Margolus N 1990 Parallel Quantum Computation, in Complexity, Entropy and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity, vol VIII p. 273 ed Zurek W H (Addison-Wesley)  Home/Search   Document Details and Download   Summary   Related Articles   Check

....that one could physically imagine would be the atomic density of solids. There is the interesting prospect of lattice gas architectures built at such a high informational density, termed nanoscale computing. There is hope that in the future computation will be achieved with quantum gates [62, 60, 11, 48, 7]. In fact the first quantum gate has recently been implemented using nuclear magnetic resonance spectroscopy where a few nuclear spins in each molecule of a liquid sample embody quantum bits [30] As the fundamental computational element s size reduces to nanoscale ranges its behavior is governed ....

Norman Margolus. Parallel quantum computation. In W.H. Zurek, editor, Complexity, Entropy, and the Physics of Information,SFI Studies in the Sciences of Complexity, vol. VIII, pages 273--287. Addison-Wesley, 1990.

....the possibility of constructing a quantum computer to simulate quantum mechanics. As the fundamental computational element s size reduces to nanoscale ranges its behavior is governed by quantum mechanics. There is hope that in the future computation will be achieved with quantum gates [46, 42, 9, 33, 4]. Follow 1 To see this, count the number of possible energy levels for a particle in a cubical box of length side X. The particle s momentum components are quantized by periodic boundaries conditions so p i = hn i X , where i = 1, 2, 3) is an index over spatial directions and n i are integers. ....

Norman Margolus. Parallel quantum computation. In W.H. Zurek, editor, Complexity, Entropy, and the Physics of Information,SFI Studies in the Sciences of Complexity, vol. VIII, pages 273--287. Addison-Wesley, 1990.

....= j0i. Hence, this gate flips the bit, and thus it is justified to call this gate the NOT gate. The NOT gate can operate on superpositions as well. From linearity of the operation, NOT (c 0 j0i c 1 j1i) c 0 j1i c 1 j0i: This linearity is responsible for the quantum parallelism (see Margolus[148]) which we will encounter in all powerful quantum algorithms. When the NOT gate operates on the first qubit in a system of n qubits, in the state P i c i ji 1 i 2 : i n i this state transforms to P i c i (NOT ji 1 i)ji 2 : i n i = P i c i j:i 1 i 2 : i n i. Formally, the time evolution of ....

....uniform quantum circuits are polynomially equivalent to quantum Turing machines, by a proof which is surprisingly complicated. This proof enables us the freedom of choosing whichever model is more convenient for us. Another model worth mentioning in this context is the quantum cellular automaton[148, 196, 88, 77]. This model resembles quantum circuits, but is different in the fact that the operations are homogeneous, or periodic, in space and in time. The definition of this model is subtle and, unlike the case of quantum circuits, it is not trivial to decide whether a given quantum cellular automaton ....

Margolus N 1990 Parallel Quantum Computation, in Complexity, Entropy and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity, vol VIII p. 273 ed Zurek W H (Addison-Wesley)

....gate arrays, or 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. ....

N. Margolus (1990) "Parallel quantum computation," in Complexity, Entropy and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity, Vol.

.... of records in [14] and Brownian computers [12] for Turing machines and Brownian enzymatic computers [3, 4, 6] with respect to reversible Boolean circuits by [9] for molecular (billiard ball) computers by [21] Brownian computing using Josephson devices in [16] quantum mechanic computers in [1, 2, 17] and notably by R. Feynman [7, 8] All these models seem mutually simulatable. For background information, see [5] In the last three decades there have been many partial precursors and isolated results to the complete mathematical theory developed in this paper. However, it is the formulation of ....

N. Margolus. Parallel quantum computation. In W.H. Zurek, editor, Complexity, Entropy and the Physics of Information, pages 273--287. Addison-Wesley, 1991.

....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, ....

