An implementation of the Deutsch–Jozsa algorithm on molecular vibronic coherences through four-wave mixing: a theoretical study

Bihary, Zsolt; Glenn, David; Lidar, Daniel A.; Apkarian, V. A.

doi:10.1016/s0009-2614(02)00808-4

Cited by 34 publications

(46 citation statements)

References 31 publications

(36 reference statements)

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“…37,37,61,64 Similar controlled gates are possible between rotation-vibration, and rotation-electronic qubits. 72 Here, we are satisfied by indicating that the requisite two-qubit CNOT gate and the one-qubit operations are naturally wired in molecular four-wave mixing, sufficient to identify the potential of the system for quantum computing. A schematic of the general conceptual approach to using the present network for a single path in vibrational vector space is provided in Fig.…”

Section: B) Universal Logic Gatesmentioning

confidence: 95%

The manipulation of massive ro-vibronic superpositions using time–frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

et al. 2001

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Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in TimeFrequency-Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 10 3 eigenstates, is followed through two-dimensional images. The first-and second-order coherences are captured using time-integrated frequencyresolved CARS, while the third-order coherence is captured using time-gated frequency-resolved CARS. The Fourier filtering provided by time integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation-vibration-electronic Hilbert space, using time circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing -all single qubit operations and the two-qubit controlled-NOT (CNOT) gate -are available in time resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally "wired" for carrying out all single qubit operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-qubit CNOT gate, wherein the vibrational qubit controls the switching of the targeted electronic qubit. † Present address:

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Section: B) Universal Logic Gatesmentioning

confidence: 95%

The manipulation of massive ro-vibronic superpositions using time–frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

et al. 2001

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“…transitions between the pre chosen quantum states of the system) are realized by specially shaped femtosecond laser pulses. 38,95,96 This new approach has been followed by numerous studies working with internal motional states of molecules such as rovibrational states 97 and vibrational states in diatomic [98][99][100] and polyatomic systems. 38,95,96,101,102 For the concept of molecular quantum computing using vibrational qubits we were able to implement a set of elemen tary quantum gates for different polyatomic systems using IR light fields.…”

Section: Optimizing Quantum Gatesmentioning

confidence: 99%

Optimal control theory – closing the gap between theory and experiment

Hoff

Thallmair

Kowalewski

et al. 2012

Phys. Chem. Chem. Phys.

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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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“…We have carried out developments of the process in the gas phase, [11,15], to clearly identify the processes involved, and to map out the optical scattering process in terms of quantum logic gates implemented in the molecular Hubert space [13]. After showing that the required logic gates for executing arbitrary quantum computing naturally occurs in TFRCARS, we have illustrated how such gates can be put together to carry out an algorithm, and in particular the Deutsch-Jozsa algorithm which has become a benchmark for such implementations [20]. The method is of course highly useful in interrogations of molecular coherences in condensed media, and we have already implemented this approach in the solid state, to develop a detailed picture of vibrational dephasing in the model system of iodine isolated in rare gas solids [13,18].…”

Section: Accomplishments and New Findingsmentioning

confidence: 99%

Dynamical Spectroscopy of Prototypes in Condensed Phase Chemistry

Apkarian¹

2001

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An implementation of the Deutsch–Jozsa algorithm on molecular vibronic coherences through four-wave mixing: a theoretical study

Cited by 34 publications

References 31 publications

The manipulation of massive ro-vibronic superpositions using time–frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

The manipulation of massive ro-vibronic superpositions using time–frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

Optimal control theory – closing the gap between theory and experiment

Dynamical Spectroscopy of Prototypes in Condensed Phase Chemistry

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