S. Lloyd, A potentially realizable quantum computer, Science, 261 (1993), pp. 1569--1571. 14  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[19] has shown that QTMs working in polynomial time can be simulated by polynomial size quantum circuits. Physicists were also interested in quantum cellular automata: Biafore [4] considered the problem of synchronization, Margolus [14] described space periodic quantum cellular automata and Lloyd [12, 13] discussed the possibility to realize a special type of quantum cellular automaton. Linear quantum cellular automata (LQCAs) were formally defined by Watrous [18] and by Durr, LeThanh and Santha [7] In the former paper it was shown that a subclass of LQCAs, partitioned linear quantum cellular ....

S. Lloyd, A potentially realizable quantum computer, Science, 261 (1993), pp. 1569--1571. 14

....Zeeman shift between magnetic sublevels of order 10 KHz per wavelength. These and other solutions to the addressing problem must all be explored in more detail. Also, one should carefully consider what kinds of information processing tasks, might be performed with quantum cellular automata [75] or special codings where one has only limited local control over the qubits [76] In the later reference it is shown that if individual qubit states can be prepared at a boundary of a chain of alternating species qubits (a qubit set with two distinguishable state spaces) then universal quantum ....

S. Lloyd, "A Potentially Realizable Quantum Computer", Science 261, 1569 (1993).

....of initial conditions. It would be interesting to see how much of this carries over to the quantum domain. There are many proposals for computation, both classical and quantum, using quantum 63 cellular automata (see, e.g. Briegel and Raussendorf [18] Fussy et al. 44] Lent et al. 77] Lloyd [84] or Meyer [88] The two main attractions of quantum cellular automata are (a) massively parallel structure, and (b) the possibility of a phase transition. We have already discussed massively parallel structure of quantum cellular automata in Section 3.4.3; here we focus our attention on phase ....

S. Lloyd, \A potentially realizable quantum computer," Science 261, 1569 (1993).

....to previously identified phase transitions in search difficulty. The conditions underlying this improvement are described. Much of the algorithm is independent of particular problem instances, making it suitable for implementation as a special purpose device. 1 Introduction Quantum computers [1, 2, 7, 8, 10, 17, 9] use quantum parallelism, i.e. the ability to operate simultaneously on a superposition of many classical states, and interference among different computational paths. A measurement on a superposition gives a definite result, with probabilities determined by the amplitudes of the superposition. A ....

Lloyd, Seth (1993), "A Potentially Realizable Quantum Computer", Science 261, 1569--1571.

....and has shown that QTMs working in polynomial time can be simulated by polynomial size quantum circuits. Also, physicists were interested in quantum cellular automata: Biafore [6] considered the problem of synchronization, Margolus [20] described space periodic quantum cellular automata and Lloyd [18, 19] discussed the possibility to realize a special type of quantum linear cellular automaton (LQCA) However these models are somehow di erent from the model of LQCA we consider in this article, and the physical realizability of our model has not yet been studied. Well formedness is an essential ....

S. Lloyd, A potentially realizable Quantum Computer, Science 261, 1569-1571, 1993.

.... hamiltonian H = J 1,2,zS z 1S z 2 h 1,z,0S z 1 h 2,z,0S z 2 , x where h 1,z,0 2# # 500MHz, h 2,z,0 2# # 125MHz, and J 1,2,z 2# # 215Hz [3] It 6 is amusing to note that the most simple spin 1 2 system, i.e. the Ising model, can be used for quantum computing [34 38] In the chloroform molecule the antiferromagnetic interaction between the spins is much weaker than the coupling to the external field and (i is a diagonal matrix with respect to the basis states chosen, the ground state of( 8) is the state with the two spins up. Following [3] we denote this state ....

S. Lloyd, "A potentially Realizable Quantum Computer, Science 261, 1569 (69i#7

....model classes. Quantum computation, in particular, has become a highly active research area. This is driven by the recent discovery of quantum algorithms for factoring that operate in polynomial time [29] the suggestion that quantum computers can be built using familiar physical systems [7, 14, 19], and the hope that errors and decoherence of the quantum state can be suppressed so that such computers can operate for long times [30, 33] If we are to understand computation in a quantum context, it might be useful to translate as many concepts as possible from classical computation theory ....

S. Lloyd, \A potentially realizable quantum computer." Science 261 (1993) 1569-1571.

.... photons and electron spins on individual atoms [24, 45] and other experimentalists work with vibrational states in assemblages of interacting atoms [14] Other proposals for implementation technologies for quantum computing, from various communities, include Teich et al. 88 [43] Lloyd 93 94 [33, 34], DiVincenzo 95 a [20] Sleator Weinfurter 95 [40] Barenco et al. 95 b [3] and Chuang Yamamoto 95 [13] The main lesson to be learned from this long list of proposals is that the details of the physical implementation of quantum computers is just an engineering concern, rather than a ....

