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arXiv:quant-ph/0110041 · Chemical Physics Letters

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, V. Ara Apkarian

Published Jul 1, 2002• 29 citations
arXivHTMLPDF
DOI
10.1016/s0009-2614(02)00808-4

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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
The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of Li2_{2}2​ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, using a second femtosecond pulse at a specific time delay.
The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of Li2{\mathrm{Li}}_{2}Li2​ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, using a second femtosecond pulse at a specific time delay.