Seth Lloyd.: Quantum-mechanical computers. Physics Today, Oct (1995) 140--145  Home/Search   Document Not in Database   Summary   Related Articles   Check

....decoherence of the qubit states and the virtue is lost quantum parallelism levies a high price for coherence of the quantum computer s wavefunction. This has spurred the development of scalable quantum error correction techniques, considered crucially important for the enterprise to continue [11, 8, 12, 13]. Because of the di#culties of quantum coherence, the first quantum computer comprised only two qubits. An historical starting point that led to quantum computing was reversible computing [14] Since microscopic physics is reversible , it is believed that quantum mechanical algorithms must be ....

Seth Lloyd.: Quantum-mechanical computers. Physics Today, Oct (1995) 140--145

....to provide a formal exposition of quantum computing but to identify its novelty and potential use in tackling NP hard problems. 1 Introduction It has been estimated that every two years for the past 50 years computers have become twice as fast while their components have become twice as small [Lloyd, 1995]. If progress continues at this rate future computer circuits will be based on nanotechnology 1 and the behaviour of such circuits will have to be given in quantum mechanical terms rather than in terms of classical physics, since on the atomic scale matter obeys the laws of quantum mechanics. ....

Lloyd, S. (1995). Quantum-mechanical computers. Scientific American.

....theorems, but the hardware available is still not adequate for many of the problems to which we would like to apply our techniques. However, this will change. Radically new computers based on exotic technologies such as DNA computing, quantum computing, and optical circuitry are on the horizon [7] [11]. As better hardware is combined with increasingly versatile, sophisticated, and friendly tools for using rigorous logic in practical ways, there will be a revolution in the foundations and developmental methodologies of many intellectual disciplines. Imagine what could happen in many fields if ....

Seth Lloyd, Quantum-Mechanical Computers, Scientific American 273 (October 1995), 140-145.

.... and computational feats that are widely believed to be classically impossible [5, 9, 19, 23, 40, 53] as shown for example by the polynomial time quantum algorithm for integer factorization due to Shor [45] As a result, the field has now been the subject of numerous popular accounts, including [1, 11, 37, 60]. But despite these remarkable theoretical advances, one outstanding question remains: Can a fully programmable quantum computer actually be built Most approaches to this problem (loc. cit. have attempted to isolate a single submicroscopic system completely from its environment, so that it can ....

....of the simulated system directly onto the joint states of the qubits without discretizing the problem. Such an analog encoding is not only precise in principle, but also more e#cient, so that quantum simulations beyond the reach of today s computers could be performed with only 20 to 30 qubits [37, 38]. In addition, since it is usually only the longterm average behavior of quantum systems that is of interest, quantum simulations would be expected to be less sensitive to errors than quantum computations. Finally, the ensemble nature of NMR allows such averages to be observed directly, saving the ....

S. Lloyd, Quantum-mechanical computers, Sci. Am., 273 (1995), pp. 140--145.

....decoherence of the qubit states and the virtue is lost quantum parallelism levies a high price for coherence of the quantum computer s wavefunction. This has spurred the development of scalable quantum error correction techniques, considered crucially important for the enterprise to continue [23, 20, 24, 25]. 6 With a fully coherent quantum computer with a million qubits, quantum algorithms such as Shor s factoring algorithm [26] or Grover s search algorithm [27] if implemented, should outstrip any classical implementation. However, fully coherent quantum computers are not likely to be ....

.... the qubit qubit decoherence time 10 (which is about 700 millisecond in alanine for example) At present, we do not know whether a quantum computer with many globally entangled qubits, say on the order of a million, will ever be constructed, although candidate architectures have been proposed [9, 10, 24, 32]. 3 Summary of Fluid Dynamics 3.1 Navier Stokes Fluids The long wavelength hydrodynamic behavior of a many body system of particles can be modeled at the macroscopic scale by an e#ective field theory, a set of coupled partial di#erential equations. The smooth fields of mass density, #, and flow ....

Seth Lloyd. Quantum-mechanical computers. Physics Today, Oct:140-- 145, 1995.

.... spin states of the qubits (writing) then pairs of adjacent qubits interact via dipole dipole coupling for example where the computing cycle is initiated by a particular sequence of light pulses, and finally light is used to measure the resulting individual spin states of the qubits (reading) [43]. This kind of controlled light and matter interaction is well known in nuclear magnetic resonance experiments where # pulses are used to tip nuclear spins. For example, recently Cory et al. have employed the quantum number m z of a nuclear spin of an atom in a molecule of a liquid placed in a ....

....Quantum parallelism levies a high demand for coherence of the quantum computer s wavefunction to be realized by avoiding uncontrolled entanglement with the external world. Developing robust algorithms and scalable error correction techniques is considered crucial for the enterprise to continue [18, 8, 43, 25]. The tremendous di#culty of maintaining quantum coherence poses a problem that must be resolved before a quantum computer can be built. Because of the stringent demand for quantum coherence, prospects for any foreseeable quantum computers are focused on those containing only a very small number ....

