Implementing the Deutsch algorithm with polarization and transverse spatial modes

In this paper we implement a simple quantum algorithm using polarization and transverse spatial modes of the electromagnetic field as qubits. The transverse spatial modes used are the Laguerre–Gaussian and Hermite–Gaussian beams of order N = 1. With these two qubits carried by the same photon, we have implemented the Deutsch algorithm using a simple linear optical setup.

[1]  M J Padgett,et al.  Poincaré-sphere equivalent for light beams containing orbital angular momentum. , 1999, Optics letters.

[2]  F. Schmidt-Kaler,et al.  Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer , 2003, Nature.

[3]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  Marco Fiorentino,et al.  Deterministic controlled-NOT gate for single-photon two-qubit quantum logic. , 2004, Physical review letters.

[5]  N. K. Langford,et al.  Linear optical controlled- NOT gate in the coincidence basis , 2002 .

[6]  S. Barnett,et al.  Measuring the orbital angular momentum of a single photon. , 2002, Physical review letters.

[7]  Miles J. Padgett,et al.  An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes , 1996 .

[8]  Milburn,et al.  Quantum optical Fredkin gate. , 1989, Physical review letters.

[9]  Jian-Wei Pan,et al.  Realization of a photonic controlled-NOT gate sufficient for quantum computation. , 2004, Physical Review Letters.

[10]  Gerard Nienhuis,et al.  Eigenfunction description of laser beams and orbital angular momentum of light , 1992 .

[11]  Carlos H. Monken,et al.  Transfer of angular spectrum and image formation in spontaneous parametric down-conversion , 1998 .

[12]  J. P. Woerdman,et al.  Astigmatic laser mode converters and transfer of orbital angular momentum , 1993 .

[13]  J. D. Franson,et al.  Probabilistic quantum logic operations using polarizing beam splitters , 2001, quant-ph/0107091.

[14]  T. Ralph,et al.  Demonstration of an all-optical quantum controlled-NOT gate , 2003, Nature.

[15]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[16]  DiVincenzo.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[17]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[18]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[19]  Allen,et al.  Paraxial wave optics and harmonic oscillators. , 1993, Physical review. A, Atomic, molecular, and optical physics.