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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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2
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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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3
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Ohtsuki Y, Goto H, Katsuki H, Ohmori K. Theoretical/numerical study on strong-laser-induced interference in the B state of I2. Phys Chem Chem Phys 2014; 16:5689-97. [DOI: 10.1039/c3cp54023e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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4
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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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von den Hoff P, Thallmair S, Kowalewski M, Siemering R, de Vivie-Riedle R. Optimal control theory--closing the gap between theory and experiment. Phys Chem Chem Phys 2012; 14:14460-85. [PMID: 23019574 DOI: 10.1039/c2cp41838j] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Optimal control theory and optimal control experiments are state-of-the-art tools to control quantum systems. Both methods have been demonstrated successfully for numerous applications in molecular physics, chemistry and biology. Modulated light pulses could be realized, driving these various control processes. Next to the control efficiency, a key issue is the understanding of the control mechanism. An obvious way is to seek support from theory. However, the underlying search strategies in theory and experiment towards the optimal laser field differ. While the optimal control theory operates in the time domain, optimal control experiments optimize the laser fields in the frequency domain. This also implies that both search procedures experience a different bias and follow different pathways on the search landscape. In this perspective we review our recent developments in optimal control theory and their applications. Especially, we focus on approaches, which close the gap between theory and experiment. To this extent we followed two ways. One uses sophisticated optimization algorithms, which enhance the capabilities of optimal control experiments. The other is to extend and modify the optimal control theory formalism in order to mimic the experimental conditions.
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Affiliation(s)
- Philipp von den Hoff
- Department of Chemistry, Ludwig-Maximilians-Universität München, München, Germany
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7
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Zaari RR, Brown A. Effect of laser pulse shaping parameters on the fidelity of quantum logic gates. J Chem Phys 2012; 137:104306. [PMID: 22979858 DOI: 10.1063/1.4747703] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT(1), NOT(2), and Hadamard(2) quantum logic gates are studied for the diatomic molecule (12)C(16)O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.
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Affiliation(s)
- Ryan R Zaari
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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MISHIMA K, YAMASHITA K. Decoherence of Entanglement in Markov Approximation in Terms of Rotating Wave Approximation. JOURNAL OF COMPUTER CHEMISTRY-JAPAN 2012. [DOI: 10.2477/jccj.2011-0016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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9
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SHARMA SITANSH, BALINT-KURTI GABRIELG, SINGH HARJINDER. Design of optimal laser pulses to control molecular rovibrational excitation in a heteronuclear diatomic molecule#. J CHEM SCI 2012. [DOI: 10.1007/s12039-011-0198-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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10
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McKemmish LK, Kedziora DJ, White GR, Hush NS, Reimers JR. Frequency-based Quantum Computers from a Chemist's Perspective. Aust J Chem 2012. [DOI: 10.1071/ch12053] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Quantum computer elements are often designed and tested using molecular or nanoscopic components that form registers of qubits in which memory is stored and information processed. Often such registers are probed and manipulated using frequency-based techniques such as nuclear-magnetic resonance spectroscopy. A major challenge is to design molecules to act as these registers. We provide a basis for rational molecular design through consideration of the generic spectroscopic properties required for quantum computing, bypassing the need for intricate knowledge of the way these molecules are used spectroscopically. Designs in which two-qubit gate times scale similarly to those for one-qubit gates are presented. The specified spectroscopic requirements are largely independent of the type of spectroscopy used (e.g. magnetic resonance or vibrational) and are often independent of technical details of the application (e.g. broadband or high-resolution spectroscopy). This should allow the design of much larger quantum registers than have currently been demonstrated.
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KUMAR PRAVEEN, SHARMA SITANSH, SINGH HARJINDER. OPTIMALLY CONTROLLED VIBRATIONAL POPULATION TRANSFER IN A DIATOMIC QUANTUM SYSTEM. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633609004605] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A time-dependent formulation of quantum control is employed to investigate optimally controlled vibrational population transfer in a diatomic quantum system. The problem of finding the optimal laser field needed to achieve a specific quantum transition from an initial state to the desired target goal is formulated using an iterative method and the conjugate gradient method (CGM). The time-dependent Schrödinger equation is solved with interaction of laser radiation with matter included within a dipole approximation in the Hamiltonian. Appropriate boundary conditions are chosen for the evolution problem. The control objective is chosen as the value of transition probability from an initial state to a target state. A comparison is made between the results obtained using the iterative method and the CGM for optimization. Finally, quantum bits are encoded using the vibrational states of the diatomic in the regime of low-vibrational excitation.
