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Title: Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics

Abstract

It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch–Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.

Authors:
;
Publication Date:
OSTI Identifier:
22617463
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 377; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; OPTICS; PHOTONS; QUBITS

Citation Formats

Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn, and Liu, Ji-Zhen. Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.01.012.
Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn, & Liu, Ji-Zhen. Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics. United States. doi:10.1016/J.AOP.2017.01.012.
Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn, and Liu, Ji-Zhen. Wed . "Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics". United States. doi:10.1016/J.AOP.2017.01.012.
@article{osti_22617463,
title = {Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics},
author = {Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn and Liu, Ji-Zhen},
abstractNote = {It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch–Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.},
doi = {10.1016/J.AOP.2017.01.012},
journal = {Annals of Physics},
number = ,
volume = 377,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2017},
month = {Wed Feb 15 00:00:00 EST 2017}
}
  • A general framework for regarding oracle-assisted quantum algorithms as tools for discriminating among unitary transformations is described. This framework is applied to the Deutsch-Jozsa problem and all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form are derived. It is also used to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution-state NMR can only succeed with greater probability than a classical algorithm when the problem size n exceeds {approx}10{sup 5}.
  • The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of Li{sub 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 optimized version of the Deutsch-Jozsa algorithm proposed by Collins et al. was implemented using the three {sup 19}F 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 behaviormore » of the different substates of the density matrix. All manipulations of the quantum states were performed under the conditions of unresolved spin-spin interactions.« less
  • We describe an experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a two-bit Boolean function in the framework of one-way quantum computation. For this purpose, a two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at {approx}1 kHz success rate, demonstrates the correct implementation of the algorithm.
  • We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate general n-qubit versions and a scalable method to produce them. For this purpose, we propose a versatile photonic on-chip setup.