Michael Biafore. Cellular automata for nanometer-scale computation. Physica D, 70(3/4), 1994.  Home/Search   Document Not in Database   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 ....

Michael Biafore. Cellular automata for nanometer-scale computation. Physica D, 70(3/4), 1994.

....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 ....

Michael Biafore. Cellular automata for nanometer-scale computation. Physica D, 70(4):415--433, 1994.

....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. ....

....class is su#cient. Particular choices of C optimally reduce the shear viscosity, but all are acceptable. At this early stage in the exploration of quantum computing there does not yet exist much evidence indicating whether this is a reasonable strategy for evolving a large array of qubits [9, 43], nevertheless I explore the quantum lattice gas paradigm because of its simplicity and because the theory and computation of classical lattice gas dynamics points the way to this new type of lattice based quantum computation. 18 In the case of the Hubbard Hamiltonian, the interchange operators ....

Michael Biafore. Cellular automata for nanometer-scale computation. Physica D, 70(3/4), 1994.

....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 ....

Michael Biafore. Cellular automata for nanometer-scale computation. Physica D, 70(3/4), 1994.

....dynamics is just a discrete Schrodinger equation with non selfadjoint Hamiltonian, made non linear by keeping the normalization fixed. There is some interest in quantum cellular automata also from the point of view of nanometer scale computers, for which quantum effects are expected to be relevant [Mai,Bia,LTPH]. The evolution of the automata considered in this paper is in general non unitary, i.e. pure states may evolve into mixed states. This might be an interesting addition to the structure of quantum computers , as studied by a number of authors recently (see [DiV] and references cited there) The ....

M. Biafore: "Cellular automata for nanometer-scale computation", Physica D 70(1994) 415--433

....isomorphic either to the integers Z or to a periodic quotient thereof, say ZN . To simulate physical systems [18] more generally, the model should be extended to allow for finite size and non periodic boundary conditions. Furthermore, envisioning a QLGA as a nanoscale quantum computer architecture [19,20,2] motivates consideration of inhomogeneities in the substrate , possibly as a step towards implementing logical gates [4] and away from simply simulating quantum physical systems. In [15] we showed how to introduce an inhomogeneous potential in the model; the purpose of this paper is to ....

.... models with inhomogeneities have been constructed in two dimensions [26,27,17] More interesting is the question of how to exploit such inhomogeneities to effect specific quantum computational tasks more efficiently than by simply implementing a quantum version of reversible billiard computing [13,20] using a homogeneous rule. The most natural use of QLGA may be to simulate other quantum physical systems; designing an inhomogeneous QLGA to be an efficient universal quantum computer may consequently be difficult. A reasonable intermediate goal would be to solve specific problems particularly ....

M. Biafore, "Cellular automata for nanometer-scale computation", Physica D 70 (1994) 415--433.

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Michael Biafore. Cellular automata for nanometer-scale computation. Physica D, 70(3/4), 1994.

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