Quantum Computation over Continuous Variables

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform “floating point” computations. Problems of noise, finite precision, and error correction are discussed.

[1]  T. Tarn,et al.  On the controllability of quantum‐mechanical systems , 1983 .

[2]  Ramakrishna,et al.  Controllability of molecular systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[3]  Seth Lloyd,et al.  ANALOG QUANTUM ERROR CORRECTION , 1998 .

[4]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[5]  David Chaum,et al.  Advances in Cryptology: Proceedings Of Crypto 83 , 2012 .

[6]  Rolf Landauer,et al.  Dissipation and noise immunity in computation and communication , 1988, Nature.

[7]  S. Lloyd.  Quantum-Mechanical Computers , 1995 .

[8]  Ekert,et al.  Practical quantum cryptography based on two-photon interferometry. , 1992, Physical review letters.

[9]  E. Knill,et al.  Resilient Quantum Computation , 1998 .

[10]  Samuel L. Braunstein,et al.  Quantum error correction for communication with linear optics , 1998, Nature.

[11]  Samuel L. Braunstein.  Error Correction for Continuous Quantum Variables , 1998 .

[12]  N. Gisin,et al.  “Plug and play” systems for quantum cryptography , 1996, quant-ph/9611042.

[13]  S. Smale,et al.  On a theory of computation and complexity over the real numbers; np-completeness , 1989 .

[14]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[15]  Lloyd,et al.  Almost any quantum logic gate is universal. , 1995, Physical review letters.

[16]  J. Preskill.  Reliable quantum computers , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

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

[18]  Kimble,et al.  Unconditional quantum teleportation , 1998, Science.

[19]  J. Rarity,et al.  Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel , 1993 .

[20]  Hall,et al.  Generation of squeezed states by parametric down conversion. , 1986, Physical review letters.

[21]  H. Kimble,et al.  Teleportation of continuous quantum variables , 1998, Technical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236).

[22]  DiVincenzo,et al.  Fault-Tolerant Error Correction with Efficient Quantum Codes. , 1996, Physical review letters.

[23]  Hood,et al.  Measurement of conditional phase shifts for quantum logic. , 1995, Physical review letters.

[24]  N. J. Cerf,et al.  Optical simulation of quantum logic , 1998 .

[25]  A. Ekert,et al.  Universality in quantum computation , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[26]  R. Landauer.  The physical nature of information , 1996 .

[27]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.