39,741 research outputs found
Population genetics models of local ancestry
Migrations have played an important role in shaping the genetic diversity of
human populations. Understanding genomic data thus requires careful modeling of
historical gene flow. Here we consider the effect of relatively recent
population structure and gene flow, and interpret genomes of individuals that
have ancestry from multiple source populations as mosaics of segments
originating from each population. We propose general and tractable models for
describing the evolution of these patterns of local ancestry and their impact
on genetic diversity. We focus on the length distribution of continuous
ancestry tracts, and the variance in total ancestry proportions among
individuals. The proposed models offer improved agreement with Wright-Fisher
simulation data when compared to state-of-the art models, and can be used to
infer various demographic parameters in gene flow models. Considering HapMap
African-American (ASW) data, we find that a model with two distinct phases of
`European' gene flow significantly improves the modeling of both tract lengths
and ancestry variances.Comment: 25 pages with 7 figures; Genetics: Published online before print
April 4, 201
Hierarchical surface code for network quantum computing with modules of arbitrary size
The network paradigm for quantum computing involves interconnecting many
modules to form a scalable machine. Typically it is assumed that the links
between modules are prone to noise while operations within modules have
significantly higher fidelity. To optimise fault tolerance in such
architectures we introduce a hierarchical generalisation of the surface code: a
small `patch' of the code exists within each module, and constitutes a single
effective qubit of the logic-level surface code. Errors primarily occur in a
two-dimensional subspace, i.e. patch perimeters extruded over time, and the
resulting noise threshold for inter-module links can exceed ~ 10% even in the
absence of purification. Increasing the number of qubits within each module
decreases the number of qubits necessary for encoding a logical qubit. But this
advantage is relatively modest, and broadly speaking a `fine grained' network
of small modules containing only ~ 8 qubits is competitive in total qubit count
versus a `course' network with modules containing many hundreds of qubits.Comment: 12 pages, 11 figure
Efficient variational quantum simulator incorporating active error minimisation
One of the key applications for quantum computers will be the simulation of
other quantum systems that arise in chemistry, materials science, etc, in order
to accelerate the process of discovery. It is important to ask: Can this be
achieved using near future quantum processors, of modest size and under
imperfect control, or must it await the more distant era of large-scale
fault-tolerant quantum computing? Here we propose a variational method
involving closely integrated classical and quantum coprocessors. We presume
that all operations in the quantum coprocessor are prone to error. The impact
of such errors is minimised by boosting them artificially and then
extrapolating to the zero-error case. In comparison to a more conventional
optimised Trotterisation technique, we find that our protocol is efficient and
appears to be fundamentally more robust against error accumulation.Comment: 13 pages, 5 figures; typos fixed and small update
Differential operators on the superline, Berezinians, and Darboux transformations
We consider differential operators on a supermanifold of dimension . We
define non-degenerate operators as those with an invertible top coefficient in
the expansion in the "superderivative" (which is the square root of the
shift generator, the partial derivative in an even variable, with the help of
an odd indeterminate). They are remarkably similar to ordinary differential
operators. We show that every non-degenerate operator can be written in terms
of `super Wronskians' (which are certain Berezinians). We apply this to Darboux
transformations (DTs), proving that every DT of an arbitrary non-degenerate
operator is the composition of elementary first order transformations. Hence
every DT corresponds to an invariant subspace of the source operator and, upon
a choice of basis in this subspace, is expressed by a super-Wronskian formula.
We consider also dressing transformations, i.e., the effect of a DT on the
coefficients of the non-degenerate operator. We calculate these transformations
in examples and make some general statements.Comment: 24 pages, LaTeX, some editorial changes (as compared with the earlier
version
Stabilisers as a design tool for new forms of Lechner-Hauke-Zoller Annealer
In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to
translate a Hamiltonian of spin- particles with 'all-to-all'
interactions into a larger physical lattice with only on-site energies and
local parity constraints. LHZ used this mapping to propose a novel form of
quantum annealing. Here we provide a stabiliser-based formulation within which
we can describe both this prior approach and a wide variety of variants.
Examples include a triangular array supporting all-to-all connectivity, and
moreover arrangements requiring only or spins but providing
interesting bespoke connectivities. Further examples show that arbitrarily high
order logical terms can be efficiently realised, even in a strictly 2D layout.
Our stabilisers can correspond to either even-parity constraints, as in the LHZ
proposal, or as odd-parity constraints. Considering the latter option applied
to the original LHZ layout, we note it may simplify the physical realisation
since the required ancillas are only spin- systems (i.e. qubits,
rather than qutrits) and moreover the interactions are very simple. We make a
preliminary assessment of the impact of this design choices by simulating small
(few-qubit) systems; we find some indications that the new variant may maintain
a larger minimum energy gap during the annealing process.Comment: A dramatically expanded revision: we now show how to use our
stabiliser formulation to construct a wide variety of new physical layouts,
including ones with fewer than Order N^2 spins but custom connectivities, and
a means to achieve higher order coupling even in 2
Towards property-based testing of RESTful web services
Developing APIs as Web Services over HTTP implies adding an extra layer to software, compared to the ones that we would need to develop an API distributed as, for example, a library. This additional layer must be included in testing too, but this implies that the software under test has an additional complexity due both to the need to use an intermediate protocol in tests and to the need to test compliance with the constraints imposed by that protocol: in this case the constraints defined by the REST architectural style. On the other hand, these requirements are common to all the Web Services, and because of that, we should be able to abstract this aspect of the testing model so that we can reuse it in testing any Web Service. In this paper, as a first step towards automating the testing of Web Services over HTTP, we describe a practical mechanism and model for testing RESTful Web Services without side effects and give an example of how we successfully adapted that mechanism to test two different existing Web Services: Storage Room by Thriventures and Google Tasks by Google. For this task we have used Erlang together with state machine models in the property-based testing tool Quviq QuickCheck, implemented using the statem module. 1
- …