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Yan TM, Fresch B, Levine RD, Remacle F. Information processing in parallel through directionally resolved molecular polarization components in coherent multidimensional spectroscopy. J Chem Phys 2015; 143:064106. [DOI: 10.1063/1.4928066] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tian-Min Yan
- Department de Chimie, B6c, Université de Liège, B4000 Liège, Belgium
| | - Barbara Fresch
- Department de Chimie, B6c, Université de Liège, B4000 Liège, Belgium
| | - R. D. Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
- Crump Institute for Molecular Imaging and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine and Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - F. Remacle
- Department de Chimie, B6c, Université de Liège, B4000 Liège, Belgium
- The Fritz Haber Research Center for Molecular Dynamics, The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Santos L, Justum Y, Vaeck N, Desouter-Lecomte M. Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap. J Chem Phys 2015; 142:134304. [DOI: 10.1063/1.4916355] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ludovic Santos
- Laboratoire de Chimie Quantique et Photophysique, CP 160/09 Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - Yves Justum
- Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, F-91405 Orsay, France
| | - Nathalie Vaeck
- Laboratoire de Chimie Quantique et Photophysique, CP 160/09 Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - M. Desouter-Lecomte
- Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, F-91405 Orsay, France
- Département de Chimie, Université de Liège, Bât B6c, Sart Tilman B-4000, Liège, Belgium
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Shyshlov D, Berrios E, Gruebele M, Babikov D. On readout of vibrational qubits using quantum beats. J Chem Phys 2014; 141:224306. [PMID: 25494748 DOI: 10.1063/1.4903055] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dmytro Shyshlov
- Chemistry Department, Marquette University, Milwaukee, Wisconsin 53201, USA
| | - Eduardo Berrios
- Department of Chemistry, Department of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
| | - Martin Gruebele
- Department of Chemistry, Department of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
| | - Dmitri Babikov
- Chemistry Department, Marquette University, Milwaukee, Wisconsin 53201, USA
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Jaouadi A, Barrez E, Justum Y, Desouter-Lecomte M. Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design. J Chem Phys 2013; 139:014310. [PMID: 23822306 DOI: 10.1063/1.4812317] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We simulate the implementation of a 3-qubit quantum Fourier transform gate in the hyperfine levels of ultracold polar alkali dimers in their first two lowest rotational levels. The chosen dimer is (41)K(87)Rb supposed to be trapped in an optical lattice. The hyperfine levels are split by a static magnetic field. The pulses operating in the microwave domain are obtained by optimal control theory. We revisit the problem of phase control in information processing. We compare the efficiency of two optimal fields. The first one is obtained from a functional based on the average of the transition probabilities for each computational basis state but constrained by a supplementary transformation to enforce phase alignment. The second is obtained from a functional constructed on the phase sensitive fidelity involving the sum of the transition amplitudes without any supplementary constrain.
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Affiliation(s)
- A Jaouadi
- Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, Orsay, France
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5
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Shyshlov D, Babikov D. Complexity and simplicity of optimal control theory pulses shaped for controlling vibrational qubits. J Chem Phys 2012. [PMID: 23181317 DOI: 10.1063/1.4765344] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the context of molecular quantum computation the optimal control theory (OCT) is used to obtain shaped laser pulses for high-fidelity control of vibrational qubits. Optimization is done in time domain and the OCT algorithm varies values of electric field in each time step independently, tuning hundreds of thousands of parameters to find one optimal solution. Such flexibility is not available in experiments, where pulse shaping is done in frequency domain and the number of "tuning knobs" is much smaller. The question of possible experimental interpretations of theoretically found OCT solutions arises. In this work we analyze very accurate optimal pulse that we obtained for implementing quantum gate CNOT for the two-qubit system encoded into the exited vibrational states of thiophosgene molecule. Next, we try to alter this pulse by reducing the number of available frequency channels and intentionally introducing systematic and random errors (in frequency domain, by modifying the values of amplitudes and phases of different frequency components). We conclude that a very limited number of frequency components (only 32 in the model of thiophosgene) are really necessary for accurate control of the vibrational two-qubit system, and such pulses can be readily constructed using OCT. If the amplitude and phase errors of different frequency components do not exceed ±3% of the optimal values, one can still achieve accurate transformations of the vibrational two-qubit system, with gate fidelity of CNOT exceeding 0.99.
