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## Quantum control theory and applications: A survey (2010)

Venue: | IET Control Theory & Applications |

Citations: | 31 - 5 self |

### Citations

1196 |
The Principles of Quantum Mechanics
- Dirac
- 1957
(Show Context)
Citation Context ...ing quantum control theory, such as quantum states, quantum measurements and quantum control models. A comprehensive introduction to quantum mechanics can be found in many excellent textbooks such as =-=[83]-=-, [84]. 2.1 Quantum states In quantum mechanics, the state of a closed quantum system can be represented by a unit vector |ψ〉 (this notation is known as the Dirac representation [83] and the state |ψ〉... |

990 |
Quantum Mechanics. Nonrelativistic Theory [in Russian
- Landau, Lifshits
- 2002
(Show Context)
Citation Context ...antum control theory, such as quantum states, quantum measurements and quantum control models. A comprehensive introduction to quantum mechanics can be found in many excellent textbooks such as [83], =-=[84]-=-. 2.1 Quantum states In quantum mechanics, the state of a closed quantum system can be represented by a unit vector |ψ〉 (this notation is known as the Dirac representation [83] and the state |ψ〉 is al... |

511 |
The Theory of Open Quantum Systems.
- Breuer, Petruccione
- 2006
(Show Context)
Citation Context ...th finite dimensional closed quantum systems, the controllability of infinite dimensional quantum systems or open quantum systems (i.e., systems considered interacting with the environment; e.g., see =-=[29]-=-) is more difficult and only a few results have been obtained [21], [26], [30]. For a controllable quantum system, it is desirable to develop a good control strategy to accomplish the required control... |

386 |
Quantum Noise
- Gardiner, Zoller
- 2000
(Show Context)
Citation Context ...vantages over open-loop methods, such as robustness and reliability. For open quantum systems, coupling with uncontrollable environments makes the introduction of noises and uncertainties unavoidable =-=[56]-=-. A requirement for robustness in the presence of uncertainties and noises has been recognized as one of the key aspects in developing practical quantum technologies [7], [57]. A natural solution to t... |

317 | An Introduction to Quantum Stochastic Calculus,
- Parthasarathy
- 1992
(Show Context)
Citation Context ...r quantity w describes the input signals and is assumed to admit the decomposition dw(t) = βw(t)dt+ dw̃(t) (20) where w̃(t) is the noise part of w(t) and βw(t) is a self-adjoint, adapted process (see =-=[95]-=-, [96]). The noise w̃(t) is a vector of self-adjoint quantum noises with Itô table dw̃(t)dw̃T (t) = Fw̃dt (21) where Fw̃ is a positive semidefinite Hermitian matrix (see [95], [96] for details). Equa... |

282 | Quantum Optics
- Scully, Zubairy
- 1997
(Show Context)
Citation Context ...d performance. Quantum feedback control has been used to improve the system performance in different tasks, including the control of squeezed states (a typical class of nonclassical states, e.g., see =-=[59]-=-) and entangled states (see Section 2.1), state reduction and quantum error correction [15], [60]-[69]. The success of feedback control is usually dependent on the acquisition of suitable feedback inf... |

267 |
On the generators of quantum dynamical semigroups.
- Lindblad
- 1976
(Show Context)
Citation Context ... be neglected [29]. For an N - dimensional open quantum system with Markovian dynamics, its state ρ(t) can be described by the following Markovian master equation (MME) (for details, see, e.g., [29], =-=[92]-=-, [93]): ρ̇(t) = −i[H(t), ρ(t)] + 1 2 N2−1∑ j,k=0 αjk{[Fjρ(t), F †k ] + [Fj , ρ(t)F †k ]}. (13) Here {Fj}N2−1j=0 is a basis for the space of linear bounded operators on H with F0 = I, the coefficient ... |

161 |
Quantum Measurement and Control
- Wiseman, Milburn
- 2010
(Show Context)
Citation Context ... readers can refer to several excellent books and review articles in the areas of chemical reactions [5], [9], [11], [12], [13], [14], [31], [32], atomic physics [6], NMR [7], [81] and quantum optics =-=[82]-=-. The remainder of this paper is organized as follows. Section 2 briefly introduces quantum states, quantum measurements and several quantum control models. In Section 3, the controllability of quantu... |

85 |
I.L.: Quantum Computation and Quantum Information. Cambridge university press,
- Nielsen, Chuang
- 2010
(Show Context)
Citation Context ...n-loop and closed-loop methods in quantum control theory from a control systems perspective. We will also briefly discuss some applications of quantum control theory to quantum information technology =-=[80]-=-. Many successful applications of quantum control in chemistry and physics are beyond the scope of this paper and, for these topics, readers can refer to several excellent books and review articles in... |

80 |
Introduction to Quantum Control and Dynamics.
- D’Alessandro
- 2007
(Show Context)
Citation Context ...h focus is on finite dimensional (finite level) quantum systems for which the controllability criteria may be expressed in terms of the structure and rank of corresponding Lie groups and Lie algebras =-=[25]-=-. This method allows for an easy mathematical treatment of the problem for the case of closed quantum systems (i.e., isolated systems considered without external influences) and in some cases, methods... |

