2,723 research outputs found
Homological Product Codes
Quantum codes with low-weight stabilizers known as LDPC codes have been
actively studied recently due to their simple syndrome readout circuits and
potential applications in fault-tolerant quantum computing. However, all
families of quantum LDPC codes known to this date suffer from a poor distance
scaling limited by the square-root of the code length. This is in a sharp
contrast with the classical case where good families of LDPC codes are known
that combine constant encoding rate and linear distance. Here we propose the
first family of good quantum codes with low-weight stabilizers. The new codes
have a constant encoding rate, linear distance, and stabilizers acting on at
most qubits, where is the code length. For comparison, all
previously known families of good quantum codes have stabilizers of linear
weight. Our proof combines two techniques: randomized constructions of good
quantum codes and the homological product operation from algebraic topology. We
conjecture that similar methods can produce good stabilizer codes with
stabilizer weight for any . Finally, we apply the homological
product to construct new small codes with low-weight stabilizers.Comment: 49 page
Quantum statistics on graphs
Quantum graphs are commonly used as models of complex quantum systems, for
example molecules, networks of wires, and states of condensed matter. We
consider quantum statistics for indistinguishable spinless particles on a
graph, concentrating on the simplest case of abelian statistics for two
particles. In spite of the fact that graphs are locally one-dimensional, anyon
statistics emerge in a generalized form. A given graph may support a family of
independent anyon phases associated with topologically inequivalent exchange
processes. In addition, for sufficiently complex graphs, there appear new
discrete-valued phases. Our analysis is simplified by considering combinatorial
rather than metric graphs -- equivalently, a many-particle tight-binding model.
The results demonstrate that graphs provide an arena in which to study new
manifestations of quantum statistics. Possible applications include topological
quantum computing, topological insulators, the fractional quantum Hall effect,
superconductivity and molecular physics.Comment: 21 pages, 6 figure
More Torsion in the Homology of the Matching Complex
A matching on a set is a collection of pairwise disjoint subsets of
of size two. Using computers, we analyze the integral homology of the matching
complex , which is the simplicial complex of matchings on the set . The main result is the detection of elements of order in the
homology for . Specifically, we show that there are
elements of order 5 in the homology of for and for . The only previously known value was , and in this particular
case we have a new computer-free proof. Moreover, we show that there are
elements of order 7 in the homology of for all odd between 23 and 41
and for . In addition, there are elements of order 11 in the homology of
and elements of order 13 in the homology of . Finally, we
compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of
for ; a complete description of the homology
already exists for . To prove the results, we use a
representation-theoretic approach, examining subcomplexes of the chain complex
of obtained by letting certain groups act on the chain complex.Comment: 35 pages, 10 figure
On the Expansions in Spin Foam Cosmology
We discuss the expansions used in spin foam cosmology. We point out that
already at the one vertex level arbitrarily complicated amplitudes contribute,
and discuss the geometric asymptotics of the five simplest ones. We discuss
what type of consistency conditions would be required to control the expansion.
We show that the factorisation of the amplitude originally considered is best
interpreted in topological terms. We then consider the next higher term in the
graph expansion. We demonstrate the tension between the truncation to small
graphs and going to the homogeneous sector, and conclude that it is necessary
to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio
Homotopy Theory of Strong and Weak Topological Insulators
We use homotopy theory to extend the notion of strong and weak topological
insulators to the non-stable regime (low numbers of occupied/empty energy
bands). We show that for strong topological insulators in d spatial dimensions
to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional
insulators, a more restrictive definition of "strong" is required. However,
this does not exclude weak topological insulators from being "truly
d-dimensional", which we demonstrate by an example. Additionally, we prove some
useful technical results, including the homotopy theoretic derivation of the
factorization of invariants over the torus into invariants over spheres in the
stable regime, as well as the rigorous justification of replacing by
and by as is common in the current
literature.Comment: 11 pages, 3 figure
Discrete Morse functions for graph configuration spaces
We present an alternative application of discrete Morse theory for
two-particle graph configuration spaces. In contrast to previous constructions,
which are based on discrete Morse vector fields, our approach is through Morse
functions, which have a nice physical interpretation as two-body potentials
constructed from one-body potentials. We also give a brief introduction to
discrete Morse theory. Our motivation comes from the problem of quantum
statistics for particles on networks, for which generalized versions of anyon
statistics can appear.Comment: 26 page
High density QCD on a Lefschetz thimble?