Seth Lloyd. A potentially realizable quantum computer. Science, 261:1569--1571, 17 September 1993. Preprint at http://www-im.lcs.mit.edu:80/poc/lloyd/lloyd.ps.Z.

....to quantum computing was reversible computing [8] Since microscopic physics is reversible 3 , it is believed that quantum mechanical algorithms must be too. Reversible quantum cellular automatons, which are meant to represent universal computation engines, have led to quantum computer designs [9, 10]. The common assumption is the quantum mechanical device itself undergoes unitary (and therefore reversible) evolution as it transitions through its computation . 4 It is known that there exist simple classical gates which are computation universal. That is, any feasible computation can 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. A potentially realizable quantum computer. Science, 261:1569.

....Cerf [AC98a] ffl Heteropolymer. This is a polymer consisting of a linear array of atoms, each of which can be either in a ground or excited energy state. Teich et al. [TOM88] first proposed classical (without quantium superpositions) molecular computations using heteropolymer. Later Lloyd [Llo93] extended the use of heteropolymers to QC, using the energy states to store the state of the qubits. The coupling of qubits may be via electric dipole moments which causes energy shifts on adjacent atoms. Unitary transitions on superpositions can be executed via pulses of a laser at particular ....

S. Lloyd. A potentially realizable quantum computer. Science, 261, 1569 (1993).

....But we think that the strongest case can be made for a quantum mechanical substratum that provides unity to experience. Such quantum mechanical models of consciousness have attracted considerable attention; this work is reviewed in [14, 15] Quantum computing in the style of Feynman and others [3, 4, 16], is considering the use of lattices or organo metallic polymers as the apparatus; on the other hand, microtubules, the skeletal basis of cells that consist of pro10 tein polymers, have been proposed by Hameroff and others [11] as supporting quantum mechanical processes. My own work has examined ....

Lloyd, S. (1993). "A potentially realizable quantum computer." Science, 261, 1569-1571.

....on a quantum computer with a small probability of error. Currently, nobody knows how to build a quantum computer, although it seems as though it might be possible within the laws of quantum mechanics. Some suggestions have been made as to possible designs for such computers [Teich et al. 1988, Lloyd 1993, 1994a, Cirac and Zoller 1995, DiVincenzo 1995, Sleator and Weinfurter 1995, Barenco et al. 1995b, Chuang and Yamomoto 1995] but there will be substantial difficulty in building any of these [Landauer 1995, Unruh 1995, Chuang et al. 1995, Palma et al. 1995] The most difficult obstacles appear ....

....quantum acyclic circuits, which are analogous to acyclic circuits in classical computer science. For other models of quantum computers, see references on quantum Turing machines [Deutsch 1989, Bernstein and Vazirani 1993, Yao 1993] and quantum cellular automata [Feynman 1986, Margolus 1986, 1990, Lloyd 1993, Biafore 1994] If they are allowed a small probability of error, quantum Turing machines and quantum gate arrays can compute the same functions in polynomial time [Yao 1993] This may also be true for the various models of quantum cellular automata, but it has not yet been proved. This gives ....

S. Lloyd (1993) "A potentially realizable quantum computer," Science 261, 1569--1571.

....for the development of the idea of quantum computers. It was assumed that quantum computers will take advantage of the superpositions that are inherent in a quantum description and thereby do more than what classical computers can achieve. For accounts of research in the quantum computing area see [2, 6, 3, 15, 17, 16, 19]. The development of the idea of a quantum mechanical computer has paralleled, more or less, the structure of a classical computer. Whether such a structure, based on local interconnections, exhausts the capabilities of quantum computing, we do not know yet. Is it possible that current quantum ....

....system, reversible logic gates, each made up of several interacting spins, are laid next to a chain of clock spins. Only one gate is active at a time step and the clock spins carry the computation forward. In this form, the system is a serial model. Parallel models have also been proposed. Lloyd [17] suggested that a quantum computer could be assembled out of organometallic polymers, where laser pulses could send the superposed states down the polymer chain analogous to electrons flowing down a wire. Landauer [15, 16] has subjected these proposals for quantum computing to a penetrating ....