76 | H∞ control of linear quantum stochastic systems
- James, Nurdin, et al.
- 2008
(Show Context)
Citation Context ...ncertainties unavoidable [56]. A requirement for robustness in the presence of uncertainties and noises has been recognized as one of the key aspects in developing practical quantum technologies [7], =-=[57]-=-. A natural solution to this problem is to develop closed-loop quantum control approaches. Two paradigms for closed-loop control have been proposed: closed-loop learning control and quantum feedback c... |

76 | An introduction to quantum filtering
- Bouten, Handel, et al.
(Show Context)
Citation Context ...ates of measured systems. Hence, research aimed at establishing a general framework for quantum feedback is accelerating the development of some related areas including quantum filtering theory [70], =-=[71]-=-, [72], quantum parameter estimation [73], [74], [75], quantum system identification [76], [77], [78] and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and c... |

75 |
Optical Control of Molecular Dynamics;
- Rice, Zhao
- 2000
(Show Context)
Citation Context ...ontrol in chemistry and physics are beyond the scope of this paper and, for these topics, readers can refer to several excellent books and review articles in the areas of chemical reactions [5], [9], =-=[11]-=-, [12], [13], [14], [31], [32], atomic physics [6], NMR [7], [81] and quantum optics [82]. The remainder of this paper is organized as follows. Section 2 briefly introduces quantum states, quantum mea... |

73 | Feedback control of quantum state reduction.
- Handel, Stockton, et al.
- 2005
(Show Context)
Citation Context ...15) Equation (14) is usually called a stochastic master equation (SME). Such a stochastic master equation can be obtained as a filtering equation from quantum filtering theory (for details, see [16], =-=[62]-=-). It is worth noting that the state ρ in the SME (14) is a conditional state since it uses information from the continuous measurements. It should be pointed out that (14) is only a typical form of S... |

68 | Teaching lasers to control molecules,” - Judson, Rabitz - 1992 |

54 | Theory of control of observable quantum systems.
- Belavkin
- 1983
(Show Context)
Citation Context ...by LQSDEs driven by quantum Wiener processes [56], [160]. This simplification provides an opportunity to develop quantum linear-quadratic-Gaussian (LQG) control to obtain an optimal feedback strategy =-=[4]-=-, [69], [70], [73], [143], [160], [161], [162]. In LQG control, the goal is to find an optimal feedback control law for a stochastic linear system by optimizing a quadratic cost functional. In some ca... |

53 | NMR techniques for quantum control and computation
- Vandersypen, Chuang
- 2005
(Show Context)
Citation Context ...ontrols. Optimal control techniques have been widely applied to control quantum phenomena in physical chemistry (for details, see, e.g., [9], [11], [12], [108], [109]) and NMR experiments [39], [40], =-=[81]-=-. Here we present a simple example to demonstrate optimal quantum control design. We consider the model (11) and assume uy(t) = 0. We can produce an x rotation of the spin by using radio-frequency (RF... |

51 | Stabilizing feedback controls for quantum systems
- Mirrahimi, Handel
- 2007
(Show Context)
Citation Context ... to design a feedback control law for asymptotically stabilizing the quantum system to an objective state. For the model (16), if S = {ρ ∈ CN×N : ρ = ρ†, trρ = 1, ρ ≥ 0}, we have the following result =-=[63]-=-: Theorem 10 Consider the system (16) evolving in the set S. Let the final state ρf = vfv † f , where vf is an eigenstate |φm〉 (1 ≤ m ≤ N), and let γ > 0. Consider the following control law: 20 1. ut ... |

48 | Whither the future of controlling quantum phenomena
- Rabitz, Vivie-Riedle, et al.
- 2000
(Show Context)
Citation Context ... coherent control, incoherent control, feedback control, robust control. 1 Introduction Quantum control theory is a rapidly evolving research area, which has developed over the last three decades [1]-=-=[9]-=-. Controlling quantum phenomena has been an implicit goal of much quantum physics and chemistry research since the establishment of quantum mechanics [5], [6]. One of the main goals in quantum control... |

48 |
Feedback-control of quantum systems using continuous state-estimation
- Doherty, Jacobs
- 1999
(Show Context)
Citation Context ... aimed at establishing a general framework for quantum feedback is accelerating the development of some related areas including quantum filtering theory [70], [71], [72], quantum parameter estimation =-=[73]-=-, [74], [75], quantum system identification [76], [77], [78] and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and closed-loop methods in quantum control the... |

47 |
Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications
- Peirce, Dahleh, et al.
- 1988
(Show Context)
Citation Context ...rol theory has been successfully applied to the design of open-loop coherent control strategies in order to find the best way of achieving given quantum control objectives in physical chemistry [12], =-=[33]-=-, [34]. Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time [35], [36], [37]. Optimal control techniques have also been su... |

46 |
Coherent control of quantum dynamics: the dream is alive
- Warren, Rabitz, et al.
- 1993
(Show Context)
Citation Context ... has developed over the last three decades [1]-[9]. Controlling quantum phenomena has been an implicit goal of much quantum physics and chemistry research since the establishment of quantum mechanics =-=[5]-=-, [6]. One of the main goals in quantum control theory is to establish a firm theoretical footing and develop a series of systematic methods for the active manipulation and control of quantum systems ... |

