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arXiv:quant-ph/0107058 · Physical Review A

Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using pure coherent molecular superpositions

Jiří Vala, Zohar Amitay, Bo Zhang, Stephen R. Leone, Ronnie Kosloff

Published Dec 26, 2002• 78 citations
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Abstract

The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of ${\mathrm{Li}}_{2}$ 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.

DOI
10.1103/physreva.66.062316

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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.
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.
A new approach to the implementation of a quantum computer by high-resolution nuclear magnetic resonance (NMR) is described. The key feature is that two or more line-selective radio-frequency pulses are applied simultaneously. A three-qubit quantum computer has been investigated using the 400 MHz NMR spectrum of the three coupled protons in 2,3-dibromopropanoic acid. It has been employed to implement the Deutsch-Jozsa algorithm for distinguishing between constant and balanced functions. The extension to systems containing more coupled spins is straightforward and does not require a more protracted experiment.
We propose a way to implement a three-qubit refined Deutsh-Jozsa (DJ) algorithm. The present proposal is based on the construction of the 35 fff-controlled phase gates, which uses single-qubit σzσ_zσz​ gates and two-qubit {\it standard} controlled-phase (CP) gates only. This proposal is implementable because a single-qubit σzσ_zσz​ gate can be easily realized by applying a single classical pulse and a two-qubit CP gate has been experimentally demonstrated in various physical systems. Finally, it is noted that this proposal is quite general, and can be applied to implement a three-qubit refined DJ algorithm in a cavity-based or noncavity-based physical system.
The optimized version of the Deutsch-Jozsa algorithm proposed by Collins et al. was implemented using the three 19F^{19}\mathrm{F}19F nuclear spins of 2,3,4-trifluoroaniline as qubits. To emulate the behavior of pure quantum-mechanical states pseudopure states of the ensemble were prepared prior to execution of the algorithm. Full tomography of the density matrix was employed to obtain detailed information about initial, intermediate, and final states. Information, thus obtained, was applied to optimize the pulse sequences used. It is shown that substantial improvement of the fidelity of the preparation may be achieved by compensating the effects caused by the different relaxation behavior of the different substates of the density matrix. All manipulations of the quantum states were performed under the conditions of unresolved spin-spin interactions.
We show that the Deutsch-Jozsa algorithm for up to four qubits can be realized with a setup of Josephson charge qubits. While existing proposals for the implementation of the algorithm (for up to three qubits) are based on certain classifications of the oracles, this approach becomes increasingly cumbersome for higher qubit numbers. Here we present a method to implement all balanced functions for the four-qubit algorithm by a fixed sequence of operations. The free parameters which define the implemented function are the rotation angles of 15 one-qubit operations.