161 research outputs found
Measurement-based quantum computation in a 2D phase of matter
Recently it has been shown that the non-local correlations needed for
measurement based quantum computation (MBQC) can be revealed in the ground
state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model involving nearest
neighbor spin-3/2 interactions on a honeycomb lattice. This state is not
singular but resides in the disordered phase of ground states of a large family
of Hamiltonians characterized by short-range-correlated valence bond solid
states. By applying local filtering and adaptive single particle measurements
we show that most states in the disordered phase can be reduced to a graph of
correlated qubits that is a scalable resource for MBQC. At the transition
between the disordered and Neel ordered phases we find a transition from
universal to non-universal states as witnessed by the scaling of percolation in
the reduced graph state.Comment: 8 pages, 6 figures, comments welcome. v2: published versio
The resource theory of quantum reference frames: manipulations and monotones
Every restriction on quantum operations defines a resource theory,
determining how quantum states that cannot be prepared under the restriction
may be manipulated and used to circumvent the restriction. A superselection
rule is a restriction that arises through the lack of a classical reference
frame and the states that circumvent it (the resource) are quantum reference
frames. We consider the resource theories that arise from three types of
superselection rule, associated respectively with lacking: (i) a phase
reference, (ii) a frame for chirality, and (iii) a frame for spatial
orientation. Focussing on pure unipartite quantum states (and in some cases
restricting our attention even further to subsets of these), we explore
single-copy and asymptotic manipulations. In particular, we identify the
necessary and sufficient conditions for a deterministic transformation between
two resource states to be possible and, when these conditions are not met, the
maximum probability with which the transformation can be achieved. We also
determine when a particular transformation can be achieved reversibly in the
limit of arbitrarily many copies and find the maximum rate of conversion. A
comparison of the three resource theories demonstrates that the extent to which
resources can be interconverted decreases as the strength of the restriction
increases. Along the way, we introduce several measures of frameness and prove
that these are monotonically nonincreasing under various classes of operations
that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio
Quantum Commuting Circuits and Complexity of Ising Partition Functions
Instantaneous quantum polynomial-time (IQP) computation is a class of quantum
computation consisting only of commuting two-qubit gates and is not universal
in the sense of standard quantum computation. Nevertheless, it has been shown
that if there is a classical algorithm that can simulate IQP efficiently, the
polynomial hierarchy (PH) collapses at the third level, which is highly
implausible. However, the origin of the classical intractability is still less
understood. Here we establish a relationship between IQP and computational
complexity of the partition functions of Ising models. We apply the established
relationship in two opposite directions. One direction is to find subclasses of
IQP that are classically efficiently simulatable in the strong sense, by using
exact solvability of certain types of Ising models. Another direction is
applying quantum computational complexity of IQP to investigate (im)possibility
of efficient classical approximations of Ising models with imaginary coupling
constants. Specifically, we show that there is no fully polynomial randomized
approximation scheme (FPRAS) for Ising models with almost all imaginary
coupling constants even on a planar graph of a bounded degree, unless the PH
collapses at the third level. Furthermore, we also show a multiplicative
approximation of such a class of Ising partition functions is at least as hard
as a multiplicative approximation for the output distribution of an arbitrary
quantum circuit.Comment: 36 pages, 5 figure
Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
Topological color codes are among the stabilizer codes with remarkable
properties from quantum information perspective. In this paper we construct a
four-valent lattice, the so called ruby lattice, governed by a 2-body
Hamiltonian. In a particular regime of coupling constants, degenerate
perturbation theory implies that the low energy spectrum of the model can be
described by a many-body effective Hamiltonian, which encodes the color code as
its ground state subspace. The gauge symmetry
of color code could already be realized by
identifying three distinct plaquette operators on the lattice. Plaquettes are
extended to closed strings or string-net structures. Non-contractible closed
strings winding the space commute with Hamiltonian but not always with each
other giving rise to exact topological degeneracy of the model. Connection to
2-colexes can be established at the non-perturbative level. The particular
structure of the 2-body Hamiltonian provides a fruitful interpretation in terms
of mapping to bosons coupled to effective spins. We show that high energy
excitations of the model have fermionic statistics. They form three families of
high energy excitations each of one color. Furthermore, we show that they
belong to a particular family of topological charges. Also, we use
Jordan-Wigner transformation in order to test the integrability of the model
via introducing of Majorana fermions. The four-valent structure of the lattice
prevents to reduce the fermionized Hamiltonian into a quadratic form due to
interacting gauge fields. We also propose another construction for 2-body
Hamiltonian based on the connection between color codes and cluster states. We
discuss this latter approach along the construction based on the ruby lattice.Comment: 56 pages, 16 figures, published version
The Baum-Connes Conjecture via Localisation of Categories
We redefine the Baum-Connes assembly map using simplicial approximation in
the equivariant Kasparov category. This new interpretation is ideal for
studying functorial properties and gives analogues of the assembly maps for all
equivariant homology theories, not just for the K-theory of the crossed