46 |
Notions of controllability for bilinear multilevel quantum systems.
- Albertini, D’Alessandro
- 2003
(Show Context)
Citation Context ...the reachable set of all states that are reachable from |ψ〉. Now, we give several definitions of controllability and their corresponding testing criteria. 10 Definition 1 (Pure State Controllability) =-=[24]-=- The quantum system (5) is pure state controllable if for every pair of initial and final states, |ψ0〉 and |ψf 〉 in SN−1C there exist control functions {uk(t)} and a time t > 0 such that the correspon... |

45 |
Principles of the Quantum Control of Molecular Processes,
- Shapiro, Brumer
- 2003
(Show Context)
Citation Context ...l control theory has been successfully applied to the design of open-loop coherent control strategies in order to find the best way of achieving given quantum control objectives in physical chemistry =-=[12]-=-, [33], [34]. Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time [35], [36], [37]. Optimal control techniques have also b... |

44 |
Lyapunov control of bilinear Schrödinger equations
- Mirrahimi, Rouchon, et al.
- 2005
(Show Context)
Citation Context ...xperiments to improve the sensitivity of these systems in the presence of relaxation [38], [39], [40]. Another useful tool in open-loop quantum control is 2 the Lyapunov-based control design approach =-=[41]-=-, [42]. In classical control, the Lyapunov method determines the control input as a function of the system state. Hence, it is a feedback control design method. In quantum control, it is difficult to ... |

44 | Quantum continual measurements and a posteriori collapse on
- Belavkin
- 1992
(Show Context)
Citation Context ...tity w describes the input signals and is assumed to admit the decomposition dw(t) = βw(t)dt+ dw̃(t) (20) where w̃(t) is the noise part of w(t) and βw(t) is a self-adjoint, adapted process (see [95], =-=[96]-=-). The noise w̃(t) is a vector of self-adjoint quantum noises with Itô table dw̃(t)dw̃T (t) = Fw̃dt (21) where Fw̃ is a positive semidefinite Hermitian matrix (see [95], [96] for details). Equation (... |

44 |
Controllability of quantum mechanical systems by root space decomposition of su(n
- Altafini
(Show Context)
Citation Context ...rollability, in the unitary case, is also called complete controllability [22], [97]. Some algorithms have been developed for testing the controllability of specific quantum systems [20], [22], [25], =-=[98]-=-. The Lie algebra method allows for a straightforward mathematical treatment of closed quantum systems. However, the relevant criteria may be computationally difficult when the dimension of the contro... |

43 |
On the controllability of quantummechanical systems.
- Huang, Tarn, et al.
- 1983
(Show Context)
Citation Context ...ol systems perspective. In much of quantum control theory, the controllability of quantum systems is a fundamental issue. This issue concerns whether one can drive a quantum system to a desired state =-=[3]-=-. This problem has practical importance since it has a close connection with the universality of quantum computation [19] and the possibility of achieving atomic or molecular scale transformations [20... |

42 |
Quantum theory of optical feedback via homodyne detection.
- Wiseman, Milburn
- 1993
(Show Context)
Citation Context ...ystems must be described by quantum theory. Quantum control theory has already attained significant successes in physical chemistry [9]-[13], atomic and molecular physics [6], [14] and quantum optics =-=[15]-=-, [16], and has also contributed to the ∗This paper has been published by IET Control Theory & Applications, vol. 4, no. 12, pp.2651-2671. †This work was supported by the Australian Research Council a... |

38 |
Optimal control of two-level quantum systems
- D’Alessandro, Dahleh
- 2001
(Show Context)
Citation Context ...ular systems in physical chemistry and spin systems in NMR. For example, consider a spin 1/2 system in a constant magnetic field along z-axis and controlled by magnetic fields along x-axis and y-axis =-=[91]-=-. We denote the Pauli matrices σ = (σx, σy, σz) as follows: σx = ( 0 1 1 0 ) , σy = ( 0 −i i 0 ) , σz = ( 1 0 0 −1 ) . (10) The quantum control system under consideration can be described as follows: ... |

36 |
Principles and applications of control in quantum systems
- Mabuchi, Khaneja
- 2005
(Show Context)
Citation Context ..., [6]. One of the main goals in quantum control theory is to establish a firm theoretical footing and develop a series of systematic methods for the active manipulation and control of quantum systems =-=[7]-=-. This goal is nontrivial since microscopic quantum systems have many unique characteristics (e.g., entanglement and coherence) which do not occur in classical mechanical systems and the dynamics of q... |

36 | Time optimal control in spin systems.
- Khaneja, Brockett, et al.
- 2001
(Show Context)
Citation Context ...en quantum control objectives in physical chemistry [12], [33], [34]. Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time =-=[35]-=-, [36], [37]. Optimal control techniques have also been successfully applied to multidimensional nuclear magnetic resonance (NMR) experiments to improve the sensitivity of these systems in the presenc... |

30 |
Optimal control in laser-induced population transfer for two- and three-level quantum systems.
- Boscain, Charlot, et al.
- 2002
(Show Context)
Citation Context ...ntum control objectives in physical chemistry [12], [33], [34]. Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time [35], =-=[36]-=-, [37]. Optimal control techniques have also been successfully applied to multidimensional nuclear magnetic resonance (NMR) experiments to improve the sensitivity of these systems in the presence of r... |