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Affiliation(s)
- Dmytro Shyshlov
- Department of Chemistry, Marquette University, PO Box 1881, Milwaukee, Wisconsin 53201, USA
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Pouthier V. Vibrons in finite size molecular lattices: a route for high-fidelity quantum state transfer at room temperature. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:445401. [PMID: 23044492 DOI: 10.1088/0953-8984/24/44/445401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
A communication protocol is proposed in which vibron-mediated quantum state transfer takes place in a molecular lattice. We consider two distant molecular groups grafted on each side of the lattice. These groups form two quantum computers where vibrational qubits are implemented and received. The lattice defines the communication channel along which a vibron delocalizes and interacts with a phonon bath. Using quasi-degenerate perturbation theory, vibron-phonon entanglement is taken into account through the effective Hamiltonian concept. A vibron is thus dressed by a virtual phonon cloud whereas a phonon is clothed by virtual vibronic transitions. It is shown that three quasi-degenerate dressed states define the relevant paths followed by a vibron to tunnel between the computers. When the coupling between the computers and the lattice is judiciously chosen, constructive interference takes place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.
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Affiliation(s)
- Vincent Pouthier
- Institut UTINAM, Université de Franche-Comté, UMR CNRS 6213, 25030 Besançon Cedex, France.
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7
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Pellegrini P, Vranckx S, Desouter-Lecomte M. Implementing quantum algorithms in hyperfine levels of ultracold polar molecules by optimal control. Phys Chem Chem Phys 2011; 13:18864-71. [DOI: 10.1039/c1cp21184f] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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8
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Bomble L, Lauvergnat D, Remacle F, Desouter-Lecomte M. Controlled full adder-subtractor by vibrational computing. Phys Chem Chem Phys 2010; 12:15628-35. [PMID: 20661490 DOI: 10.1039/c003687k] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The implementation of a quantum-controlled full adder-subtractor of two binary digits and of a "carry in" or a "borrow in" is simulated by encoding four qubits in the vibrational eigenstates of a tetra-atomic molecule (trans-HONO). The laser field of the gate is computed using optimal control theory by treating dynamics in full dimensionality. A controlled qubit enforces the addition or the subtraction. The global unitary transformation that connects the inputs to the outputs is driven by a single laser pulse. This decreases the duration of the operation and allows for a better use of the optical resources and for an improvement of the fidelity (>97%). Initialization and reading out are discussed. The timescale of the sequence initialization, gate and read out is<100 ps.
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Affiliation(s)
- Laëtitia Bomble
- Laboratoire de Chimie Physique, Université de Paris-Sud, UMR8000, Orsay, F-91405, France
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Weidinger D, Gruebele M. Quantum computation with vibrationally excited polyatomic molecules: effects of rotation, level structure, and field gradients. Mol Phys 2010. [DOI: 10.1080/00268970701504335] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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10
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Maximov II, Salomon J, Turinici G, Nielsen NC. A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design. J Chem Phys 2010; 132:084107. [DOI: 10.1063/1.3328783] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Zaari RR, Brown A. Quantum gate operations using midinfrared binary shaped pulses on the rovibrational states of carbon monoxide. J Chem Phys 2010; 132:014307. [PMID: 20078161 DOI: 10.1063/1.3290957] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Frequency domain shaped binary laser pulses were optimized to perform 2 qubit quantum gate operations in (12)C(16)O. The qubit rovibrational state representation was chosen so that all gate operations consisted of one-photon transitions. The amplitude and phase varied binary pulses were determined using a genetic algorithm optimization routine. Binary pulses have two possible amplitudes, 0 or 1, and two phases, 0 or pi, for each frequency component of the pulse. Binary pulses are the simplest to shape experimentally and provide a minimum fidelity limit for amplitude and phase shaped pulses. With the current choice of qubit representation and using optimized binary pulses, fidelities of 0.80 and as high as 0.97 were achieved for the controlled-NOT and alternative controlled-NOT quantum gates. This indicates that with a judicious choice of qubits, most of the required control can be obtained with a binary pulse. Limited control was observed for 2 qubit NOT and Hadamard gates due to the need to control multiple excitations. The current choice of qubit representation produces pulses with decreased energies and superior fidelities when compared with rovibrational qubit representations consisting of two-photon transitions. The choice of input pulse energy is important and applying pulses of increased energy does not necessarily lead to a better fidelity.
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Affiliation(s)
- Ryan R Zaari
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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Gu Y, Babikov D. On the role of vibrational anharmonicities in a two-qubit system. J Chem Phys 2009; 131:034306. [PMID: 19624196 DOI: 10.1063/1.3152487] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Anharmonicities of vibrational modes allow controlling state-to-state transitions and encoding quantum information bits into vibrational eigenstates. Resonances between different transitions hinder the control. In this paper all resonances that can occur in a two-qubit system are identified and studied. Computational experiments are carried out using optimal control theory and numerical propagation of vibrational wave packets. Useful insight is obtained into the mechanisms of negative effect of these resonances onto the control tasks. A set of general criteria is derived for evaluation of candidate molecules for practical realization of vibrational two-qubit system. Several simple strategies for avoiding such resonances by choosing suitable vibrational characteristics (mode frequencies and anharmonicities) are proposed.