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Seth Lloyd. Quantum-mechanical computers. Physics Today, Oct:140--145, 1995.

....held at Washington University, St. Louis, MO on 9 August 1999. 1 the areas of classical universal logic, communications, factoring and search algorithms, error correction, and control theory Many theoretical physicists, over the past several years, have focused on aspects of question No.3 [12, 5, 13, 14]. Many experimental physicists have more recently considered No.2, building prototype single gate quantum computers as a first step [8, 9, 10, 11] The primary objective of my lattice gas research (task 2304CP initiated in 1992) has been to answer No.1 [15, 16, 17] In addition, the objective of ....

Seth Lloyd. Quantum-mechanical computers. Physics Today, Oct:140-- 145, 1995.

....decoherence of the qubit states and the virtue is lost quantum parallelism levies a high price for coherence of the quantum computer s wavefunction. This has spurred the development of scalable quantum error correction techniques, considered crucially important for the enterprise to continue [11, 8, 12, 13]. Because of the di#culties of quantum coherence, the first quantum computer comprised only two qubits. An historical starting point that led to quantum computing was reversible computing [14] Since microscopic physics is reversible 4 , it is believed that quantum mechanical algorithms must be ....

Seth Lloyd.: Quantum-mechanical computers. Physics Today, Oct (1995) 140--145

....also required to classify interference crossover techniques and methods and relate them to existing, classical crossover techniques and methods. It has been estimated that every two years for the past 50 years computers have become twice as fast while their components have become twice as small [4]. If progress continues at this rate future computer circuits will be based on nanotechnology 3 and the behaviour of such circuits will have to be given in quantum mechanical terms rather than in terms of classical physics, since on the atomic scale matter obeys the laws of quantum mechanics ....

S. Lloyd. Quantum-mechanical computers. Scientific American, October 1995.

....and inaccuracies, are uncorrelated. This decreases the number of simulations which must be performed. Models to Reduce the Complexity of Simulating a Quantum Computer 1 1. 0 Introduction A quantum computer consists of atomic particles which obey the laws of quantum mechanics [LaTu95] TuHo95][Lloy95]. The complexity of a quantum system is exponential with respect to the number of particles. Performing computation using these quantum particles results in an exponential amount of calculation in a polynomial amount of space and time [Feyn85] Beni82] Deut85] This quantum parallelism is only ....

S. Lloyd. "Quantum-Mechanical Computers." Scientific American. Vol. 273, No. 4, pp 140-145. October 1995.

....a quantum computer can factor more efficiently than a classical computer if the error rate is of order 10 Gamma6 . Keywords: Quantum Simulation, Ion Trap, Factoring, Database Search 1 Introduction A quantum computer consists of atomic particles which obey the laws of quantum mechanics [TuHo95][Lloy95]. The complexity of a quantum system is exponential with respect to the number of particles. Performing computation using these quantum particles results in an exponential amount of calculation in a polynomial amount of space and time [Feyn85] Deut85] This quantum parallelism is only applicable ....

S. Lloyd. "Quantum-Mechanical Computers." Scientific American. Vol. 273, No. 4, pp 140-145. October 1995.

....a formal exposition of quantum inspired computing but to identify its novelty and potential use in tackling NP hard problems. 1 Introduction It has been estimated that every two years for the past 50 years computers have become twice as fast while their components have become twice as small [Lloyd, 1995]. If progress continues at this rate future computer circuits will be based on nanotechnology 1 and the behaviour of such circuits will have to be given in quantum mechanical terms rather than in terms of classical physics, since on the atomic scale matter obeys the laws of quantum mechanics. ....

Lloyd, S. (1995). Quantum-mechanical computers. Scientific American.

....defines a two dimensional vector space of superpositions for a quantum bit. There are a number of proposals for implementing quantum bits, i.e. devices whose quantum mechanical properties can be controlled to produce desired superpositions of two classical values. One example (DiVincenzo, 1995; Lloyd, 1995) is an atom whose ground state corresponds to the value 0 and an excited state to the value 1. The use of lasers of appropriate frequencies can switch such an atom between the two states or create superpositions of the two classical states. This ability to manipulate quantum superpositions has ....

Lloyd, S. (1995). Quantum-mechanical computers. Scientific American, 273 (4), 140--145.

....slightly modified from his original suggestion [14] In Figs. 1 2 we show COPY, NOT, and AND gates constructed from coupled rf SQUIDs, in the spirit of the parametric quantron structure described by Likharev. They are functionally equivalent to the three conceptual atomic gates that Lloyd [15] proposed as the basis for a general quantum computer. The qubits are circulating currents; the assignment of the 0 state is indicated on the diagrams. For example, the COPY gate in Fig.1 has two SQUID loops A and B that are externally biased with one half of a flux quantum and inductively ....

S. Lloyd, "Quantum mechanical computers," Scientific American, p. 140, Oct. 1995.

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Lloyd, S., "Quantum-Mechanical Computers," Sci. Am., 140--145 (Oct

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