29 |
Continuous quantum error correction via quantum feedback control
- Ahn, Doherty, et al.
- 2002
(Show Context)
Citation Context ...ian feedback than Markovian feedback due to the existence of the estimation step [145]. Bayesian feedback has also been applied in the preparation of quantum states [155] and quantum error correction =-=[66]-=-, [67]. If the feedback delay cannot be ignored, the feedback Hamiltonian must include a delay parameter [156] which in some cases has a qualitatively similar effect to that of unprecise measurement [... |

28 |
A straightforward introduction to continuous quantum measurement,
- Jacobs, Steck
- 2006
(Show Context)
Citation Context ...r related time-scales for a given task [87]. However, this framework may not be sufficient to describe some important situations such as continuously monitoring some aspects of a quantum system [88], =-=[89]-=-. In quantum feedback control, it is important to continuously extract feedback information to adjust the system evolution. Hence, there is an essential requirement to develop a continuous measurement... |

26 | Complete controllability of quantum systems
- Schirmer, Fu, et al.
- 2000
(Show Context)
Citation Context ...e state controllability is also called wavefunction controllability in some references (e.g., [27], [28], [43]). Operator controllability, in the unitary case, is also called complete controllability =-=[22]-=-, [97]. Some algorithms have been developed for testing the controllability of specific quantum systems [20], [22], [25], [98]. The Lie algebra method allows for a straightforward mathematical treatme... |

25 | A discrete invitation to quantum filtering and feedback control
- Bouten, Handel, et al.
- 2009
(Show Context)
Citation Context ...f measured systems. Hence, research aimed at establishing a general framework for quantum feedback is accelerating the development of some related areas including quantum filtering theory [70], [71], =-=[72]-=-, quantum parameter estimation [73], [74], [75], quantum system identification [76], [77], [78] and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and closed-... |

24 | Quantum technology: The second quantum revolution - Dowling, Milburn |

22 |
Controllabi1lity properties for finite dimensional quantum Markovian master equations
- Altafini
- 2002
(Show Context)
Citation Context ...dimensional quantum systems or open quantum systems (i.e., systems considered interacting with the environment; e.g., see [29]) is more difficult and only a few results have been obtained [21], [26], =-=[30]-=-. For a controllable quantum system, it is desirable to develop a good control strategy to accomplish the required control tasks on the quantum system [9]. The coherent control strategy is a widely us... |

17 |
Coherent quantum feedback,” Phys
- Lloyd
- 2000
(Show Context)
Citation Context ...logy, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia (email: i.r.petersen@gmail.com). 1 understanding of fundamental aspects of quantum mechanics =-=[17]-=-. In recent years, the development of the general principles of quantum control theory has been recognized as an essential requirement for the future application of quantum technologies [18]. Quantum ... |

16 | Modelling and feedback control design for quantum state preparation - Handel, Stockton, et al. - 2005 |

16 | Time minimal trajectories for a spin 1/2 particle in a magnetic field
- Boscain, Mason
- 2006
(Show Context)
Citation Context ...ontrol objectives in physical chemistry [12], [33], [34]. Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time [35], [36], =-=[37]-=-. Optimal control techniques have also been successfully applied to multidimensional nuclear magnetic resonance (NMR) experiments to improve the sensitivity of these systems in the presence of relaxat... |

16 |
Feedback control of quantum entanglement in a two-spin system
- Yamamoto, Tsumura, et al.
- 2007
(Show Context)
Citation Context ...trol. Quantum entanglement is the most important resource in quantum information technology. Several optimal control and feedback control approaches have been proposed to control quantum entanglement =-=[61]-=-, [69], [131], [132], [133], [181], [182]. However, existing results are only a first step in entanglement control. Quantum entanglement has many unique characteristics which have no classical counter... |

15 | Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry - Geremia, Stockton, et al. |

14 |
Quantum wavefunction controllability.
- Turinici, Rabitz
(Show Context)
Citation Context ...nsion of the quantum system to be controlled is large. Therefore, a controllability method based on graph theory has been proposed, and the corresponding controllability criterion is easier to verify =-=[27]-=-, [28]. Compared with finite dimensional closed quantum systems, the controllability of infinite dimensional quantum systems or open quantum systems (i.e., systems considered interacting with the envi... |

14 | Optimal control of spin dynamics in the presence of relaxation
- Khaneja, Reiss, et al.
- 2003
(Show Context)
Citation Context ...control techniques have also been successfully applied to multidimensional nuclear magnetic resonance (NMR) experiments to improve the sensitivity of these systems in the presence of relaxation [38], =-=[39]-=-, [40]. Another useful tool in open-loop quantum control is 2 the Lyapunov-based control design approach [41], [42]. In classical control, the Lyapunov method determines the control input as a functio... |

14 |
Practical scheme for error control using feedback,”
- Sarovar, Ahn, et al.
- 2004
(Show Context)
Citation Context ...edback than Markovian feedback due to the existence of the estimation step [145]. Bayesian feedback has also been applied in the preparation of quantum states [155] and quantum error correction [66], =-=[67]-=-. If the feedback delay cannot be ignored, the feedback Hamiltonian must include a delay parameter [156] which in some cases has a qualitatively similar effect to that of unprecise measurement [157]. ... |

14 |
Robust quantum parameter estimation: Coherent magnetometry with feedback, Phys
- Stockton, Geremia, et al.
(Show Context)
Citation Context ...tablishing a general framework for quantum feedback is accelerating the development of some related areas including quantum filtering theory [70], [71], [72], quantum parameter estimation [73], [74], =-=[75]-=-, quantum system identification [76], [77], [78] and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and closed-loop methods in quantum control theory from a c... |