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Affiliation(s)
- Yingying Gu
- Department of Chemistry, Marquette University, P.O. Box 1881, Milwaukee, Wisconsin 53201, USA
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Abstract
This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, National Institutes of Natural Sciences; The Graduate University for Advanced Studies (SOKENDAI); and CREST, Japan Science and Technology Agency, Myodaiji, Okazaki 444-8585, Japan
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Bomble L, Lavorel B, Remacle F, Desouter-Lecomte M. Computational investigation and experimental considerations for the classical implementation of a full adder on SO2 by optical pump-probe schemes. J Chem Phys 2008; 128:194308. [PMID: 18500866 DOI: 10.1063/1.2920486] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Following the scheme recently proposed by Remacle and Levine [Phys. Rev. A 73, 033820 (2006)], we investigate the concrete implementation of a classical full adder on two electronic states (X 1A1 and C 1B2) of the SO2 molecule by optical pump-probe laser pulses using intuitive and counterintuitive (stimulated Raman adiabatic passage) excitation schemes. The resources needed for providing the inputs and reading out are discussed, as well as the conditions for achieving robustness in both the intuitive and counterintuitive pump-dump sequences. The fidelity of the scheme is analyzed with respect to experimental noise and two kinds of perturbations: The coupling to the neighboring rovibrational states and a finite rotational temperature that leads to a mixture for the initial state. It is shown that the logic processing of a full addition cycle can be realistically experimentally implemented on a picosecond time scale while the readout takes a few nanoseconds.
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Affiliation(s)
- L Bomble
- Laboratoire de Chimie Physique, Université de Paris-Sud, Unité Mixte de Recherches 8000, Orsay F-91405, France
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15
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Kryachko ES, Remacle F. Implementation of simple logic gates on gold–ammonia bonding patterns in different charge states. Mol Phys 2008. [DOI: 10.1080/00268970701881170] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Bomble L, Lauvergnat D, Remacle F, Desouter-Lecomte M. Vibrational computing: simulation of a full adder by optimal control. J Chem Phys 2008; 128:064110. [PMID: 18282031 DOI: 10.1063/1.2806800] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale.
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Affiliation(s)
- L Bomble
- Laboratoire de Chimie Physique, Université Paris-Sud, UMR 8000, Orsay F-91405, France
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18
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Mishima K, Yamashita K. Partitioning of entangling interactions in terms of rotating wave approximation: An approach to the Bell state generation by laser fields. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.09.041] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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19
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de Vivie-Riedle R, Troppmann U. Femtosecond Lasers for Quantum Information Technology. Chem Rev 2007; 107:5082-100. [DOI: 10.1021/cr040094l] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Regina de Vivie-Riedle
- Department Chemie, Ludwig Maximilians Universität, Butenandtstrasse 11, 81377 München, Germany
| | - Ulrike Troppmann
- Department Chemie, Ludwig Maximilians Universität, Butenandtstrasse 11, 81377 München, Germany
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Schneider B, Gollub C, Kompa KL, de Vivie-Riedle R. Robustness of quantum gates operating on the high frequency modes of MnBr(CO)5. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.05.027] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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21
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Cheng T, Brown A. Quantum computing based on vibrational eigenstates: pulse area theorem analysis. J Chem Phys 2007; 124:034111. [PMID: 16438571 DOI: 10.1063/1.2164457] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.
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Affiliation(s)
- Taiwang Cheng
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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23
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Ndong M, Lauvergnat D, Chapuisat X, Desouter-Lecomte M. Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment. J Chem Phys 2007; 126:244505. [PMID: 17614562 DOI: 10.1063/1.2743429] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.
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Affiliation(s)
- M Ndong
- Laboratoire de Chimie Physique, Université Paris-Sud, UMR8000, Orsay, F-91405, France
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Zhao M, Babikov D. Anharmonic properties of the vibrational quantum computer. J Chem Phys 2007; 126:204102. [PMID: 17552749 DOI: 10.1063/1.2736693] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We developed an efficient approach to study the coherent control of vibrational state-to-state transitions. The approximations employed in our model are valid in the regime of the low vibrational excitation specific to the vibrational quantum computer. Using this approach we explored how the vibrational properties of a two-qubit system affect the accuracy of subpicosecond quantum gates. The optimal control theory and numerical propagation of laser-driven vibrational wave packets were employed. The focus was on understanding the effect of the three anharmonicity parameters of the system. In the three-dimensional anharmonicity parameter space we identified several spots of high fidelity separated by low fidelity planar regions. The seemingly complicated picture is explained in terms of interferences between different state-to-state transitions. Very general analytic relationships between the anharmonicity parameters and the frequencies are derived to describe the observed features. Geometrically, these expressions represent planes in the three-dimensional anharmonicity parameter space. Results of this work should help to choose a suitable candidate molecule for the practical implementation of the vibrational two-qubit system.