Norman Margolus. Parallel quantum computation. In Wojciech H. Zurek, editor, Complexity, Entropy, and the Physics and Information, volume VIII of SFI Studies in the Sciences of Complexity, pages 273--287. Addison--Wesley, Redwood City, 1990. http://feynman.stanford. edu/qcomp/margolus/index.html.

....[Be79] Theoretical speed limits are just given by the lengths of the communication pathways and the speed of light. Nonlocal interactions introduce longer communication pathways. Therefore it appears important to investigate the power of quantum computers with only local interactions as done in [Fe86, Ma86, GZ88, Ma90]. This work is about the speed of locally connected computing systems. Quantum mechanical, locally connected computing systems Between two measurements, every closed, pure state physical system can be described by the Schroedinger equation j (t)i = U(t) j (0)i ; 1) where j (0)i is the wave ....

....to take care for the correct order of U i while some of them might correspond to subsystems which are very far apart. This is not possible by just acting locally. For a serially working computer, Feynman [Fe86] has found a way to write down a Hamiltonian being the sum of local pieces. Margolus [Ma90] was able to use this idea for special one dimensional cellular automata. It must be emphasized that in both cases the Hamiltonian does not give U ideal . This seems to be impossible if we are dealing with only locally coupled subsystems. However, if exponentiated, the Hamiltonian gives a ....

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N.Margolus. "Parallel Quantum Computation" in "Complexity, Entropy, and the Physics of Information, SFI Studies in the Sciences of Complexity", Vol. VIII, Ed. W.H.Zurek, Addison-Wesley 1990, pp.273-287.

.... 1 Introduction In 1985, Feynman introduced a model for a serial computer that is able to model the computation of a deterministic computation in a closed, locally interacting quantum system [Fe85] Margolus was able to generalize Feynman s ideas to a quantum model of a cellular automaton [Ma86, Ma90]. The result of a Feynman or Margolus computer is obtained by performing a quantum measurement. The outcome of such a measurement is not certain. A final result will only be obtained with a probability that is smaller than one. However, in case a final result is measured, this result can be ....

....computers have been analyzed in detail in [Gr94] for the Feynman computer and in [Bi93] for the Margolus computer. Of particular interest is the average number of computational steps per time unit that a quantum computer performs. Quantum computational speed has first been defined in [Ma86] In [Ma90] it has been shown that the Margolus automaton computes at a constant rate, in other words, that its computational speed is constant. This also applies to the Feynman computer with an infinite clock [Gr94] In [Bi93] it is shown that the maximal speed is proportional to the number of sites of a ....

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N.Margolus (1990): "Parallel Quantum Computation" in "Complexity, Entropy, and the Physics of Information, SFI Studies in the Sciences of Complexity", VIII, Ed. W.H.Zurek, Addison-Wesley, pp. 273-287.

....give rise to reduced computational speed. Third: Quantum computers with nonlocal interactions are probably more difficult to realize because long range interactions have to be implemented on a submicroscopical level. The power of quantum computers with only local interactions is investigated in [Pe85, Fe85, Ma86, GZ88, Ma90, Bi93, Gr94, Gr95]. For a critical discussion about the realizability of quantum computers see [Zu84, La86, La92, Un94a, Un94b, CZ95] 2 The Feynman computer Consider a deterministic classical computer that consists of k gates, connected in a serial way, as depicted in figure 1. It passes through a number k of ....

....the control bit state, which reads in vector notation as [1; 0; 0; 0] the 1 at position 0) is transformed to [0; 1; 0; 0] the 1 at position 1) and so on. In the cyclic case [0; 0; 0; 1] is transformed to [1; 0; 0; 0] The states are simply rotated. In contrast to [Ma90, Bi93, Gr95] we will restrict ourselves to finite size quantum computers. In sections 4 to 6, computers with cyclic architecture are considered. In sections 7 and 8 the non cyclic case will be analyzed. 4 Eigensystem of the Hamiltonian for the cyclic case Now we will calculate the eigensystem of the ....

