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## The physical implementation of quantum computation (2000)

Venue: | Fortschr. Phys |

Citations: | 72 - 0 self |

### Citations

960 |
Quantum Cryptography: Public Key Distribution and Coin Tossing
- Bennett, Brassard
- 1984
(Show Context)
Citation Context ... are tasks that are doable in the quantum world that have no counterpart classically: quantum cryptography provides an absolute secrecy of communication between parties that is impossible classically =-=[18]-=-. And for some games, winning strategies become possible with the use of quantum resources that are not available otherwise [19, 20]. This issue, and this chapter, are primarily concerned with the ``h... |

763 |
Quantum Computation and Quantum Information,” Cambridge Univ
- Nielsen, Chuang
- 2000
(Show Context)
Citation Context ...uantum states of the qubit can play a role (in a special form of state decay called ``leakageº in quantum computing [29, 30]), is rather more technical than I want to get here; but see Refs. [31] and =-=[32]-=- for a good general discussion of all these. Even the simplest discussion of decoherence that I have given here should also be extended to include the possibility that the decoherence of neighboring q... |

428 | Quantum mechanics helps in searching for a needle in a haystack
- Grover
- 1997
(Show Context)
Citation Context ...are not sped up at all [10] by using quantum tools (e.g., obtaining the nth iterate of a function f …f …...f …x† ...†† [11]), some are sped up moderately (locating an entry in a database of n entries =-=[12]-=-), and some are apparently sped up exponentially (Shor's algorithm for factoring an n-digit number [13]). In other types of information processing tasks, particularly those involving communication [14... |

350 | Quantum lower bounds by polynomials
- Beals, Buhrman, et al.
(Show Context)
Citation Context ...amount. By a standard complexity measure (i.e., the way in which the number of computational steps required to complete a task grows with the ``sizeº n of the task), some tasks are not sped up at all =-=[10]-=- by using quantum tools (e.g., obtaining the nth iterate of a function f …f …...f …x† ...†† [11]), some are sped up moderately (locating an entry in a database of n entries [12]), and some are apparen... |

180 | Two-bit gates are universal for quantum computation
- DiVincenzo
- 1995
(Show Context)
Citation Context ... problem for a quantum computation specified with three-qubit unitary transformations; fortunately, of course, these can always be re-expressed in terms of sequences of one- and two-body interactions =-=[35]-=-, and the two-body interactions can be of just one type [36], the ``quantum XORº or ``cNOTº. There are some implementations in which multi-qubit gates can be implemented directly [37]. However, this s... |

169 |
Elementary gates for quantum computation,” Phys
- Barenco, Bennett, et al.
- 1995
(Show Context)
Citation Context ...t unitary transformations; fortunately, of course, these can always be re-expressed in terms of sequences of one- and two-body interactions [35], and the two-body interactions can be of just one type =-=[36]-=-, the ``quantum XORº or ``cNOTº. There are some implementations in which multi-qubit gates can be implemented directly [37]. However, this still leaves a lot of work to do. In some systems, notably in... |

158 | Quantum vs. classical communication and computation
- Buhrman, Cleve, et al.
- 1998
(Show Context)
Citation Context ...y for an appointment between two parties from out of n days) there is a quadratic reduction of the amount of communicated data required, if quantum states rather than classical states are transmitted =-=[16]-=-. For some tasks (the ``set disjointness problemº, related to allocating non-overlapping segments of a shared memory in a distributed computation) the reduction of required communication is exponentia... |

116 | A modular functor which is universal for quantum computation
- Freedman, Larsen, et al.
(Show Context)
Citation Context ...But further research in, for example, the quantum Hall effect might reveal such a system; more likely, perhaps, is that further understanding of this approach, and that of Freedman and his colleagues =-=[50]-=-, will shed more light on doing quantum computing using the ``standardº approach being considered in this book. I am convinced of one thing: the ideas of quantum information theory will continue to ex... |

84 |
Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer
- Shor
- 1997
(Show Context)
Citation Context ...…...f …x† ...†† [11]), some are sped up moderately (locating an entry in a database of n entries [12]), and some are apparently sped up exponentially (Shor's algorithm for factoring an n-digit number =-=[13]-=-). In other types of information processing tasks, particularly those involving communication [14], both quantitative and qualitative improvements are seen [15]: for certain tasks (choosing a free day... |

83 |
Measurement of conditional phase shifts for quantum logic
- Turchette, Hood, et al.
- 1995
(Show Context)
Citation Context ... of this special issue. The scope of the approaches, proposed and underway, to the implementation of quantum hardware is remarkable, emerging from specialties in atomic physics [1], in quantum optics =-=[2]-=-, in nuclear [3] and electron [4] magnetic resonance spectroscopy, in superconducting device physics [5], in electron physics [6], and in mesoscopic and quantum dot research [7]. This amazing variety ... |