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Affiliation(s)
- Meiyu Zhao
- Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881, USA
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25
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Abstract
In order to use molecular vibrations for quantum information processing one should be able to shape infrared laser pulses so that they can play the role of accurate quantum gates and drive the required vibrational transitions. In this paper we studied theoretically how the relative phase of the optimized transitions affects accuracy of the quantum gates in such a system. Optimal control theory and numerical propagation of laser-driven vibrational wave packets were employed. The dependencies observed for one-qubit gates NOT, pi-rotation, and Hadamard transform are qualitatively similar to each other. The results of the numerical tests agree well with the analytical predictions.
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Affiliation(s)
- Meiyu Zhao
- Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, WI 53201-1881, USA
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26
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Control strategies for reactive processes involving vibrationally hot product states. J Photochem Photobiol A Chem 2006. [DOI: 10.1016/j.jphotochem.2006.02.017] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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27
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Shen Z, Hsieh M, Rabitz H. Quantum optimal control: Hessian analysis of the control landscape. J Chem Phys 2006; 124:204106. [PMID: 16774318 DOI: 10.1063/1.2198836] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Seeking an effective quantum control entails searching over a landscape defined as the objective as a functional of the control field. This paper considers the problem of driving a state-to-state transition in a finite level quantum system, and analyzes the local topology of the landscape of the final transition probability in terms of the variables specifying the control field. Numerical calculation of the eigenvalues of the Hessian of the transition probability with respect to the control field variables reveals systematic structure in the spectra reflecting the existence of a generic and simple control landscape topology. An illustration shows that the number of nonzero Hessian eigenvalues is determined by the number of quantum states in the system. The Hessian eigenvectors associated with its nonzero eigenvalues are shown to give insight into the cooperative roles of the control variables. The practical consequences of these findings for quantum control are discussed.
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Affiliation(s)
- Zhenwen Shen
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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28
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Cheng T, Brown A. Pulse shaping for optimal control of molecular processes. J Chem Phys 2006; 124:144109. [PMID: 16626182 DOI: 10.1063/1.2187977] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this paper, a new method is proposed to design optimized control fields with desired temporal and/or spectral properties. The method is based on penalizing the difference between an optimized field obtained from an iterative scheme and a reference field with desired temporal and/or spectral properties. Compared with the standard optimal control theory, the current method allows a simple, experimentally accessible field be found on the fly; while compared with parameter space searching optimization, the iterative nature of this method allows automatic exploration of the intrinsic mechanism of the population transfer. The method is illustrated by examing the optimal control of vibrational excitation of the Cl-O bond with both temporally and spectrally restricted pulses.
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Affiliation(s)
- Taiwang Cheng
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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Korff BMR, Troppmann U, Kompa KL, de Vivie-Riedle R. Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime. J Chem Phys 2005; 123:244509. [PMID: 16396551 DOI: 10.1063/1.2141615] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Our concept for a quantum computational system is based on qubits encoded in vibrational normal modes of polyatomic molecules. The quantum gates are implemented by shaped femtosecond laser pulses. We adopt this concept to the new species manganese pentacarbonyl bromide [MnBr(CO)5] and show that it is a promising candidate in the mid-infrared (IR) frequency range to connect theory and experiment. As direct reference for the ab initio calculations we evaluated experimentally the absorption bands of MnBr(CO)5 in the mid-IR as well as the related transition dipole moments. The two-dimensional potential-energy surface spanned by the two strongest IR active modes and the dipole vector surfaces are calculated with density-functional theory. The vibrational eigenstates representing the qubit system are determined. Laser pulses are optimized by multitarget optimal control theory to form a set of global quantum gates: NOT, CNOT, Pi, and Hadamard. For all of them simply structured pulses with low pulse energies around 1 microJ could be obtained. Exemplarily for the CNOT gate we investigated the possible transfer to experimental shaping, based on the mask function for pulse shaping in the frequency regime as well as decomposition into a train of subpulses.
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Affiliation(s)
- B M R Korff
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
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