S. Lloyd, A potentially realizable quantum computer. Science 261: 15691571 (1993).

.... include Grover s quantum searching algorithm [12] and various oracle results regarding the power of quantum computers [1, 3, 4, 7, 25] The above examples regard the power of universal quantum machines (e.g. quantum Turing machines [1, 5] quantum circuits [6, 27] quantum cellular automata [8, 16, 17, 26]) In this paper, we define two new, much more restricted quantum computational models: 1 way and 2 way quantum finite state automata (1qfa s and 2qfa s) The main focus of this paper will be on 2qfa s, which are the quantum analogue of deterministic, nondeterministic and probabilistic 2 way ....

S. Lloyd. A potentially realizable quantum computer. Science, 261: 1569--1571, 1993.

....and has shown that QTMs working in polynomial time can be simulated by polynomial size quantum circuits. Also, physicists were interested in quantum cellular automata: Biafore [6] considered the problem of synchronization, Margolus [20] described space periodic quantum cellular automata and Lloyd [18, 19] discussed the possibility to realize a special type of quantum linear cellular automaton (LQCA) However these models are somehow different from the model of LQCA we consider in this article, and the physical realizability of our model has not yet been studied. Well formedness is an essential ....

S. Lloyd, A potentially realizable Quantum Computer, Science 261, 1569--1571, 1993.

....quantum mechanical systems. Recent work by David Meyer [39, 40, 41, 42] goes along this pathway. The other direction is to try to actually construct a controllable qca. Several authors have suggested that qca like systems are more likely to be build than quantum Turing machines oriented structures [8, 34, 35, 36]. If such a construction would indeed be possible in the future, we would have equipped ourselves with a new remarkable tool. A tool whose computational power we are just beginning to unravel [11, 22, 56] Appendix A Unitary Transformations Because of their central role in quantum computing, ....

Seth Lloyd. A potentially realizable quantum computer. Science, 261:1569--1571, 1993.

....superpositions of physical states, which is one of the inherent properties of quantum physics. Several researchers have suggested that the QTM might have a potential for a new type of computer [4, 7, 19] Several researchers have proposed possible designs of computers based on Deutsch s QTM [11, 12, 18]. The possible advantages of the QTM are as follows: ffl Every finitely realizable physical system can be perfectly simulated by a QTM. ffl A computer based on the QTM may be capable of dissipating very small amount of energy per step. ffl Several researchers pointed out the possibilities of ....

S. Lloyd, "A Potentially Realizable Quantum Computer", Science, 261(1993), pp. 1569-1571.

....a non trivial problem and a vital step in the CAM Brain work, if the project is to be successful. This paper also shows Cellular Automata (CA) 2] will have a bright future in general computing and the simulation of complex systems. The prospect of nano technology [3] quantumcomputation [4] and the expected progress in traditional micro electronics make it foreseeable that computer systems will continue to shrink to molecular scales. But the operation of systems which are huge in comparison to the molecular size of their basic components will necessitate working in parallel, ....

Lloyd, S. 'A Potentially Realizable Quantum Computer ', Science 261, 1569-1571 1993.

....end up in a linear rather than an exponential programming effort: The effort will be proportional to the number of subsystems. Of course, computers with only local connections are much easier to build anyway. Models for potentially realizable quantum computing only exhibit short range interactions [HOB88, Ll93]. Also, the communication pathways are extremely short. This results in high computational speeds. A system which consists of k non interacting subsystems has a Hamiltonian which is the sum of k locally acting Hamiltonians. If the subsystems interact, this is not that simple. It is insightful to ....

S.Lloyd. "A potentially realizable quantum computer." Science, Vol. 261, 1993, pp. 1569-1571.

....adversaries with infinite computing power. There are two problems with the first type of assumption. First, one needs to specify a model of computation and, for instance in view of analog implementations of neural networks or, more severely, of the potential realizability of quantum computers [15], it is not clear whether a Turing machine or any standard discrete computer model is sufficiently general. In other words, one could argue that even the assumption that an adversary has the computing power corresponding to 10 20 of the newest generation CRAY computers is not satisfactory. The ....

S. Lloyd, A potentially realizable quantum computer, Science, Vol. 261, 1993, pp. 1569-- 1571.

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Lloyd, S., "A potentially realizable quantum computer." Science 261:1569-71. 17 Sept 1993.

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Lloyd, S., A potentially realizable quantum computer, Science, 261(1993), pp. 1569--1571.

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Lloyd, S., "A Potentially Realizable Quantum Computer," Science 261, 1569--

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Lloyd, S. 'A Potentially Realizable Quantum Computer', Science 261, 1569-1571 1993.

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Lloyd, S., "A potentially realizable quantum computer", Science, vol. 261, 17 September 1993, pp. 1569 -- 1571.

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