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An Implementation of the Deutsch-Jozsa Algorithm on Molecular Vibronic Coherences Through Four-Wave Mixing: a Theoretical Study

Zsolt Bihary, David R. Glenn, Daniel A. Lidar, Vartkess Ara Apkarian

Published Jan 1, 2002• 29 citations
OpenAlex

Abstract

Time-Frequency Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) was recently proposed as a means to implement quantum logic using the molecular ro-vibrational manifold as a quantum register [R. Zadoyan et al., Chem. Phys. 266, (2001) 323]. We give a concrete example of how this can be accomplished through an illustrative algorithm that solves the Deutsch-Jozsa problem. We use realistic molecular parameters to recognize that, as the problem size expands, shaped pulses must be tailored to maintain fidelity of the algorithm. Key words: Four-wave mixing, coherent spectroscopy, quantum computing

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Quantum Science and Technology•Jul 4, 2023•1 citation
Time-Frequency Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) was recently proposed as a means to implement quantum logic using the molecular ro-vibrational manifold as a quantum register [R. Zadoyan et al., Chem. Phys. 266, (2001) 323]. We give a concrete example of how this can be accomplished through an illustrative algorithm that solves the Deutsch-Jozsa problem. We use realistic molecular parameters to recognize that, as the problem size expands, shaped pulses must be tailored to maintain fidelity of the algorithm. Key words: Four-wave mixing, coherent spectroscopy, quantum computing
We present a numerical investigation of the implementation of quantum logic gates through time–frequency resolved coherent anti-Stokes Raman scattering (TFRCARS) in iodine vapour. A specific scheme is given whereby two qubits are encoded in the tensor product space of vibrational and rotational molecular eigenstates. Single-qubit and controlled-logic gates are applied to test the viability of this encoding scheme. Possible experimental constraints are investigated, including the necessary precision in the timing of successive CARS pulses and the minimum resolution of spectral components within a given pulse. It is found that these requirements can be satisfied by current technology. The two-qubit Grover search is performed to demonstrate the implementation of a sequence of quantum operations. The results of our simulations suggest that TFRCARS is a promising experimental system for simple quantum information processing applications.
While formally quantum computation has become a rather well defined theoretical science, physical demonstrations are few, limited to several qubits, and to several steps in processing. At present, there is not a recognized, scalable physical method of implementation that meets the promise of true computation. We have proposed nonlinear spectroscopic methods of coherence manipulation, and in particular, Time-Frequency Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) in the molecular re-vibronic Hilbert space as a novel scheme for implementing quantum logic. The method has advantages with its demonstrable massive parallelism, therefore well suited for information transfer, while its scalability remains unresolved, both theoretically and with regard to physical implementations. We are actively following the latter, with the concept of an inhomogeneously indexed array of single quantum centers as the physical realization.
A chirped-pulse quantum control scheme applicable to Coherent Anti-Stokes Raman Scattering spectroscopy, named as C-CARS, is presented aimed at maximizing the vibrational coherence in molecules. It implies chirping of three incoming pulses in the four-wave mixing process of CARS, the pump, the Stokes and the probe, to fulfil the conditions of adiabatic passage. The scheme is derived in the framework of rotating wave approximation and adiabatic elimination of excited state manifold simplifying the four-level model system into a ``super-effective'' two level system. The robustness, spectral selectivity and adiabatic nature of this method are helpful in improving the existing methods of CARS spectroscopy for sensing, imaging and detection. We also show that the selectivity of excitation of vibrational degrees of freedom can be controlled by carefully choosing the spectral chirp rate of the pulses.
Abstract A chirped-pulse quantum control scheme applicable to coherent anti-Stokes Raman scattering spectroscopy, named as C-CARS, is presented aimed at maximizing the vibrational coherence in molecules. It implies chirping of three incoming pulses in the four-wave mixing process of CARS, the pump, the Stokes and the probe, to fulfill the conditions of adiabatic passage. The scheme is derived in the framework of rotating wave approximation and adiabatic elimination of excited state manifold simplifying the four-level model system into a ‘super-effective’ two level system. We demonstrate that the selectivity of excitation of vibrational degrees of freedom can be controlled by carefully choosing the spectral chirp rate of the pulses. The robustness, spectral selectivity and adiabatic nature of this method are advantageous for improving the existing methods of CARS spectroscopy for sensing, imaging and detection.