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Bangbang control design for quantum state transfer based on hyperspherical coordinates and optimal timeenergy control
 J. Phys. A: Math. Theor
, 2011
"... Abstract. We present a constructive control scheme for solving quantum state engineering problems based on a parametrization of the state vector in terms of complex hyperspherical coordinates. Unlike many control schemes based on factorization of unitary operators, the scheme gives explicit expressi ..."
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Abstract. We present a constructive control scheme for solving quantum state engineering problems based on a parametrization of the state vector in terms of complex hyperspherical coordinates. Unlike many control schemes based on factorization of unitary operators, the scheme gives explicit expressions for all generalized Euler angles in terms of the hyperspherical coordinates of the initial and final states. The factorization, when applicable, has added benefits that phase rotations can be combined and performed concurrently. The control procedure can be realized using simple bangbang or squarewavefunction controls. Optimal timeenergy control is considered to find the optimal control amplitude. The extension of the scheme to implement arbitrary unitary operators is also discussed.
FewQubit Magnetic Resonance Quantum Information Processors: Simulating Chemistry and Physics
, 2014
"... 1.2 Quantum Algorithms for Chemistry............... 4 ..."
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1.2 Quantum Algorithms for Chemistry............... 4
Coherent Control of Hyperfinecoupled Electron and Nuclear Spins for Quantum Information Processing
, 2008
"... Coupled electronnuclear spins are promising physical systems for quantum information processing: By combining the long coherence times of the nuclear spins with the ability to initialize, control, and measure the electron spin state, the favorable properties of each spin species are utilized. Thi ..."
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Coupled electronnuclear spins are promising physical systems for quantum information processing: By combining the long coherence times of the nuclear spins with the ability to initialize, control, and measure the electron spin state, the favorable properties of each spin species are utilized. This thesis discusses a procedure to initialize these nuclear spin qubits, and presents a vision of how these systems could be used as the fundamental processing unit of a quantum computer. The focus of this thesis is on control of a system in which a single electron spin is coupled to N nuclear spins via resolvable anisotropic hyperfine (AHF) interactions. Highfidelity universal control of this leNn system is possible using only excitations on a single electron spin transition. This electron spin actuator control is implemented by using optimal control theory to find the modulation sequences that generate the desired unitary operations. Decoherence and the challenge of making useful qubits from these systems are also discussed. Experimental evidence of control using an electron spin actuator was acquired with a custombuilt pulsed electron spin resonance spectrometer. Complex mod
c ○ Rinton Press HIGHFIDELITY QUANTUM CONTROL USING ION CRYSTALS IN A PENNING TRAP
, 2009
"... We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser ..."
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We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled [1], and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays [5, 6, 7, 8]. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials [9, 10]. We discuss the use of twodimensional 9Be + ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz groundstate electron spin flip transition, which we drive using microwaves [11, 12]. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement [1] on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary highfidelity rotations (τπ ∼200 µs). Randomized Benchmarking [13] demonstrates an error per gate (a Paulirandomized π/2 and π pulse pair) of 8±1×10−4. Ramsey interferometry and spinlocking [14] measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical freeinduction decay coherence time of T2 ∼2 ms, and a limiting T1ρ ∼688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the errorsuppressing capabilities of dynamical
The final publication is available at www.springerlink.com
"... Quantum information processing manuscript No. (will be inserted by the editor) Classicalprocessing and quantumprocessing signal separation methods for qubit uncoupling ..."
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Quantum information processing manuscript No. (will be inserted by the editor) Classicalprocessing and quantumprocessing signal separation methods for qubit uncoupling
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"... Decoherence of manyspin systems in NMR: From molecular characterization to an environmentally induced quantum dynamical phase transition por ..."
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Decoherence of manyspin systems in NMR: From molecular characterization to an environmentally induced quantum dynamical phase transition por
Control Paradigms for Quantum Engineering (Invited Paper)
, 805
"... Abstract—We give an overview of different paradigms for control of quantum systems and their applications, illustrated with specific examples. We further discuss the implications of faulttolerance requirements for quantum process engineering using optimal control, and explore the possibilities for a ..."
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Abstract—We give an overview of different paradigms for control of quantum systems and their applications, illustrated with specific examples. We further discuss the implications of faulttolerance requirements for quantum process engineering using optimal control, and explore the possibilities for architecture simplification and effective control using a minimum number of simple switch actuators. I.
Acknowledgments
, 705
"... Decoherence of manyspin systems in NMR: From molecular characterization to an environmentally induced quantum dynamical phase transition ..."
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Decoherence of manyspin systems in NMR: From molecular characterization to an environmentally induced quantum dynamical phase transition