## An Introduction to Quantum Computing for Non-Physicists (2000)

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Venue: | Los Alamos Physics Preprint Archive http://xxx.lanl.gov/abs/quant-ph/9809016 |

Citations: | 93 - 5 self |

### BibTeX

@INPROCEEDINGS{Rieffel00anintroduction,

author = {Eleanor Rieffel},

title = {An Introduction to Quantum Computing for Non-Physicists},

booktitle = {Los Alamos Physics Preprint Archive http://xxx.lanl.gov/abs/quant-ph/9809016},

year = {2000}

}

### Years of Citing Articles

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### Abstract

### Citations

875 | Polynomial-time algorithm for prime factorization and discrete logarithm on quantum computer - Shor - 1997 |

843 | An Introduction to the Theory of Numbers - Hardy, Wright - 2005 |

840 | A fast quantum mechanical algorithm for database search - Grover - 1996 |

807 | Algorithms for Quantum Computation: Discrete Logarithms and Factoring - Shor - 1994 |

650 | Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer - Deutsch - 1985 |

392 | Simulating physics with computers - Feynman - 1982 |

339 | Rapid solutions of problems by quantum computation - Deutsch, Jozsa - 1992 |

313 | Strengths and weaknesses of quantum computing - Bennett, Bernstein, et al. - 1997 |

266 |
The Feynman Lectures on
- Feynman, Leighton, et al.
- 1963
(Show Context)
Citation Context .... 2 Quantum Mechanics Quantum phenomena are difficult to understand since most of our everyday experiences are not applicable. This paper cannot provide a deep understanding of quantum mechanics (see =-=[9]-=-, [10], or [11] for details). Instead, we will give some feeling as to the nature of quantum mechanics and some of the mathematical formalisms needed to work with quantum mechanics to the extent neede... |

200 | Elementary gates for quantum computation - Barenco, Bennett, et al. - 1995 |

197 | Experimental quantum cryptography - Bennett, Bessette, et al. - 1990 |

142 | A single quantum cannot be cloned. Nature 299, 802. Discussion P. Marcer (BCS Cybernetic Machine Group - Wootters, Zurek - 1982 |

138 | Unconditional security in quantum cryptography - Mayers - 1998 |

133 | Quantum Computations with Cold Trapped Ions - Cirac, Zoller - 1995 |

129 | Unconditional Security of Quantum Key Distribution over Arbitrarily Long Distances - Lo, Chau - 1999 |

119 | Quantum cryptography using any two nonorthogonal states - Bennett - 1992 |

101 | Quantum counting - Brassard, Høyer, et al. |

97 |
Feynman lectures on computation
- Feynman
- 1996
(Show Context)
Citation Context ...they are reversible. Thus quantum gates must be reversible. Bennett, Fredkin, and Toffoli had already looked at reversible versions of standard computing models. See Feynman’s Lectures on Computation =-=[18]-=- for an account of some of the central ideas in this work. 154.1 Simple Quantum Gates The following are some examples of useful single-qubit quantum state transformations. Because of linearity, the t... |

92 | Grover’s quantum searching algorithm is optimal
- Zalka
- 1999
(Show Context)
Citation Context ...ly more efficient than any algorithm that could run on a classical computer. Grover’s search algorithm searches a completely unstructured solution space. While Grover’s algorithm is optimal [28] [29] =-=[30]-=-, for completely unstructured searches, most search problems involve searching a structured solution space. One would expect that this structure would enable more efficient searching 30strategies. Fo... |

85 | Bulk spin resonance quantum computation - Gershenfeld, Chuang - 1997 |

85 | Quantum networks for elementary arithmetic operations - Vedral, Barenco, et al. - 1995 |

84 | A framework for fast quantum mechanical algorithms. To appear - Grover - 1998 |

54 |
Nature 299
- Wooters, Zurek
- 1982
(Show Context)
Citation Context ...omposition of the form W1 = H, Wn+1 = H ⊗ Wn. 4.1.2 No Cloning The unitary property implies that quantum state cannot be cloned. The no cloning proof given here, originally due to Wootters and Zurek (=-=[19]-=-), is a simple application of the linearity of unitary transformations. 17Assume that U is a unitary transformation that clones, in that U(|a0〉) = |aa〉 for all quantum states |a〉. Let |a〉 and |b〉 be ... |

35 |
Nonlinear quantum mechanics implies polynomialtime solution for NP-complete and #P
- Abrams, Lloyd
- 1998
(Show Context)
Citation Context ...ons might be slightly non-linear. So far all experiments that have been done are consistent with the standard linear quantum mechanics, but a slight non-linearity is still possible. Abrams and Lloyd (=-=[38]-=-) show that even a very slight non-linearity could be exploited to solve all NP hard problem on a quantum computer in polynomial time. This result further highlights the fact that computation is funda... |

34 | Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys - Boschi, Branca, et al. - 1998 |

30 | Generalized Grover search algorithm for arbitrary initial amplitude distribution - Biron, Biham, et al. |

