P. Benioff, The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines,J. Stat. Phys.
22:563–591 (1980); R. Landauer, Uncertainty principle and minimal energy dissipation in the computer,Int. J. Theor. Phys.
21:283–297 (1982); R. P. Feynman, Quantum mechnical computers,Found. Phys.
16:507–531 (1986); and references therein.
R. P. Feynman, Simulating physics with computers,Int. J. Theor. Phys.
D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer,Proc. R. Soc. Lond. A
D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation,Proc. R. Soc. Lond. A
439:553–558 (1992); A. Berthiaume and G. Brassard, The quantum challenge to structural complexity theory, inProceedings of the 7th Structure in Complexity Theory Conference, (IEEE Computer Society Press, Los Alamitos, California, 1992), pp. 132–137; E. Bernstein and U. Vazirani, Quantum complexity theory, inProceedings of the 25th ACM Symposium on Theory of Computing (ACM Press, New York, 1993), pp. 11–20; D. R. Simon, On the power of quantum computation, inProceedings of the 35th Symposium on Foundations of Computer Science, S. Goldwasser, ed. (IEEE Computer Society Press, Los Alamitos, California, 1994), pp. 116–123.
P. W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, inProceedings of the 35th Symposium on Foundations of Computer Science, S. Goldwasser, ed. (IEEE Computer Society Press, Los Alamitos, California, 1994), pp. 124–134.
R. L. Rivest, A. Shamir, and L. Adleman, A method of obtaining digital signatures and public-key cryptosystems,Commun. ACM
D. P. DiVincenzo, Two-bit gates are universal for quantum computation,Phys. Rev. A
51:1015–1022 (1995); J. I. Cirac and P. Zoller, Quantum computations with cold trapped ions,Phys. Rev. Lett.
74:4091–4094 (1995); A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin and H. Weinfurter, Elementary gates for quantum computation,Phys. Rev. A
52:3457–3467 (1995); I. L. Chuang and Y. Yamamoto, A simple quantum computer,Phys. Rev. A,52:3489–3496 (1995).
W. G. Teich, K. Obermeyer, and G. Mahler, Structural basis of multistationary quantum systems. II. Effective few-particle dynamics,Phys. Rev. B
C. S. Lent and P. D. Tougaw, Logical devices implemented using quantum cellular automata,J. Appl. Phys.
W. G. Teich and G. Mahler, Stochastic dynamics of individual quantum systems: Stationary rate equations,Phys. Rev. A
45:3300–3318 (1992) H. Körner and G. Mahler, Optically driven quantum networks: Applications in molecular electronics,Phys. Rev. B
W. D. Hillis, New computer architectures and their relationship to physics or why computer science is no good,Int. J. Theor. Phys.
21:255–262 (1982); N. Margolus, Parallel quantum computation, inComplexity, Entropy, and the Physics of Information, W. H. Zurek, ed. (Addison-Wesley, Redwood City, California, 1990), pp. 273–287; B. Hasslacher, Parallel billiards and monster systems, inA New Era in Computation, N. Metropolis and G.-C. Rota, eds. (MIT Press, Cambridge, Massachussetts, 1993), pp. 53–65; M. Biafore, Cellular automata for nanometer-scale computation,Physica D
70:415–433 (1994); R. Mainieri, Design constraints for nanometer scale quantum computers, preprint LA-UR 93-4333, [cond-mat/9410109] (1993).
S. Ulam, Random processes and transformations inProceedings of the International Congress of Mathematicians, L. M. Graves, E. Hille, P. A. Smith and O. Zariski, eds. (AMS, Providence, Rhode Island, 1952), Vol II, pp. 264–275. J. von Neumann,Theory of Self-Reproducing Automata, edited and completed by A. W. Burks (University of Illinois Press, Urbana, Illinois, 1966).
G. Grössing and A. Zeilinger, Quantum cellular automata,Complex Systems
S. Fussy, G. Grössing, H. Schwabl and A. Scrinzi, Nonlocal computation in quantum cellular automata,Phys. Rev. A,48:3470–3477 (1993).
K. Morita and M. Harao, Computation universality of one-dimensional reversible (injective) cellular automata,Trans. IEICE Japan E
G. V. Riazanov, The Feynman path integral for the Dirac equation,Sov. Phys. JETP
6:1107–1113 (1958); R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, (McGraw-Hill, New York, 1965), pp. 34–36.
