2,746 research outputs found
Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
We consider measurement-based quantum computation (MBQC) on thermal states of
the interacting cluster Hamiltonian containing interactions between the cluster
stabilizers that undergoes thermal phase transitions. We show that the
long-range order of the symmetry breaking thermal states below a critical
temperature drastically enhance the robustness of MBQC against thermal
excitations. Specifically, we show the enhancement in two-dimensional cases and
prove that MBQC is topologically protected below the critical temperature in
three-dimensional cases. The interacting cluster Hamiltonian allows us to
perform MBQC even at a temperature an order of magnitude higher than that of
the free cluster Hamiltonian.Comment: 8 pages, 7 figure
Conformal boundary states in SU(2)_1/G
We construct boundary states in a particular c=1 conformal field theory, the
SU(2)_1/G orbifold with G a binary finite subgroup of SU(2). These states
preserve the conformal symmetry, at least, but break rational symmetries of the
SU(2)_1/G orbifold in general.Comment: 12 pages, PTPTeX, V2: changed title, much improved presentation,
published versio
Detecting subsystem symmetry protected topological order via entanglement entropy
Subsystem symmetry protected topological (SSPT) order is a type of quantum
order that is protected by symmetries acting on lower-dimensional subsystems of
the entire system. In this paper, we show how SSPT order can be characterized
and detected by a constant correction to the entanglement area law, similar to
the topological entanglement entropy. Focusing on the paradigmatic
two-dimensional cluster phase as an example, we use tensor network methods to
give an analytic argument that almost all states in the phase exhibit the same
correction to the area law, such that this correction may be used to reliably
detect the SSPT order of the cluster phase. Based on this idea, we formulate a
numerical method that uses tensor networks to extract this correction from
ground-state wave functions. We use this method to study the fate of the SSPT
order of the cluster state under various external fields and interactions, and
find that the correction persists unless a phase transition is crossed, or the
subsystem symmetry is explicitly broken. Surprisingly, these results uncover
that the SSPT order of the cluster state persists beyond the cluster phase,
thanks to a new type of subsystem time-reversal symmetry. Finally, we discuss
the correction to the area law found in three-dimensional cluster states on
different lattices, indicating rich behavior for general subsystem symmetriesComment: 17 pages. v2: Published version, minor changes throughou
Symmetry breaking boundaries II. More structures; examples
Various structural properties of the space of symmetry breaking boundary
conditions that preserve an orbifold subalgebra are established. To each such
boundary condition we associate its automorphism type. It is shown that
correlation functions in the presence of such boundary conditions are
expressible in terms of twisted boundary blocks which obey twisted Ward
identities. The subset of boundary conditions that share the same automorphism
type is controlled by a classifying algebra, whose structure constants are
shown to be traces on spaces of chiral blocks. T-duality on boundary conditions
is not a one-to-one map in general. These structures are illustrated in a
number of examples. Several applications, including the construction of non-BPS
boundary conditions in string theory, are exhibited.Comment: 51 pages, LaTeX2
D-branes in lens spaces
We realize the CFT with target a lens space SU(2)/Z_l as a simple current
construction. This allows us to compute the boundary states and the annuli
coefficients, and in particular to study the B-type branes, in purely algebraic
terms. Several issues, like the appearance of fractional branes and symmetry
breaking boundary conditions, can be addressed more directly in this approach
than in a more geometric treatment.Comment: 13 page
Effective quantum memory Hamiltonian from local two-body interactions
In [Phys. Rev. A 88, 062313 (2013)] we proposed and studied a model for a
self-correcting quantum memory in which the energetic cost for introducing a
defect in the memory grows without bounds as a function of system size. This
positive behavior is due to attractive long-range interactions mediated by a
bosonic field to which the memory is coupled. The crucial ingredients for the
implementation of such a memory are the physical realization of the bosonic
field as well as local five-body interactions between the stabilizer operators
of the memory and the bosonic field. Here, we show that both of these
ingredients appear in a low-energy effective theory of a Hamiltonian that
involves only two-body interactions between neighboring spins. In particular,
we consider the low-energy, long-wavelength excitations of an ordered
Heisenberg ferromagnet (magnons) as a realization of the bosonic field.
Furthermore, we present perturbative gadgets for generating the required
five-spin operators. Our Hamiltonian involving only local two-body interactions
is thus expected to exhibit self-correcting properties as long as the noise
affecting it is in the regime where the effective low-energy description
remains valid.Comment: 14 pages, 3 figure
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