It is sometimes speculated that the sign problem that afflicts many quantum
field theories might be reduced or even eliminated by choosing an alternative
domain of integration within a complexified extension of the path integral (in
the spirit of the stationary phase integration method). In this paper we start
to explore this possibility somewhat systematically. A first inspection reveals
the presence of many difficulties but - quite surprisingly - most of them have
an interesting solution. In particular, it is possible to regularize the
lattice theory on a Lefschetz thimble, where the imaginary part of the action
is constant and disappears from all observables. This regularization can be
justified in terms of symmetries and perturbation theory. Moreover, it is
possible to design a Monte Carlo algorithm that samples the configurations in
the thimble. This is done by simulating, effectively, a five dimensional
system. We describe the algorithm in detail and analyze its expected cost and
stability. Unfortunately, the measure term also produces a phase which is not
constant and it is currently very expensive to compute. This residual sign
problem is expected to be much milder, as the dominant part of the integral is
not affected, but we have still no convincing evidence of this. However, the
main goal of this paper is to introduce a new approach to the sign problem,
that seems to offer much room for improvements. An appealing feature of this
approach is its generality. It is illustrated first in the simple case of a
scalar field theory with chemical potential, and then extended to the more
challenging case of QCD at finite baryonic density.Comment: Misleading footnote 1 corrected: locality deserves better
investigations. Formula (31) corrected (we thank Giovanni Eruzzi for this
observation). Note different title in journal versio
A monument to the player: Preserving a landscape of socio-cultural capital in the transitional MMORPG
This is the pre-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 Taylor & Francis LtdMassively multiplayer online role-playing games (MMORPGs) produce dynamic socio-ludic worlds that nurture both culture and gameplay to shape experiences. Despite the persistent nature of these games, however, the virtual spaces that anchor these worlds may not always be able to exist in perpetuity. Encouraging a community to migrate from one space to another is a challenge now facing some game developers. This paper examines the case of Guild Wars® and its “Hall of Monuments”, a feature that bridges the accomplishments of players from the current game to the forthcoming sequel. Two factor analyses describe the perspectives of 105 and 187 self-selected participants. The results reveal four factors affecting attitudes towards the feature, but they do not strongly correlate with existing motivational frameworks, and significant differences were found between different cultures within the game. This informs a discussion about the implications and facilitation of such transitions, investigating themes of capital, value perception and assumptive worlds. It is concluded that the way subcultures produce meaning needs to be considered when attempting to preserve the socio-cultural landscape
Differences in client and therapist views of the working alliance in drug treatment
Background - There is growing evidence that the therapeutic alliance is one of the most consistent predictors of retention and outcomes in drug treatment. Recent psychotherapy research has indicated that there is a lack of agreement between client, therapist and observer ratings of the therapeutic alliance; however, the clinical implications of this lack of consensus have not been explored.
Aims - The aims of the study are to (1) explore the extent to which, in drug treatment, clients and counsellors agree in their perceptions of their alliance, and (2) investigate whether the degree of disagreement between clients and counsellors is related to retention in treatment.
Methods - The study recruited 187 clients starting residential rehabilitation treatment for drug misuse in three UK services. Client and counsellor ratings of the therapeutic alliance (using the WAI-S) were obtained during weeks 1-12. Retention was in this study defined as remaining in treatment for at least 12 weeks.
Results - Client and counsellor ratings of the alliance were only weakly related (correlations ranging from r = 0.07 to 0.42) and tended to become more dissimilar over the first 12 weeks in treatment. However, whether or not clients and counsellors agreed on the quality of their relationship did not influence whether clients were retained in treatment.
Conclusions - The low consensus between client and counsellor views of the alliance found in this and other studies highlights the need for drug counsellors to attend closely to their clients' perceptions of the alliance and to seek regular feedback from clients regarding their feelings about their therapeutic relationship
Technical Note: Molecular characterization of aerosol-derived water soluble organic carbon using ultrahigh resolution electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry
Despite the acknowledged relevance of aerosol-derived water-soluble organic carbon (WSOC) to climate and biogeochemical cycling, characterization of aerosol WSOC has been limited. Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS) was utilized in this study to provide detailed molecular level characterization of the high molecular weight (HMW; m/z>223) component of aerosol-derived WSOC collected from rural sites in Virginia and New York, USA. More than 3000 peaks were detected by ESI FT-ICR MS within a m/z range of 223–600 for each sample. Approximately 86% (Virginia) and 78% (New York) of these peaks were assigned molecular formulas using only carbon (C), hydrogen (H), oxygen (O), nitrogen (N), and sulfur (S) as elemental constituents. H/C and O/C molar ratios were plotted on van Krevelen diagrams and indicated a strong contribution of lignin-like and lipid-like compounds to the aerosol-derived WSOC samples. Approximately 1–4% of the peaks in the aerosol-derived WSOC mass spectra were classified as black carbon (BC) on the basis of double bond equivalents calculated from the assigned molecular formulas. In addition, several high-magnitude peaks in the mass spectra of samples from both sites corresponded to molecular formulas proposed in previous secondary organic aerosol (SOA) laboratory investigations indicating that SOAs are important constituents of the WSOC. Overall, ESI FT-ICR MS provides a level of resolution adequate for detailed compositional and source information of the HMW constituents of aerosol-derived WSOC
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