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Affiliation(s)
- PRAVEEN KUMAR
- Department of Chemistry, Panjab University, Chandigarh 160014, India
| | - SITANSH SHARMA
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500032, India
| | - HARJINDER SINGH
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500032, India
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12
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Zaari RR, Brown A. Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations. J Chem Phys 2011; 135:044317. [DOI: 10.1063/1.3617248] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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13
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The operations of quantum logic gates with pure and mixed initial states. J Chem Phys 2011; 134:134103. [DOI: 10.1063/1.3571597] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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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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15
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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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16
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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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17
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Optical modification of the vibrational distribution of the iodine molecule. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.04.073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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18
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Hosaka K, Shimada H, Chiba H, Katsuki H, Teranishi Y, Ohtsuki Y, Ohmori K. Ultrafast Fourier transform with a femtosecond-laser-driven molecule. PHYSICAL REVIEW LETTERS 2010; 104:180501. [PMID: 20482157 DOI: 10.1103/physrevlett.104.180501] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2010] [Indexed: 05/29/2023]
Abstract
Wave functions of electrically neutral systems can be used as information carriers to replace real charges in the present Si-based circuit, whose further integration will result in a possible disaster where current leakage is unavoidable with insulators thinned to atomic levels. We have experimentally demonstrated a new logic gate based on the temporal evolution of a wave function. An optically tailored vibrational wave packet in the iodine molecule implements four- and eight-element discrete Fourier transform with arbitrary real and imaginary inputs. The evolution time is 145 fs, which is shorter than the typical clock period of the current fastest Si-based computers by 3 orders of magnitudes.
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Affiliation(s)
- Kouichi Hosaka
- Institute for Molecular Science, National Institutes of Natural Sciences, Myodaiji, Okazaki 444-8585, Japan
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19
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Schröder M, Brown A. Realization of the CNOT quantum gate operation in six-dimensional ammonia using the OCT-MCTDH approach. J Chem Phys 2009; 131:034101. [DOI: 10.1063/1.3168438] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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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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22
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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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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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25
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Mishima K, Tokumo K, Yamashita K. Quantum computing using molecular electronic and vibrational states. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.10.027] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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26
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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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27
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Sugawara M, Tamaki M, Yabushita S. A new control scheme of multilevel quantum system based on effective decomposition by intense CW lasers. J Phys Chem A 2007; 111:9446-53. [PMID: 17718547 DOI: 10.1021/jp073268m] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
We propose a new scheme for quantum dynamics control of multilevel system using intense lasers. To do so, we apply intense CW lasers to create a strongly coupled subsystem with which one can make the complementary space effectively isolated, and we apply the established control schemes to the isolated subsystem. We have also obtained an effective Hamiltonian for the target subsystem with the help of the second-order perturbation theory. Numerical demonstrations on model systems show that the present decomposition scheme effectively works for population dynamics control. It is also found that relaxation processes can be suppressed under the proposed scheme.
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Affiliation(s)
- M Sugawara
- Department of Fundamental Science and Technology, Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan.
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28
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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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29
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30
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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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31
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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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32
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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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Shioya K, Mishima K, Yamashita K. Quantum computing using molecular vibrational and rotational modes. Mol Phys 2007. [DOI: 10.1080/00268970701439573] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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34
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Nagaya K, Lin SH, Nakamura H. Control of nonadiabatic dissociation dynamics with the use of laser-induced wave packet interferences. J Chem Phys 2006; 125:214311. [PMID: 17166025 DOI: 10.1063/1.2362819] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on wave packet interferences induced by a stationary laser field, a simple way of controlling nonadiabatic dissociation dynamics is proposed. We treat a simple two-state model of diatomic molecules. In this model, there exist two dissociative potential energy curves which cross and are strongly coupled at an internuclear distance, and thus dissociations into one channel are predominant. We propose a control scheme to selectively dissociate a molecule into any favorite channel by choosing the laser frequency and intensity appropriately. The semiclassical estimation of desirable laser parameters can be performed easily by regarding the dissociation processes as nonadiabatic transitions between the Floquet states. The agreement between the semiclassical estimation and the quantum wave packet calculation is found to be satisfactory in the high frequency region (> or =1000 cm(-1)) where the Floquet state picture is valid. In the low frequency region (<1000 cm(-1)), on the other hand, there are discrepancies between them due to the invalidity of the Floquet picture and the dissociation probability is sensitive to the laser phase. This control scheme is applied to the predissociation dynamics of NaI, NaI-->Na+I.
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Affiliation(s)
- K Nagaya
- Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 106, Taiwan, Republic of China.
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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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36
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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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Teranishi Y, Ohtsuki Y, Hosaka K, Chiba H, Katsuki H, Ohmori K. Implementation of quantum gate operations in molecules with weak laser fields. J Chem Phys 2006; 124:114110. [PMID: 16555877 DOI: 10.1063/1.2172605] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.
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Affiliation(s)
- Yoshiaki Teranishi
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan.
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Suzuki S, Mishima K, Yamashita K. Ab initio study of optimal control of ammonia molecular vibrational wavepackets: Towards molecular quantum computing. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.05.090] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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