J. Hardy, Y. Pomeau, and O. de Pazzis, Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions,J. Math. Phys.
14:1746–1759. (1973); J. Hardy, O. de Pazzis, and Y. Pomeau, Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions,Phys. Rev. A
13:1949–1961 (1976); U. Frisch, B. Hasslacher, and Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation,Phys. Rev. Lett.
S. Succi and R. Benzi, Lattice Boltzmann equation for quantum mechanics,Physica D
69:327–332 (1993); S. Succi, Numerical solution of the Schroedinger equation using a quantum lattice Boltzmann equation, preprint [comp-gas/9307001] (1993).
I. Bialynicki-Birula, Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata,Phys. Rev. D
R. Landauer, Is quantum mechanics useful?Phil. Trans. R. Soc. Lond. A,353:367–376 (1995).
M. B. Plenio and P. L. Knight, Realistic lower, bounds for the factorization time of large numbers on a quantum computer, preprint [quant-ph/9512001] (1995); D. Beckman, A. N. Chari, S. Devabhaktuni, and J. Preskill, Efficient networks for quantum factoring, preprint CALT-68-2021, [quant-ph/9602016] (1996).
W. G. Unruh, Maintaining coherence, in quantum computers,Phys. Rev. A,51:992–997, (1995); G. M. Palma, K.-A. Souminen and A. Ekert, Quantum computers and dissipation,Proc. R. Soc. Lond. A
I. L. Chuang, R. Laflamme, P. Shor, and W. H. Zurek, Quantum computers, factoring and decoherence,Science
270:1633–1635 (1995); C. Miquel, J. P. Paz, and R. Perazzo, Factoring in a dissipative quantum computer, preprint [quant-ph/9601021] (1996).
H. Weyl,The Theory of Groups and Quantum Mechanics (Dover, New York, 1950).
S. Wolfram, Computation theory of cellular automata,Commun. Math. Phys.
P. Ruján, Cellular automata and statistical mechanical models,J. Stat. Phys.
49:139–222. (1987); A. Georges and P. Le Doussal, From equilibrium spin models to probabilistic cellular automata,J. Stat. Phys.
T. Toffoli and N. H. Margolus, Invertible cellular automata: A review,Physica D
Y. L. Luke,The Special Functions and Their Approximations (Academic Press, New York, 1969), Vol. I, p. 49.
T. Jacobson and L. S. Schulman, Quantum stochastics: the passage from a relativistic to a non-relativistic path integral,J. Phys. A: Math. Gen.
D. A. Meyer, In preparation.
B. Hasslacher and D. A. Meyer, Lattice gases and exactly solvable models,J. Stat. Phys.
R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982).
C. Destri and H. J. de Vega, Light-cone lattice approach to fermionic theories in 2D,Nucl. Phys. B
D. Kandel, E. Domany, and B. Nienhuis, A six-vertex model as a diffusion problem: Derivation of correlation functions,J. Phys. A: Math. Gen.
23:L755-L762 (1990); P. Orland Six-vertex models as Fermi gases,Int. J. Mod. Phys. B
M. Hénon, On the relation between lattice gases and cellular automata; inDiscrete Kinetic Theory, Lattice Gas Dynamics and Foundations of Hydrodynamics, R. Monaco, ed. (World Scientific, Singapore, 1989), pp. 160–161.
H. Hrgovčić, Quantum mechanics on a space-time lattice using path integrals in a Minkowski metric,Int. J. Theor. Phys.
33:745–795 (1994); T. M. Samols, A stochastic model of a quantum field theory,J. Stat. Phys.
H. B. Nielsen and M. Ninomiya, A no-go theorem for regularizing chiral fermions,Phys. Lett. B
105:219–223 (1981), and references therein.
Y. Nakawaki, A new choice for two-dimensional Dirac equation on a spatial lattice,Prog. Theor. Phys.
61:1855–1857 (1979); R. Stacey, Eliminating lattice fermion doubling,Phys. Rev. D
26:468–472 (1982); J. M. Rabin, Homology theory of lattice fermion doubling,Nucl. Phys. B
L. Susskind, Lattice fermions,Phys. Rev. D.
K. G. Wilson, Confinement of quarks,Phys. Rev. D
L. Bombelli, J. Lee, D. A. Meyer, and R. D. Sorkin Spacetime as a causal set,Phys. Rev. Lett.
59:521–524 (1987); D. A. Meyer, Spacetime Ising models, UCSD preprint (1995); D. A. Meyer, Induced actions for causal sets, UCSD preprint (1995).