N.Margolus (1990): "Parallel Quantum Computation" in "Complexity, Entropy, and the Physics of Information, SFI Studies in the Sciences of Complexity", VIII, Ed. W.H.Zurek, Addison-Wesley, pp. 273-287.

....0 means that if a cell is in state q, with its left neighbour in state p and its right neighbour in state r, then it will go to state q 0 . Of course, it is understood that all cells change at the same time, which seems inconsistent with our principle of asynchrony. But never mind, following [Margolus], we decompose transitions so that each cell looks alternatively at each of his neighbours. More precisely, we take Sigma = f Gamma q j q 2 Qg [ f Gamma Gamma (p; q) j p; q 2 Qg [ f Gamma q j q 2 Qg [ f Gamma Gamma (p; q) j p; q 2 Qg and R consisting of the following rules: Gamma ....

N. Margolus, Parallel Quantum Computation (1989).

.... also been demonstrated (Muller, Klein, Lee, Clarke, McEuen, Schultz, 1995) There are also a number of other proposals under investigation (Barenco, Deutsch, Ekert, 1995; Sleator Weinfurter, 1995; Cirac Zoller, 1995) including the possibility of multiple simultaneous quantum operations (Margolus, 1990). A simple computation on a quantum bit is the logical NOT operation, i.e. NOT(j0i) j1i and NOT(j1i) j0i. This operator simply exchanges the state vector s components: NOT 0 1 j NOT( 0 j0i 1 j1i) 0 j1i 1 j0i j 1 0 (5) Hogg This operation can also be ....

Margolus, N. (1990). Parallel quantum computation. In Zurek, W. H. (Ed.), Complexity, Entropy and the Physics of Information, pp. 273--287. Addison-Wesley, New York.

.... enzymatic computers [3, 4, 6] with respect to reversible Boolean circuits by [9] for molecular (billiard ball) comput 0 0 0 0 1 1 1 1 OUTPUT INPUT 0 0 1 1 0 1 1 0 Figure 3: A billiard ball computer ers by [23] Brownian computing using Josephson devices in [17] quantum mechanic computers in [1, 2, 18] and notably by R. Feynman [7, 8] All these models seem mutually simulatable. For background information, see [5] Implementations in current solid state technologies (nMOS, CMOS, CCD) of two methods of using switches to implement reversible computations are presented in [21] We note that ....

N. Margolus. Parallel quantum computation. In W.H. Zurek, editor, Complexity, entropy and the physics of information, pages 273--287. AddisonWesley, 1991.

....computer, which could simulate any other quantum computer (or any other physical system) with arbitrarily high accuracy. Feynman s ideas were generalized for a parallel computer by Norman Margolus, who introduced his model of a quantum cellular automaton in 1986 [12] and developed it further in [13]. This was the rst time a quantum computer was made to mimic a classical parallel system. Later, also other quantum cellular automata have been developed [24] 1.2 Motivation Petri nets [16] have proved to be a useful tool in modeling of many classical systems, including classical computers. ....

....as well. Margolus s cellular automaton was a natural choice for the target of modeling, because it is parallel (concurrent events are easily represented using Petri nets) and because there exists a simple and straightforward method for representing the automaton behavior as a quantum system [12] [13]. Petri nets have been earlier used for modeling a serial quantum processor by Ojala et al. in [15] 14] In this work, we adopt the same approach as in [3] 15] and [14] to compute the automaton state at successive discrete moments of time, based on the solutions of di erential equations which ....

[Article contains additional citation context not shown here]

Norman Margolus. Parallel quantum computation. In W.H.Zurek, editor, Complexity, Entropy, and the Physics of Information, volume VIII of SFI Studies in the Sciences of Complexity, pages 273-287. Addison-Wesley, 1990.

