111,445 research outputs found
Quantum Chaos & Quantum Computers
The standard generic quantum computer model is studied analytically and
numerically and the border for emergence of quantum chaos, induced by
imperfections and residual inter-qubit couplings, is determined. This
phenomenon appears in an isolated quantum computer without any external
decoherence. The onset of quantum chaos leads to quantum computer hardware
melting, strong quantum entropy growth and destruction of computer operability.
The time scales for development of quantum chaos and ergodicity are determined.
In spite the fact that this phenomenon is rather dangerous for quantum
computing it is shown that the quantum chaos border for inter-qubit coupling is
exponentially larger than the energy level spacing between quantum computer
eigenstates and drops only linearly with the number of qubits n. As a result
the ideal multi-qubit structure of the computer remains rather robust against
imperfections. This opens a broad parameter region for a possible realization
of quantum computer. The obtained results are related to the recent studies of
quantum chaos in such many-body systems as nuclei, complex atoms and molecules,
finite Fermi systems and quantum spin glass shards which are also reviewed in
the paper.Comment: Lecture at Nobel symposium on "Quantum chaos", June 2000, Sweden;
revtex, 10 pages, 9 figure
Quantum Robots and Quantum Computers
Validation of a presumably universal theory, such as quantum mechanics,
requires a quantum mechanical description of systems that carry out theoretical
calculations and experiments. The description of quantum computers is under
active development. No description of systems to carry out experiments has been
given. A small step in this direction is taken here by giving a description of
quantum robots as mobile systems with on board quantum computers that interact
with environments. Some properties of these systems are discussed. A specific
model based on the literature descriptions of quantum Turing machines is
presented.Comment: 18 pages, RevTex, one postscript figure. Paper considerably revised
and enlarged. submitted to Phys. Rev.
Reliable Quantum Computers
The new field of quantum error correction has developed spectacularly since
its origin less than two years ago. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment. Recovery from errors can work effectively even if occasional
mistakes occur during the recovery procedure. Furthermore, encoded quantum
information can be processed without serious propagation of errors. Hence, an
arbitrarily long quantum computation can be performed reliably, provided that
the average probability of error per quantum gate is less than a certain
critical value, the accuracy threshold. A quantum computer storing about 10^6
qubits, with a probability of error per quantum gate of order 10^{-6}, would be
a formidable factoring engine. Even a smaller, less accurate quantum computer
would be able to perform many useful tasks. (This paper is based on a talk
presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18
December 1996.)Comment: 24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
Quantum Computers and Quantum Coherence
If the states of spins in solids can be created, manipulated, and measured at
the single-quantum level, an entirely new form of information processing,
quantum computing, will be possible. We first give an overview of quantum
information processing, showing that the famous Shor speedup of integer
factoring is just one of a host of important applications for qubits, including
cryptography, counterfeit protection, channel capacity enhancement, distributed
computing, and others. We review our proposed spin-quantum dot architecture for
a quantum computer, and we indicate a variety of first generation materials,
optical, and electrical measurements which should be considered. We analyze the
efficiency of a two-dot device as a transmitter of quantum information via the
ballistic propagation of carriers in a Fermi sea.Comment: 13 pages, latex, one eps figure. Prepared for special issue of J.
Mag. Magn. Matl., "Magnetism beyond 2000". Version 2: small revisions and
correction
Quantum Walks, Quantum Gates and Quantum Computers
The physics of quantum walks on graphs is formulated in Hamiltonian language,
both for simple quantum walks and for composite walks, where extra discrete
degrees of freedom live at each node of the graph. It is shown how to map
between quantum walk Hamiltonians and Hamiltonians for qubit systems and
quantum circuits; this is done for both a single- and multi-excitation coding,
and for more general mappings. Specific examples of spin chains, as well as
static and dynamic systems of qubits, are mapped to quantum walks, and walks on
hyperlattices and hypercubes are mapped to various gate systems. We also show
how to map a quantum circuit performing the quantum Fourier transform, the key
element of Shor's algorithm, to a quantum walk system doing the same. The
results herein are an essential preliminary to a Hamiltonian formulation of
quantum walks in which coupling to a dynamic quantum environment is included.Comment: 17 pages, 10 figure
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