13 |
Rapid state reduction of quantum systems using feedback control,”
- Combes, Jacobs
- 2006
(Show Context)
Citation Context ...ortant progress has been made and feedback has been used to improve the control performance for squeezed states [60], [130], quantum entanglement [131], [132], [133], and quantum state reduction [62]-=-=[65]-=-, [134]-[138] in many areas such as quantum optics [15], [82], superconducting quantum systems [138], Bose-Einstein condensate [139] and nanomechanical systems [140]. Quantum feedback control has also... |

12 |
Selective quantum evolution of a qubit state due to continuous measurement.
- Korotkov
- 2001
(Show Context)
Citation Context ...urement theory for quantum feedback control. Fortunately, recent results have shown that continuous measurements are experimentally realizable for practical quantum systems such as solid-state qubits =-=[90]-=-. In continuous measurements, one can continuously monitor an observable of a quantum system and the evolution of the system described in terms of the measurement record can be obtained from a stochas... |

12 |
Degrees of controllability for quantum systems and application to atomic systems
- Schirmer, Solomon, et al.
- 2002
(Show Context)
Citation Context ...e controllability is also called wavefunction controllability in some references (e.g., [27], [28], [43]). Operator controllability, in the unitary case, is also called complete controllability [22], =-=[97]-=-. Some algorithms have been developed for testing the controllability of specific quantum systems [20], [22], [25], [98]. The Lie algebra method allows for a straightforward mathematical treatment of ... |

11 |
Boundary of quantum evolution under decoherence,
- Khaneja, Luy, et al.
- 2003
(Show Context)
Citation Context ...timal control techniques have also been successfully applied to multidimensional nuclear magnetic resonance (NMR) experiments to improve the sensitivity of these systems in the presence of relaxation =-=[38]-=-, [39], [40]. Another useful tool in open-loop quantum control is 2 the Lyapunov-based control design approach [41], [42]. In classical control, the Lyapunov method determines the control input as a f... |

11 | How to project qubits faster using quantum feedback, Phys - Jacobs - 2003 |

10 |
Wavefunction controllability for finite-dimensional bilinear quantum systems
- Turinici, Rabitz
(Show Context)
Citation Context ...of the quantum system to be controlled is large. Therefore, a controllability method based on graph theory has been proposed, and the corresponding controllability criterion is easier to verify [27], =-=[28]-=-. Compared with finite dimensional closed quantum systems, the controllability of infinite dimensional quantum systems or open quantum systems (i.e., systems considered interacting with the environmen... |

10 |
Lyapunov control methods of closed quantum systems,”
- Kuang, Cong
- 2008
(Show Context)
Citation Context ...ents to improve the sensitivity of these systems in the presence of relaxation [38], [39], [40]. Another useful tool in open-loop quantum control is 2 the Lyapunov-based control design approach [41], =-=[42]-=-. In classical control, the Lyapunov method determines the control input as a function of the system state. Hence, it is a feedback control design method. In quantum control, it is difficult to acquir... |

10 | filtering and control in quantum open dynamical systems - Belavkin, “Measurement - 1999 |

10 |
Optimal identification of Hamiltonian information by closed-loop laser control of quantum systems
- Geremia, Rabitz
- 2002
(Show Context)
Citation Context ...uantum feedback is accelerating the development of some related areas including quantum filtering theory [70], [71], [72], quantum parameter estimation [73], [74], [75], quantum system identification =-=[76]-=-, [77], [78] and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and closed-loop methods in quantum control theory from a control systems perspective. We will ... |

9 | Experimental coherent laser control of physicochemical processes - Dantus, Lozovoy |

9 |
Controllability of molecular systems’’, Phys
- Ramakrishna, Salapaka, et al.
- 1995
(Show Context)
Citation Context ...[3]. This problem has practical importance since it has a close connection with the universality of quantum computation [19] and the possibility of achieving atomic or molecular scale transformations =-=[20]-=-, [21]. Different notions of controllability, such as pure state controllability, complete controllability, eigenstate controllability and kinematic controllability, have been proposed [20]-[26]. A co... |

9 | Controllability of open quantum systems with Kraus-map dynamics - Wu, Pechen, et al. - 2007 |

9 |
Optimal control of uncertain quantum systems
- Dahleh, Peirce, et al.
- 1990
(Show Context)
Citation Context ...eory has been successfully applied to the design of open-loop coherent control strategies in order to find the best way of achieving given quantum control objectives in physical chemistry [12], [33], =-=[34]-=-. Recently, time-optimal control problems for spin systems have been solved to achieve specified control objectives in minimum time [35], [36], [37]. Optimal control techniques have also been successf... |

9 |
Optimal control of entanglement via quantum feedback,” Phys
- Mancini, Wiseman
- 2007
(Show Context)
Citation Context ...asks, including the control of squeezed states (a typical class of nonclassical states, e.g., see [59]) and entangled states (see Section 2.1), state reduction and quantum error correction [15], [60]-=-=[69]-=-. The success of feedback control is usually dependent on the acquisition of suitable feedback information. This problem becomes more complex and subtle in quantum control since quantum measurements u... |