28 | Experimental quantum teleportation - Bouwmeester, Pan, et al. - 1997 |

25 |
The Principles of Quantum Mechanics, 4th ed
- Dirac
- 1958
(Show Context)
Citation Context ...found. Quantum state spaces and the tranformations acting on them can be described in terms of vectors and matrices or in the more compact bra/ket notation. The bra/ket notation was invented by Dirac =-=[12]-=-. Kets like |x〉 denote column vectors and are typically used to describe quantum states. The matching bra, 〈x|, denotes the conjugate transpose of |x〉. For example, the orthonormal basis{(1, 0) T , (0... |

25 | An Introduction to the Theory of Numbers (Oxford - Hardy, Wright - 2006 |

23 | Complete quantum teleportation using nuclear magnetic resonance - Nielsen, Knill, et al. - 1998 |

22 |
et al, Nature 390
- Bouwmeester
- 1997
(Show Context)
Citation Context ...tum state at the receiver. Since quantum state cannot be cloned, the quantum state of the given particle will necessarily be destroyed. Single bit teleportation has been realized experimentally 1997 (=-=[20]-=-). Alice Bob Decoder Encoder EPR source Alice: Alice wants to send the state of the qubit φ = a|0〉 + b|1〉 to Bob through classical channels. As with dense coding, Alice and Bob each possess one qubit ... |

21 | Practical quantum cryptography based on two-photon interferometry - Rarity, Tapster, et al. - 1992 |

21 | Quantum computing and phase transitions in combinatorial search - Hogg - 1996 |

19 | C.P.Williams, Nested quantum search and NP-complete problems, Phys - Cerf - 2000 |

16 | Highly structured searches with quantum computers, Phys - Hogg - 1998 |

16 | The Development of the Number Field Sieve, volume 1554 - Lenstra, Lenstra |

16 | The ion trap quantum information processor
- Steane
- 1997
(Show Context)
Citation Context ...be built. There are a number of proposals for building quantum computers most of which are based either on ion traps or on nuclear magnetic resonance (NMR) technology. In an ion trap quantum computer =-=[4, 5]-=- a linear sequence of ions (qubits) are confined by electric fields. Lasers are directed at individual atoms to perform single bit quantum gates. Two-bit operations are realized by using a laser on on... |

15 | Algebra - Hungerford - 1974 |

13 | Quantum computation, Reports on - Steane - 1998 |

13 |
Scalable NMR quantum computation
- Schulman, Vazirani
- 1998
(Show Context)
Citation Context ...te can be measured with NMR techniques. The main problem with the technique is that it doesn’t scale well; the measured signal scales as 1/2 n with the number of qubits n. However, a recent proposal (=-=[6]-=-) has been made that may overcome this problem. NMR computers with two qubits have been built successfully [7, 8]. This paper will not discuss further the physical and engineering problems of building... |

11 | Relationships between quantum and classical space-bounded complexity classes - WATROUS - 1998 |

10 | The Quantum Challenge - GREENSTEIN, ZAJONC - 1997 |

9 | Quantum Public Key Distribution Reinvented - Bennett, Brassard - 1987 |

8 |
Optics News 11
- Feynman
- 1985
(Show Context)
Citation Context ...s related to quantum computing than the present paper, and has more references as well. Richard Feynman’s Lectures on Computation [18] contains a reprint of the lecture “Quantum Mechanical Computers” =-=[39]-=- which began the whole field. It also discusses the thermodynamics of computations which is closely tied with reversible computing and information theory. Colin Williams and Scott Clearwater’s book Ex... |

7 |
Introductory Quantum Mechanics (3rd edition
- LIBOFF
- 1997
(Show Context)
Citation Context ...chanics Quantum phenomena are difficult to understand since most of our everyday experiences are not applicable. This paper cannot provide a deep understanding of quantum mechanics (see [9], [10], or =-=[11]-=- for details). Instead, we will give some feeling as to the nature of quantum mechanics and some of the mathematical formalisms needed to work with quantum mechanics to the extent needed for quantum c... |

6 |
Single quantum querying of a database
- TERHAL, SMOLIN
- 1997
(Show Context)
Citation Context ...time algorithm [35] that can distinguish whether a function is balanced or constant. Grover ([36]) describes an efficient algorithm for estimating the median of a set of values and Terhal and Smolin (=-=[37]-=-) can solve the coin weighing problem in a single step. Beyond these algorithms not much more is known about what could be done with a practical quantum computer. It is an open question whether or not... |

5 | Practical quantum cryptography for secure free-space communications. Preprint at Los Alamos Physics Preprint Archive - HUGHES, BUTTLER, et al. - 1999 |

4 | Experimental quantum error correction. Preprint at Los Alamos Physics Preprint Archive - CORY, MASS, et al. - 1998 |

4 | Secure communications using quantum cryptography - HUGHES, BUTTLER, et al. - 1997 |

4 | Realization of effective pure states for bulk quantum computation - Vandersypen, Yannoni, et al. - 1999 |