13,189 research outputs found
Undecidability of the Spectral Gap (full version)
We show that the spectral gap problem is undecidable. Specifically, we
construct families of translationally-invariant, nearest-neighbour Hamiltonians
on a 2D square lattice of d-level quantum systems (d constant), for which
determining whether the system is gapped or gapless is an undecidable problem.
This is true even with the promise that each Hamiltonian is either gapped or
gapless in the strongest sense: it is promised to either have continuous
spectrum above the ground state in the thermodynamic limit, or its spectral gap
is lower-bounded by a constant in the thermodynamic limit. Moreover, this
constant can be taken equal to the local interaction strength of the
Hamiltonian.Comment: v1: 146 pages, 56 theorems etc., 15 figures. See shorter companion
paper arXiv:1502.04135 (same title and authors) for a short version omitting
technical details. v2: Small but important fix to wording of abstract. v3:
Simplified and shortened some parts of the proof; minor fixes to other parts.
Now only 127 pages, 55 theorems etc., 10 figures. v4: Minor updates to
introductio
Time and Space Bounds for Reversible Simulation
We prove a general upper bound on the tradeoff between time and space that
suffices for the reversible simulation of irreversible computation. Previously,
only simulations using exponential time or quadratic space were known.
The tradeoff shows for the first time that we can simultaneously achieve
subexponential time and subquadratic space.
The boundary values are the exponential time with hardly any extra space
required by the Lange-McKenzie-Tapp method and the ()th power time with
square space required by the Bennett method. We also give the first general
lower bound on the extra storage space required by general reversible
simulation. This lower bound is optimal in that it is achieved by some
reversible simulations.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science,
Vol xxx Springer-Verlag, Berlin, 200
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
A digital computer is generally believed to be an efficient universal
computing device; that is, it is believed able to simulate any physical
computing device with an increase in computation time of at most a polynomial
factor. This may not be true when quantum mechanics is taken into
consideration. This paper considers factoring integers and finding discrete
logarithms, two problems which are generally thought to be hard on a classical
computer and have been used as the basis of several proposed cryptosystems.
Efficient randomized algorithms are given for these two problems on a
hypothetical quantum computer. These algorithms take a number of steps
polynomial in the input size, e.g., the number of digits of the integer to be
factored.Comment: 28 pages, LaTeX. This is an expanded version of a paper that appeared
in the Proceedings of the 35th Annual Symposium on Foundations of Computer
Science, Santa Fe, NM, Nov. 20--22, 1994. Minor revisions made January, 199
Labeless and reversible immunosensor assay based upon an electrochemical current-transient protocol
A novel labeless and reversible immunoassay based upon an electrochemical
current-transient protocol is reported which offers many advantages in
comparison to classical immuno-biochemical analyses in terms of simplicity,
speed of response, reusability and possibility of multiple determinations.
Conducting polypyrrole films containing antibodies against 1) Bovine Serum
Albumin (BSA) and 2) Digoxin were deposited on the surface of platinum
electrodes to produce conductive affinity matrices having clearly defined
binding characteristics. The deposition process has been investigated using 125I
labelled anti-digoxin to determine optimal fabrication protocols. Antibody
integrity and activity, together with non-specific binding of antigen on the
conducting matrix have also been investigated using tritiated digoxin to probe
polypyrrole/anti-digoxin films. Amperometric responses to digoxin were recorded
in flow conditions using these films, but the technique was limited in use
mainly due to baseline instability. Anti-BSA - polypyrrole matrices were
investigated in more detail in both flow and quiescent conditions. No observable
response was found in flow conditions, however under quiescent conditions (in
non-stirred batch cell), anti-BSA – polypyrrole films have been demonstrated to
function as novel quantitative chronoamperometric immuno-biosensors when
interrogated using a pulsed potential waveform. The behaviour of the electrodes
showed that the antibody/antigen binding and/or interaction process underlying
the response observed was reversible in nature, indicating that the electrodes
could be used for multiple sensing protocols. Calibration profiles for BSA
demonstrated linearity for a concentration range of 0-50 ppm but tended towards
a plateau at higher concentrations. Factors relating to replicate sensor
production, sample measurement and reproducibility are discuss
Effective Theories for Circuits and Automata
Abstracting an effective theory from a complicated process is central to the
study of complexity. Even when the underlying mechanisms are understood, or at
least measurable, the presence of dissipation and irreversibility in
biological, computational and social systems makes the problem harder. Here we
demonstrate the construction of effective theories in the presence of both
irreversibility and noise, in a dynamical model with underlying feedback. We
use the Krohn-Rhodes theorem to show how the composition of underlying
mechanisms can lead to innovations in the emergent effective theory. We show
how dissipation and irreversibility fundamentally limit the lifetimes of these
emergent structures, even though, on short timescales, the group properties may
be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure
Intrinsically universal one-dimensional quantum cellular automata in two flavours
We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better
explained and formalized, and a novel result about intrinsic universality
with only finite initial configurations is give
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