8 |
Cold atoms and quantum control
- Chu
- 2002
(Show Context)
Citation Context ...developed over the last three decades [1]-[9]. Controlling quantum phenomena has been an implicit goal of much quantum physics and chemistry research since the establishment of quantum mechanics [5], =-=[6]-=-. One of the main goals in quantum control theory is to establish a firm theoretical footing and develop a series of systematic methods for the active manipulation and control of quantum systems [7]. ... |

8 |
Incoherent control and entanglement for twodimensional coupled systems
- Romano, D'Alessandro
(Show Context)
Citation Context ...on the interaction of the system to be controlled, the auxiliary system, and the environment, the system dynamics is completely controllable by varying the initial state of the auxiliary system [49], =-=[50]-=- or manipulating the local Hamiltonian of the auxiliary system [128], which has potential applications to quantum networks [129]. Furthermore, if all kinds of coherent and incoherent resources are ava... |

8 |
Spin squeezing via quantum feedback, Phys. Rev. A 65
- Thomsen, Mancini, et al.
- 2002
(Show Context)
Citation Context ...ent tasks, including the control of squeezed states (a typical class of nonclassical states, e.g., see [59]) and entangled states (see Section 2.1), state reduction and quantum error correction [15], =-=[60]-=--[69]. The success of feedback control is usually dependent on the acquisition of suitable feedback information. This problem becomes more complex and subtle in quantum control since quantum measureme... |

7 | Observer-based Hamiltonian identification for quantum systems
- Bonnabel, Mirrahimi, et al.
- 2009
(Show Context)
Citation Context ... feedback is accelerating the development of some related areas including quantum filtering theory [70], [71], [72], quantum parameter estimation [73], [74], [75], quantum system identification [76], =-=[77]-=-, [78] and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and closed-loop methods in quantum control theory from a control systems perspective. We will also b... |

7 |
Engineering quantum dynamics,” Phys
- Lloyd, Viola
- 2002
(Show Context)
Citation Context ...ble [26] and a specific Kraus map can be constructed for transformation from an arbitrary initial state to a predefined target state if some incoherent resources are available as control tools [100], =-=[101]-=-. A control approach involving generating Kraus type dynamics can be potentially robust to variations of the initial system state [26]. 3.2 Optimal control Most results on the controllability of quant... |

7 |
Cartan decomposition of su(2n) and control of spin systems
- Klianeja, Glaser
- 2001
(Show Context)
Citation Context ...ased on a Lie group decomposition, where the desired system evolution operator Uf is decomposed as the product of basic unitary operators which are easy to generate using simple controls [25], [102], =-=[103]-=-. This method is constructive and exact. However, it may be difficult to complete the decomposition for most practical systems. For many practical quantum control problems, optimal control theory is a... |

6 |
robustness in quantum feedback networks, Phys
- D’Helon, James, et al.
(Show Context)
Citation Context ...ome related areas including quantum filtering theory [70], [71], [72], quantum parameter estimation [73], [74], [75], quantum system identification [76], [77], [78] and 3 quantum robust control [57], =-=[79]-=-. This paper will survey the development of open-loop and closed-loop methods in quantum control theory from a control systems perspective. We will also briefly discuss some applications of quantum co... |

6 | Quantum reinforcement learning,”
- Dong, Chen, et al.
- 2008
(Show Context)
Citation Context ...nd the state |ψ〉 of a qubit can be written as |ψ〉 = cos θ 2 |0〉 + eiϕ sin θ 2 |1〉 (1) 4 where θ ∈ [0, π], ϕ ∈ [0, 2π]. Then |0〉 and |1〉 correspond to the states zero and one for a classical bit [80], =-=[85]-=-. In practical applications, the quantum systems to be controlled are usually not simple closed systems. They may be quantum ensembles or open quantum systems and their states cannot be written in the... |

6 |
Quantum control by decompositions of SU(2),’ Phys
- Ramakrishna, Flores, et al.
(Show Context)
Citation Context ...aw is based on a Lie group decomposition, where the desired system evolution operator Uf is decomposed as the product of basic unitary operators which are easy to generate using simple controls [25], =-=[102]-=-, [103]. This method is constructive and exact. However, it may be difficult to complete the decomposition for most practical systems. For many practical quantum control problems, optimal control theo... |

5 |
Relation between quantum computing and quantum controllability,” Phys
- Ramakrishna
- 1996
(Show Context)
Citation Context .... This issue concerns whether one can drive a quantum system to a desired state [3]. This problem has practical importance since it has a close connection with the universality of quantum computation =-=[19]-=- and the possibility of achieving atomic or molecular scale transformations [20], [21]. Different notions of controllability, such as pure state controllability, complete controllability, eigenstate c... |

5 |
Quantum control of bound and continuum state dynamics
- Shapiro, Brumer
(Show Context)
Citation Context ...d destructive interference, e.g., see [5]). An early paradigm of quantum control was openloop coherent control [5], which has successfully been used in the quantum control of chemical reactions [31], =-=[32]-=-. Rigorous optimal control theory has been successfully applied to the design of open-loop coherent control strategies in order to find the best way of achieving given quantum control objectives in ph... |