55 | Quantum communication complexity of sampling
- Ambainis, Schulman, et al.
(Show Context)
Citation Context ...For some tasks (the ``set disjointness problemº, related to allocating non-overlapping segments of a shared memory in a distributed computation) the reduction of required communication is exponential =-=[17]-=-. Finally, there are tasks that are doable in the quantum world that have no counterpart classically: quantum cryptography provides an absolute secrecy of communication between parties that is impossi... |

44 | Fault-tolerant quantum computation with local gates
- Gottesman
- 2000
(Show Context)
Citation Context ...ate each interaction. On the other hand, the constraint that interactions are only among nearest neighbors in a lattice, as in many of the solid-state proposals, does allow for sufficient parallelism =-=[41]-=-. Quantum gates cannot be implemented perfectly; we must expect both systematic and random errors in the implementation of the necessary Hamiltonians. Both types of errors can be viewed as another sou... |

20 | Science 275: 350 - Gershenfeld - 1997 |

17 |
A 52, 2493
- Rev
- 1995
(Show Context)
Citation Context ...sical system implementing the computation. Fortunately, in one of the great discoveries of quantum information theory (in 1995 ±1996), it was found that error correction of quantum states is possible =-=[33]-=- and that this correction procedure can be successfully applied in quantum computation [34], putting much more reasonable (although still daunting) requirements on the needed decoherence times. In bri... |

14 |
A 57, 120
- Rev
- 1998
(Show Context)
Citation Context ...[1], in quantum optics [2], in nuclear [3] and electron [4] magnetic resonance spectroscopy, in superconducting device physics [5], in electron physics [6], and in mesoscopic and quantum dot research =-=[7]-=-. This amazing variety of approaches has arisen because, as we will see, the principles of quantum computing are posed using the most fundamental ideas of quantum mechanics, ones whose embodiment can ... |

13 |
Science 261,1569
- Lloyd
- 1993
(Show Context)
Citation Context ...s known that general-purpose computation is performable, although with considerable overhead, by a cellular automaton. This is true as well for the quantum version of the cellular automaton, as Lloyd =-=[47]-=- indicated in his original work. New theoretical work by Benjamin [48] shows very explicitly how relatively simple local rules would permit the implementation of some quantum computations. This could ... |

9 |
K.B.Whaley ”Universal Fault-Tolerant Computation on Decoherence-Free Subspaces Phys
- Bacon, Kempe, et al.
- 2000
(Show Context)
Citation Context ...coherence free subspaces and subsystems, codes are introduced using blocks of three and four qubits for which two-qubit exchange interactions alone are enough to implement general quantum computation =-=[42, 43]-=-. This simplification could be very useful in the quantum-dot [7] or semiconductor-impurity [4] implementations. 5. A qubit-specific measurement capability Finally, the result of a computation must be... |

7 |
Nature 393:133
- Kane
- 1998
(Show Context)
Citation Context ... of the approaches, proposed and underway, to the implementation of quantum hardware is remarkable, emerging from specialties in atomic physics [1], in quantum optics [2], in nuclear [3] and electron =-=[4]-=- magnetic resonance spectroscopy, in superconducting device physics [5], in electron physics [6], and in mesoscopic and quantum dot research [7]. This amazing variety of approaches has arisen because,... |

7 |
Mesoscopic Electron Transport, in
- DiVincenzo
- 1997
(Show Context)
Citation Context ...ng the basic steps required to make quantum computation work, I can think of no better plan than to review a set of basic criteria that my coworkers and I have been discussing over the last few years =-=[24]-=- for the realization of quantum computation (and communication), and to discuss the application of these criteria to the multitude of physical implementations that are found below. So, without further... |

6 |
Physics Today 48
- Bennett
- 1995
(Show Context)
Citation Context ...mely brief mention. There is no shortage of other places to obtain more information about these things; I recommend the recent articles by Aharonov [21] and by Cleve [22]; other general introductions =-=[23]-=- will give the reader pointers to the already vast specialized literature on this subject. 3. Realizing Quantum Computation Let me proceed with the main topic: the physical realization of quantum info... |

5 |
Physicists triumph at ‘Guess my number
- Steane, vanDam
- 2000
(Show Context)
Citation Context ...secrecy of communication between parties that is impossible classically [18]. And for some games, winning strategies become possible with the use of quantum resources that are not available otherwise =-=[19, 20]-=-. This issue, and this chapter, are primarily concerned with the ``howsº of quantum computing rather than the ``whys,º so we will leave behind the computer science after this extremely brief mention. ... |

