Bang-bang control suppression of amplitude damping in a three-level atom

For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems, with the help of concept in quantum system control, one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state. Therefore, the quantum state trajectory tracking problem becomes a steering one. State steering control law of the system transformed is designed by means of the Lyapunov stability theorem. Finally, numerical simulation experiments are given for a five-level energy quantum system. The comparison analysis of original system's trajectory tracking with other method illustrates the advantage in control time of the method proposed. In recent years, state preparation and steering problem have been extensively studied [13] due to their great important applications in quantum teleportation [4], quantum computation and quantum information [5]. Quantum trajectory tracking is of equal importance as quantum state steering. It requires controlled state to be able to follow a time-variant target state, which is more complicated than the control of state steering. On the other hand, the convergence of quantum tracking is as much important as its control law design. The probability of state in a quantum system makes a stable control not enough any more. The asymptotic convergence of control strategy in such a case is needed to make sure that the experiments are practicable. Therefore the convergence of the control of quantum system directly determines whether a proper control law is designed. At the same time the condition of convergence can provide the methods and ways to derive an effective control law. Especially in quantum systems, the complexity of controlled system model, various characteristics of different quantum states and the probability of controlled variables lead to great difficulties in state transferring. Furthermore, non-autonomic system appears in tracking control, all of which show many difficulties in a quantum system's trajectory tracking control.In [6], with the help of some concepts in system control, we studied trajectory tracking of quantum state: introducing an error state e(t) by defining subtraction between target state ˆ( ) f t  and system state ˆ( ) t  . We changed the tracking

Section: Resultsmentioning

confidence: 84%

Trajectory tracking control of quantum systems

Cong

Liu

2012

“…It can be seen that past quantum control studies were mostly in the areas of physics and chemistry, but in recent years research from engineering fields has grown very quickly. Moreover, several monographs have been published on quantum control with authors coming from chemistry, quantum optics and control theory [32][33][34][35][36][37]. In this review, we aim to give a general review over the fundamental problems and theory from the viewpoint of system control.…”

mentioning

confidence: 99%

Control problems in quantum systems

Zhang

et al. 2012

Self Cite

The past decade or two has witnessed tremendous progress in theory and practice of quantum control technologies. Bridging different scientific disciplines ranging from fundamental particle physics to nanotechnology, the goal of quantum control has been to develop effective and efficient tools for common analysis and design, but more importantly would pave the way for future technological applications. This article briefly reviews basic quantum control theory from the perspective of modeling, analysis and design, as well as considers future research directions. quantum control, control theory, quantum physics Citation: Wu R B, Zhang J, Li C W, et al. Control problems in quantum systems. Chin Sci Bull, 2012Bull, , 57: 2194Bull, -2199Bull, , doi: 10.1007 Quantum control refers to the design of control strategies in systems that obey the principles of quantum mechanics, e.g. microscopic systems with few atoms or photons that were addressed early in the lecture "Plenty of Room at the Bottom" given by Richard Feynman in 1959 [1]. This dream has been pursued since 1960s right after the invention of lasers, which illuminated the hope to coherently control chemical reaction processes, but it was not until the end of 20th century when a burst of successes occurred in controlling ultrafast quantum dynamics. Nowadays, quantum control protocols are being introduced to more fields such as quantum information processing [2] and nanomaterials and nanodevices [3].The inherent power afforded quantum control results from the unique nonclassical features of quantum mechanics. Essentially, orthogonal eigenstates of a quantum observable (corresponding classically identifiable states) can form superpositions and thereby span a much larger space of quantum states available for coherent manipulation; quantum tunneling allows crossing of energy barriers without as much work as in classical mechanics, thus potentially improve sensitivity and controllability. However, there is no free lunch *Corresponding author (email: rbwu@tsinghua.edu.cn) on the other side; these advantages can only be exploited under extreme spatial (atomic or subatomic) and temporal (femtosecond and attosecond) physical scales. To realize the power of quantum control, vulnerable coherence and entanglement in quantum states need to be protected and measured before being destroyed by intermediate interacting environments. The earliest quantum control studies from the 1960s to the 1980s focused on (macroscopic) quantum ensembles in plasmas and laser devices, nuclear accelerators, and nuclear power plants [4] (mostly in former Soviet Union), in which the systems were modeled as quantum harmonic oscillators, which have little difference with those from classical systems [5, 6]. In the 1980s, Tarn's group completed a series of studies on general (linear or nonlinear) quantum systems in regard to modeling [7], controllability [8], invertibility [9], and quantum nondemolition filter problems [10]. In Europe, Belavkin's investigations [11][12][13] on the optimal estimat...

“…To protect qubits in quantum registers, dynamical decoupling (DD) methods were introduced to suppress decoherence by isolating the qubit from its environment [2]. During recent years, both theory and experimental progresses have been made to demonstrate the power of various DD sequences in preserving quantum states and generating coherent operations [3][4][5][6][7][8][9].General DD methods employ sequence of discrete pulses to eliminate system-bath coupling. On the other hand, certain couplings need to be switched on for a finite time in order to perform quantum control operations.…”

mentioning

confidence: 99%

Available control in dynamical decoupled quantum systems

Pan

Cui

2012

Dynamical decoupling (DD) eliminates qubit-bath coupling by applying a sequence of instantaneous pulses. While qubit-bath couplings generally lead to qubit relaxation and dephasing, qubit-qubit couplings are often used to manipulate or control quantum states. We investigate the available control operations in two DD schemes, named periodic DD (PDD) and Uhrig DD (UDD), to see whether universal quantum computation can be realized in these decoupled systems. We find that universal control is possible using Heisenberg interaction in both periodically decoupled system and Uhrig decoupled system, and the available control operations under two kinds of DD sequences obey the same commutation relation. In the UDD case, we also derive a rough bound for control errors. A quantum bit, commonly represented by a two-level quantum system, is constantly interacting with its surrounding environment. However, the coupling between qubit and environment is detrimental to quantum coherence, which is the crucial resource enabling quantum computation [1]. To protect qubits in quantum registers, dynamical decoupling (DD) methods were introduced to suppress decoherence by isolating the qubit from its environment [2]. During recent years, both theory and experimental progresses have been made to demonstrate the power of various DD sequences in preserving quantum states and generating coherent operations [3][4][5][6][7][8][9].General DD methods employ sequence of discrete pulses to eliminate system-bath coupling. On the other hand, certain couplings need to be switched on for a finite time in order to perform quantum control operations. For example, qubit-qubit interaction is required when implementing twoqubit gates. Besides its ability to keep quantum coherent states in quantum registers, to perform high-fidelity quantum computation on DD-proteced qubits without extra resources, dynamical decoupling process should leave the controlled interaction intact. We will see the ability to accomplish this *Corresponding author (email: zrxi@iss.ac.cn) task is closely related to the selected DD sequence used in different decoupling schemes.The first type of DD sequence is provided by nuclear magnetic resonance spectroscopy, known as "periodic DD" (PDD) [2], which averages out the non-unitary evolution of a qubit by applying a predetermined sequence periodically. In a single period, the pulse locations are equidistant, and cycle time T c is required to be as small as possible to ensure the higher-order terms vanish where the propagator during T c can be expanded into a standard Magnus series. Recently, a kind of optimized DD sequence, Uhrig DD (UDD) [3], makes an enormous progress over PDD by canceling qubit-bath coupling order by order with each additional pulse. In UDD, pulse locations are not equidistant but optimized and restriction on T c → 0 is relaxed. It was first discovered for a pure dephasing spin-boson model, and later proved to be applicable to qubit relaxation as well [10].In this paper, we first investigate the possibility of perf...