5 | Quantum control by von Neumann measurements - Pechen, Il’in, et al. - 2006 |

5 |
Incoherent control of locally controllable quantum systems
- Dong, Zhang, et al.
- 2008
(Show Context)
Citation Context ...e effects of quantum measurements and incoherent environments to be combined with unitary transformations to complete quantum control tasks and enhance the performance of quantum control systems [45]-=-=[55]-=-. Incoherent control strategies have also been recognized as important techniques to assist coherent control strategies in quantum control systems. Although open-loop strategies using coherent or inco... |

5 |
Coupling strength estimation for spin chains despite restricted access’, Phys
- Burgarth, Maruyama, et al.
(Show Context)
Citation Context ...ack is accelerating the development of some related areas including quantum filtering theory [70], [71], [72], quantum parameter estimation [73], [74], [75], quantum system identification [76], [77], =-=[78]-=- and 3 quantum robust control [57], [79]. This paper will survey the development of open-loop and closed-loop methods in quantum control theory from a control systems perspective. We will also briefly... |

5 | Analytic controllability of time-dependent quantum control systems.
- Lan, Tarn, et al.
- 2005
(Show Context)
Citation Context ...conditions on the corresponding Lie algebra, can guarantee its analytic controllability. The controllability of infinite dimensional quantum control systems has also been extensively studied in [21], =-=[99]-=-. Another interesting focus is on the controllability of open quantum systems. It has been proven that a finite dimensional open quantum system with Markovian dynamics (i.e., MME (13)) is not controll... |

4 | Focus on quantum control - Rabitz |

4 |
Smooth controllability of infinitedimensional quantum-mechanical systems.
- Wu, Tarn, et al.
- 2006
(Show Context)
Citation Context ...his problem has practical importance since it has a close connection with the universality of quantum computation [19] and the possibility of achieving atomic or molecular scale transformations [20], =-=[21]-=-. Different notions of controllability, such as pure state controllability, complete controllability, eigenstate controllability and kinematic controllability, have been proposed [20]-[26]. A common r... |

4 |
Variable structure control of uncontrollable quantum
- Dong, Petersen
- 2009
(Show Context)
Citation Context ...e control and incoherent control (i.e., one is allowed to destroy coherence of the quantum systems during the control process). For example, a variable structure control method has been introduced in =-=[43]-=-, [44] to enhance the capabilities of quantum control for some specific systems which are not controllable. Incoherent control enables the effects of quantum measurements and incoherent environments t... |

4 |
Environment-mediated control of a quantum system
- Romano, D’Alessandro
- 2006
(Show Context)
Citation Context ...rt of the dynamics. There exist some physical situations where it is not possible or very difficult to control the state of a quantum system directly with coherent resources (unitary transformations) =-=[49]-=-. For example, it has been proven that a finite dimensional open quantum system with Markovian dynamics is not controllable using only coherent control [30], [124]. A natural extension of these quantu... |

4 |
Robust incoherent control of qubit systems via switching and optimisation
- Dong, Lam, et al.
- 2010
(Show Context)
Citation Context ...e Bloch sphere [52]. This minimum time β can be calculated according to the following equation: β = | arccos(sin θf cosϕf )− arccos(sin θ0 cosϕ0)| . (27) A formal proof of this result can be found in =-=[53]-=-. Under the assumption of bounded control (i.e., |u(t)| ≤ V ∈ R+), an interesting case is bang-bang control where the control u(t) switches between two values ±V . The solutions to many optimal proble... |

3 |
Z.H.: ‘Control of non-controllable quantum systems: a quantum control algorithm based on Grover iteration
- Zhang, Dong, et al.
(Show Context)
Citation Context ... (7) is operator controllable if there exist control functions {uk(t)} which drive the unitary operator U in (7) from I to Uf , for any Uf ∈ U(N) (or SU(N)). Definition 3 (Eigenstate Controllability) =-=[23]-=- Suppose |φ1〉, . . . , |φN 〉 are the N eigenstates of the free Hamiltonian H0. The quantum system (5) is eigenstate controllable if ⋃N i=1R(|φi〉) = SN−1C . Theorem 4 [25] The quantum system (5) is pur... |

3 |
Broadband relaxation optimized polarization transfer in magnetic resonance
- Khaneja, Li, et al.
- 2004
(Show Context)
Citation Context ...l techniques have also been successfully applied to multidimensional nuclear magnetic resonance (NMR) experiments to improve the sensitivity of these systems in the presence of relaxation [38], [39], =-=[40]-=-. Another useful tool in open-loop quantum control is 2 the Lyapunov-based control design approach [41], [42]. In classical control, the Lyapunov method determines the control input as a function of t... |

3 | Controllability of quantum systems with switching control - Dong, Petersen |

3 |
Incoherent Control of Quantum Systems with Wavefunction Controllable Subspaces via Quantum Reinforcement Learning [J
- Dong, Chen, et al.
- 2008
(Show Context)
Citation Context ...ote control of quantum systems [48]. Projective measurements on several identical initial states are used to help complete the control design of quantum systems with pure state controllable subspaces =-=[51]-=-. Projective measurements are also combined with amplitude amplification for the state control of locally controllable quantum systems [55]. In these incoherent control schemes, we emphasize the role ... |

3 |
Teaching the environment to control quantum systems’, Phys
- Pechen, Rabitz
(Show Context)
Citation Context ...um incoherent control. Hence, it is desirable to develop systematic and new approaches to construct quantum incoherent (or coherent/incoherent hybrid) controllers which are easily physically realized =-=[54]-=-. (2) Quantum feedback control. Feedback plays a key role in classical control theory. It is desirable to develop systematic feedback control methods for emerging quantum engineering applications. Alt... |