product. We extend many of the known techniques for proving the Baum-Connes
conjecture to this more general setting
Mapping all classical spin models to a lattice gauge theory
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the
partition function of all classical spin models, including all discrete
standard statistical models and all Abelian discrete lattice gauge theories
(LGTs), can be expressed as a special instance of the partition function of a
4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a
unification of models with apparently very different features into a single
complete model. The result uses an equality between the Hamilton function of
any classical spin model and the Hamilton function of a model with all possible
k-body Ising-type interactions, for all k, which we also prove. Here, we
elaborate on the proof of the result, and we illustrate it by computing
quantities of a specific model as a function of the partition function of the
4D Z_2 LGT. The result also allows one to establish a new method to compute the
mean-field theory of Z_2 LGTs with d > 3, and to show that computing the
partition function of the 4D Z_2 LGT is computationally hard (#P hard). The
proof uses techniques from quantum information.Comment: 21 pages, 21 figures; published versio
The Intrinsic Shapes of Low Surface Brightness Galaxies (LSBGs):A Discriminant of LSBG Galaxy Formation Mechanisms
We use the low surface brightness galaxy (LSBG) samples created from the Hyper Suprime-Cam Subaru Strategic Program (781 galaxies), the Dark Energy Survey (20977 galaxies), and the Legacy Survey (selected via H I detection in the Arecibo Legacy Fast ALFA Survey, 188 galaxies) to infer the intrinsic shape distribution of the LSBG population. To take into account the effect of the surface brightness cuts employed when constructing LSBG samples, we simultaneously model both the projected ellipticity and the apparent surface brightness in our shape inference. We find that the LSBG samples are well characterized by oblate spheroids, with no significant difference between red and blue LSBGs. This inferred shape distribution is in good agreement with similar inferences made for ultra-diffuse cluster galaxy samples, indicating that environment does not play a key role in determining the intrinsic shape of LSBGs. We also find some evidence that LSBGs are more thickened than similarly massive high surface brightness dwarfs. We compare our results to intrinsic shape measures from contemporary cosmological simulations, and find that the observed LSBG intrinsic shapes place considerable constraints on the formation path of such galaxies. In particular, LSBG production via the migration of star formation to large radii produces intrinsic shapes in good agreement with our observational findings
Optical generation of matter qubit graph states
We present a scheme for rapidly entangling matter qubits in order to create
graph states for one-way quantum computing. The qubits can be simple 3-level
systems in separate cavities. Coupling involves only local fields and a static
(unswitched) linear optics network. Fusion of graph state sections occurs with,
in principle, zero probability of damaging the nascent graph state. We avoid
the finite thresholds of other schemes by operating on two entangled pairs, so
that each generates exactly one photon. We do not require the relatively slow
single qubit local flips to be applied during the growth phase: growth of the
graph state can then become a purely optical process. The scheme naturally
generates graph states with vertices of high degree and so is easily able to
construct minimal graph states, with consequent resource savings. The most
efficient approach will be to create new graph state edges even as qubits
elsewhere are measured, in a `just in time' approach. An error analysis
indicates that the scheme is relatively robust against imperfections in the
apparatus.Comment: 10 pages in 2 column format, includes 4 figures. Problems with
figures resolve
Ethics of Engagement and Insider-Outsider Perspectives: Issues and Dilemmas in Cross-Cultural Interpretation
This article offers insights into the ethics of engagement and methodological issues and dilemmas in cross-cultural interpretation for researchers who are positioned at different points of the insider-outsider spectrum. The discussion uses examples from qualitative research with Sikh families in Britain and focuses on the design of the methodology and co-interpretation of data from in-depth interviews, both during the interactive data gathering phase and the post-interview analysis and interpretation phase. The researchers represent differing degrees of insider-outsiderness in relation to the British Sikh community; one is a cultural insider (a Sikh) whilst the other is an outsider (non-Sikh). In other respects they share a number of characteristics, including gender, a history of migration, bilingualism and living and teaching in superdiverse communities which all impact on the nature of their engagement with the research participants and with each other as co-researchers. Our reflexive analysis shows that established binary distinctions and polarities in research practice, such as insider/outsider, are inadequate for conceptualising the fluidity and complexity of the ethics of engagement in co-researching. We argue that both theoretically and empirically a more nuanced conceptualisation reflects the realities of multiple researcher positionalities, interpretations and power relations
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
We present an efficient quantum algorithm for the exact evaluation of either
the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function
Z for a family of graphs related to irreducible cyclic codes. This problem is
related to the evaluation of the Jones and Tutte polynomials. We consider the
connection between the weight enumerator polynomial from coding theory and Z
and exploit the fact that there exists a quantum algorithm for efficiently
estimating Gauss sums in order to obtain the weight enumerator for a certain
class of linear codes. In this way we demonstrate that for a certain class of
sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon)
graphs, quantum computers provide a polynomial speed up in the difference
between the number of edges and vertices of the graph, and an exponential speed
up in q, over the best classical algorithms known to date
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