Quantum control techniques for switched electrical networks

Flores, Kathryn L.; Ramakrishna, Viswanath

doi:10.1109/cdc.2000.912268

Cited by 6 publications

(5 citation statements)

References 4 publications

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“…This technique of control can be applied to the dynamics of a rigid body where the angular velocity is seen as control. The same technique can also be employed for the control of switched electrical networks [6], with minimum number of switches. In recent years there has been a large amount of interest in the control of systems of the form (1) with A and B in the Lie algebra su (2).…”

Section: Applicationsmentioning

confidence: 99%

“…The fundamental matrix of equation (1) represents the orientation of the rigid body. Another example is the lossless electrical network dealt with in [6]. A two level quantum system driven by a single time varying component of an electro-magnetic field also has the structure (1) [5], where x represents the state ∈ C I 2 and the matrices A and B are in the Lie algebra su (2).…”

Section: Introductionmentioning

confidence: 99%

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Optimal evaluation of generalized Euler angles with applications to control

D’Alessandro¹

2004

Automatica

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Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal evaluation of generalized Euler angles with applications to control

D’Alessandro¹

2004

Automatica

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“…Cartan symmetries have the property that applied two times to any state return the physical state unchanged. For example, the time reversal symmetry and the parity (11) are Cartan symmetries while the space translation symmetry (10) is not a Cartan symmetry.…”

Section: Definition 31 a Symmetry Is Called A Cartan Symmetry If And ...mentioning

confidence: 99%

Quantum symmetries and Cartan decompositions in arbitrary dimensions

D’Alessandro

Albertini

2007

J. Phys. A: Math. Theor.

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Decompositions of Lie groups are used in systems and control, both to analyse dynamics and to design control algorithms for systems with state varying on a Lie group. In this paper, we investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition, there corresponds a quantum symmetry which is the identity when applied twice. As an application, we describe a new and general method to obtain Cartan decompositions of the unitary group of evolutions of multipartite systems from Cartan decompositions on the single subsystems. The resulting decomposition, which we call of the odd–even type, contains, as a special case, the concurrence canonical decomposition (CCD) presented in [6–8] in the context of entanglement theory. The CCD is therefore extended from the case of a multipartite system of N qubits to the case where the component subsystems have arbitrary dimensions. We present an example of application of the results to control design for quantum systems.

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“…Though, in principle, the Euler angles D, E and F may be obtained from more common Euler angle parametrizations [23], an explicit formula for them in terms of the Cayley-Klein coordinates goes a long way towards making the techniques of this paper genuinely constructive. Therefore, the following relations are very useful, [24]:…”

Section: Review Of Basic Su (2) Factsmentioning

confidence: 99%

Control of a coupled two-spin system without hard pulses

Ramakrishna

Ober

Flores³

et al. 2002

Phys. Rev. A

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Constructive techniques for controlling a coupled, heteronuclear spin system, via bounded amplitude sinusoidal pulses are presented. The technique prepares exactly any desired unitary generator in a rotating frame, through constant controls. Passage to the original coordinates provides a procedure to prepare arbitrary unitary generators, via bounded amplitude piecewise sinusoidal pulses whose frequency is one of the two Larmor frequencies and whose phase takes one of two values. The techniques are based on a certain Cartan decomposition of SU (4) available in the literature. A method for determining the parameters entering this Cartan decomposition, in terms of the entries of the target unitary generator, is also provided.

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Quantum control techniques for switched electrical networks

Cited by 6 publications

References 4 publications

Optimal evaluation of generalized Euler angles with applications to control

Optimal evaluation of generalized Euler angles with applications to control

Quantum symmetries and Cartan decompositions in arbitrary dimensions

Control of a coupled two-spin system without hard pulses

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