2 |
Probabilistic quantum control via indirect measurement’, Phys
- Mandilara, Clark
(Show Context)
Citation Context ... quantum systems in some situations. Indeed, sometimes a quantum system which is not unitarily controllable can be controlled by the joint action of projective measurement and unitary evolution [45], =-=[48]-=-. Let us consider the model (5), and let G(A) denote the Lie group generated by the operators {−iH0,−iH1, . . . ,−iHK}. Also, let O(N) be the N -dimensional orthogonal group. We then have the followin... |

2 | Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols - Jacobs, Shabani - 2008 |

2 |
Optimal feedback control for rapid preparation of a qubit
- Jacobs
(Show Context)
Citation Context ...e., the coupling strength between the measurement apparatus and the measured system) is large enough and the measurement time-scale is much shorter than all other related time-scales for a given task =-=[87]-=-. However, this framework may not be sufficient to describe some important situations such as continuously monitoring some aspects of a quantum system [88], [89]. In quantum feedback control, it is im... |

2 |
On the quantum master equation under feedback control
- Qi
(Show Context)
Citation Context ...rmation from the continuous measurements. It should be pointed out that (14) is only a typical form of SME and there exist many different types of SMEs which depend on different measurement processes =-=[94]-=-. Stochastic master equations have been derived for some quantum optical systems under continuous measurements. For example, we consider an atomic ensemble interacting with an electromagnetic field co... |

1 |
Samoilenko, Yu.I.: ‘Control of quantum systems
- Butkovskii
(Show Context)
Citation Context ...ity, coherent control, incoherent control, feedback control, robust control. 1 Introduction Quantum control theory is a rapidly evolving research area, which has developed over the last three decades =-=[1]-=--[9]. Controlling quantum phenomena has been an implicit goal of much quantum physics and chemistry research since the establishment of quantum mechanics [5], [6]. One of the main goals in quantum con... |

1 | The role of theory in the laboratory control of quantum dynamics phenomena’, Theor - Rabitz |

1 |
Theoretical exploration of ultrafast dynamics in atomic clusters: analysis and control
- Bonačić-Koutecký, Mitrić
(Show Context)
Citation Context ...he dynamics of quantum systems must be described by quantum theory. Quantum control theory has already attained significant successes in physical chemistry [9]-[13], atomic and molecular physics [6], =-=[14]-=- and quantum optics [15], [16], and has also contributed to the ∗This paper has been published by IET Control Theory & Applications, vol. 4, no. 12, pp.2651-2671. †This work was supported by the Austr... |

1 |
Interfering for the good of a chemical reaction
- Rice
(Show Context)
Citation Context ...ive and destructive interference, e.g., see [5]). An early paradigm of quantum control was openloop coherent control [5], which has successfully been used in the quantum control of chemical reactions =-=[31]-=-, [32]. Rigorous optimal control theory has been successfully applied to the design of open-loop coherent control strategies in order to find the best way of achieving given quantum control objectives... |

1 |
Quantum control and the Strocchi map’, Phys
- Mendes, R, et al.
(Show Context)
Citation Context ...es the effects of quantum measurements and incoherent environments to be combined with unitary transformations to complete quantum control tasks and enhance the performance of quantum control systems =-=[45]-=--[55]. Incoherent control strategies have also been recognized as important techniques to assist coherent control strategies in quantum control systems. Although open-loop strategies using coherent or... |

1 | Observation-assisted optimal control of quantum dynamics - Shuang, Pechen, et al. |

1 |
T.J.: ‘Rapid incoherent control of quantum systems based on continuous measurements and reference model
- Dong, Lam, et al.
(Show Context)
Citation Context ...∈ [0, π], ϕ0, ϕf ∈ [0, 2π] and |ψf 〉 = Uf |ψ0〉. We can give an analytical expression for the minimal time required to accomplish this control task using geometric 13 manipulations on the Bloch sphere =-=[52]-=-. This minimum time β can be calculated according to the following equation: β = | arccos(sin θf cosϕf )− arccos(sin θ0 cosϕ0)| . (27) A formal proof of this result can be found in [53]. Under the ass... |

1 |
Available electronically via http://www.theory.caltech.edu/people/preskill/ph229
- Preskill
- 1998
(Show Context)
Citation Context ...te pure state |ψ〉AB , if it can be written as a tensor product of pure states |ϕ〉A ∈ HA and |χ〉B ∈ HB, |ψ〉AB = |ϕ〉A ⊗ |χ〉B , (3) we call it a separable state; otherwise, we call it an entangled state =-=[86]-=-. Quantum entanglement is a uniquely quantum mechanical phenomenon which plays a key role in many interesting applications of quantum communication and quantum computation, and a detailed discussion c... |

1 |
A simple mode of quantum trajectories
- Brun
(Show Context)
Citation Context ...l other related time-scales for a given task [87]. However, this framework may not be sufficient to describe some important situations such as continuously monitoring some aspects of a quantum system =-=[88]-=-, [89]. In quantum feedback control, it is important to continuously extract feedback information to adjust the system evolution. Hence, there is an essential requirement to develop a continuous measu... |