relationship is established between quantum CFC and non-selective quantum MFC in the form of operator-sum representation. Using several examples of quantum feedback control, we show that quantum MFC can theoretically achieve better performance than quantum CFC in stabilizing a quantum state and dealing with Hamiltonian parameter uncertainty. The results enrich understanding of the relative advantages between quantum MFC and quantum CFC, and can provide useful information in choosing suitable feedback protocols for quantum systems.

quant-ph↗

arXiv2014

Performance Analysis and Coherent Guaranteed Cost Control for Uncertain Quantum Systems

This paper presents several results on performance analysis for a class of uncertain linear quantum systems subject to either quadratic or non-quadratic perturbations in the system Hamiltonian. Also, coherent guaranteed cost controllers are designed for the uncertain quantum systems to achieve improved control performance. The coherent controller is realized by adding a control Hamiltonian to the quantum system and its performance is demonstrated by an example.

quant-ph↗

arXiv2013

Quantum Ensemble Classification: A Sampling-based Learning Control Approach

Quantum ensemble classification has significant applications in discrimination of atoms (or molecules), separation of isotopic molecules and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast quantum ensemble classification as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). Firstly a new discrimination method is proposed for two similar quantum systems. Then an SLC method is presented for quantum ensemble classification. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

quant-ph↗

arXiv2013

Quantum State Tomography via Linear Regression Estimation

A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. The asymptotic mean squared error (MSE) bound of the estimate can be given analytically, which can guide one to choose optimal measurement sets. The LRE is asymptotically optimal in the sense that the MSE may achieve the Cramér-Rao bound asymptotically. The computational complexity of LRE is O(d^4), where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography.

quant-ph↗

arXiv2013

Sampling-based Learning Control for Quantum Systems with Hamiltonian Uncertainties

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with Hamiltonian uncertainties. The SLC method includes two steps of "training" and "testing and evaluation". In the training step, an augmented system is constructed by sampling uncertainties according to possible distributions of uncertainty parameters. A gradient flow based learning and optimization algorithm is adopted to find the control for the augmented system. In the process of testing and evaluation, a number of samples obtained through sampling the uncertainties are tested to evaluate the control performance. Numerical results demonstrate the success of the SLC approach. The SLC method has potential applications for robust control design of quantum systems.

eess.SY↗