....principle nearly ideal logic density. At the highest logic density that is physically possible, there is the interesting prospect of lattice gas architectures built out of quantum hardware. There is the expectation that in the future, computation will be achieved on quantum computers [38, 39, 40, 41]. As the fundamental computational element s size 8 reduces to nano scale ranges its behavior is governed by quantum mechanics. Quantum mechanics requires unitary, and hence invertible, time evolution the microscopic reversibility of the lattice gas dynamics is important here. Even before ....

Norman Margolus. Parallel quantum computation. In W.H. Zurek, editor, Complexity, Entropy, and the Physics of Information,SFI Studies in the Sciences of Complexity, vol. VIII, pages 273--287. Addison-Wesley, 1990.

....evolution specified by the unitary operator U Gamma1 = U y always exists; as a consequence, several workers recognized that reversible computation could be executed within a quantum mechanical system. Quantum mechanical Turing machines [5, 6] gate arrays [7] and cellular automata [8] have been discussed, and physical realizations of Toffoli s[9, 10, 11] and Fredkin s[12, 13, 14] universal three bit gates within various quantum mechanical physical systems have been proposed. While reversible computation is contained within quantum mechanics, it is a small subset: the time ....

N. Margolus, "Parallel Quantum Computation", in Complexity, Entropy, and the Physics of Information, Santa Fe Institute studies in the Sciences of Complexity, vol. VIII, ed. W. H. Zurek, (Addison-Wesley, 1990), p. 273.

....computer, this would correspond to the maximum number of operations per second. For a quantum system, the notion of distinct states is well defined: two states are distinct if they are orthogonal. The connection between orthogonality and rate of information processing has previously been discussed[9, 2, 6, 10, 11, 4], but no universal bound was proposed. The minimum time needed for a quantum system to pass from one orthogonal Supported by NSF grant DMS 9596217 and by DARPA contract DABT63 95 C 0130 1 Although many of the computing and communications properies of quantum systems are novel[14, 16, 3] ....

Margolus, N., "Parallel quantum computation," Complexity, Entropy, and the Physics of Information (Wojciech Zurek ed.), Addison-Wesley, 1990.

....elements that are very narrow, and trying to drive them with near atomic scale systems will be a tremendous problem. One solution is to build computers that have no wires[18, 8, 1] Uniform arrays of computing elements, each interacting directly with adjacent elements, can perform any computation[9, 11]. Since the speed of light is a constraint on information propagation, short signal paths translate into fast operation. With very little time or space wasted on signal propagation, clock speeds and logic densities can be very high. In fact, these kinds of Cellular Automata (CA) based computers ....

N. Margolus, "Parallel Quantum Computation," Complexity, Entropy, and the Physics of Information (Wojciech Zurek ed.), Addison-Wesley, 1990.

....evolution specified by the unitary operator U Gamma1 = U y always exists; as a consequence, several workers recognized that reversible computation could be executed within a quantum mechanical system. Quantum mechanical Turing machines [5, 6] gate arrays [7] and cellular automata [8] have been discussed, and physical realizations of Toffoli s[9, 10, 11] and Fredkin s[12, 13, 14] universal three bit gates within various quantum mechanical physical systems have been proposed. While reversible computation is contained within quantum mechanics, it is a small subset: the time ....

N. Margolus, "Parallel Quantum Computation", in Complexity, Entropy, and the Physics of Information, Santa Fe Institute studies in the Sciences of Complexity, vol. VIII, ed. W. H. Zurek, (Addison-Wesley, 1990), p. 273.

No context found.

Margolus N 1990 Parallel Quantum Computation, in Complexity, Entropy and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity, vol VIII p. 273 ed Zurek W H (Addison-Wesley)

No context found.

Norman Margolus. Parallel quantum computation. In W.H. Zurek, editor, Complexity, Entropy, and the Physics of Information,SFI Studies in the Sciences of Complexity, vol. VIII, pages 273--287. Addison-Wesley, 1990.

No context found.

N. Margolus, "Parallel Quantum Computation" (preprint).

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