4 |
Quantum computers cannot speed up iterated applications of a black box, (quant-ph/9712051
- Ozhigov
(Show Context)
Citation Context ...ps required to complete a task grows with the ``sizeº n of the task), some tasks are not sped up at all [10] by using quantum tools (e.g., obtaining the nth iterate of a function f …f …...f …x† ...†† =-=[11]-=-), some are sped up moderately (locating an entry in a database of n entries [12]), and some are apparently sped up exponentially (Shor's algorithm for factoring an n-digit number [13]). In other type... |

4 |
Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices. Phys
- LEUNG, CHUANG, et al.
- 2000
(Show Context)
Citation Context ...tion, but the particular form of the fixed interactions permit their effects to be annulled by particular ``refocusingº sequences of the controllable interactions, and it has recently been discovered =-=[38]-=- that these refocusing sequences can be designed and implemented efficiently. For many other systems, the two-body Hamiltonian needed to generate directly the cNOT unitary transformation is not availa... |

4 |
Quantum computation and spin electronics
- Vincenzo, Burkard, et al.
- 2000
(Show Context)
Citation Context ...coherence free subspaces and subsystems, codes are introduced using blocks of three and four qubits for which two-qubit exchange interactions alone are enough to implement general quantum computation =-=[42, 43]-=-. This simplification could be very useful in the quantum-dot [7] or semiconductor-impurity [4] implementations. 5. A qubit-specific measurement capability Finally, the result of a computation must be... |

4 |
Fault-tolerant quantum computation with anyons
- Kitaev
(Show Context)
Citation Context ...d towards this at the moment, but the tradeoffs are very different, and I don't believe it should be excluded in the future. Second, even more speculative, but very elegant, is the proposal of Kitaev =-=[49]-=- to use quantum systems with particular kinds of topological excitations, for example nonabelian anyons, for quantum computing. It is hard to see at the moment how to turn this exciting proposal into ... |

3 |
An Introduction to Quantum Complexity Theory, to appear
- Cleve
- 2000
(Show Context)
Citation Context ... computer science after this extremely brief mention. There is no shortage of other places to obtain more information about these things; I recommend the recent articles by Aharonov [21] and by Cleve =-=[22]-=-; other general introductions [23] will give the reader pointers to the already vast specialized literature on this subject. 3. Realizing Quantum Computation Let me proceed with the main topic: the ph... |

1 |
Demonstration of a fundamental quantum logic gate, Phys
- Lett
- 1995
(Show Context)
Citation Context ...ported in the remainder of this special issue. The scope of the approaches, proposed and underway, to the implementation of quantum hardware is remarkable, emerging from specialties in atomic physics =-=[1]-=-, in quantum optics [2], in nuclear [3] and electron [4] magnetic resonance spectroscopy, in superconducting device physics [5], in electron physics [6], and in mesoscopic and quantum dot research [7]... |

1 |
Science 285
- Averin, Commun
- 1998
(Show Context)
Citation Context ...ntum hardware is remarkable, emerging from specialties in atomic physics [1], in quantum optics [2], in nuclear [3] and electron [4] magnetic resonance spectroscopy, in superconducting device physics =-=[5]-=-, in electron physics [6], and in mesoscopic and quantum dot research [7]. This amazing variety of approaches has arisen because, as we will see, the principles of quantum computing are posed using th... |

1 |
Quantum Computers and Quantum
- DiVincenzo, Loss
- 1999
(Show Context)
Citation Context ...12]), and some are apparently sped up exponentially (Shor's algorithm for factoring an n-digit number [13]). In other types of information processing tasks, particularly those involving communication =-=[14]-=-, both quantitative and qualitative improvements are seen [15]: for certain tasks (choosing a free day for an appointment between two parties from out of n days) there is a quadratic reduction of the ... |

1 |
Quantum games and quantum strategies, Phys
- Lett
- 1999
(Show Context)
Citation Context ...secrecy of communication between parties that is impossible classically [18]. And for some games, winning strategies become possible with the use of quantum resources that are not available otherwise =-=[19, 20]-=-. This issue, and this chapter, are primarily concerned with the ``howsº of quantum computing rather than the ``whys,º so we will leave behind the computer science after this extremely brief mention. ... |

1 |
Science 279
- Shor
- 1997
(Show Context)
Citation Context ...quantum information theory (in 1995 ±1996), it was found that error correction of quantum states is possible [33] and that this correction procedure can be successfully applied in quantum computation =-=[34]-=-, putting much more reasonable (although still daunting) requirements on the needed decoherence times. In brief, quantum error correction starts with coding; as in binary error correction codes, in wh... |