1,037 research outputs found
Topological phases with parafermions: theory and blueprints
We concisely review the recent evolution in the study of parafermions --
exotic emergent excitations that generalize Majorana fermions and similarly
underpin a host of novel phenomena. First we illustrate the intimate connection
between Z_3-symmetric "spin" chains and one-dimensional parafermion lattice
models, highlighting how the latter host a topological phase featuring
protected edge zero modes. We then tour several blueprints for the laboratory
realization of parafermion zero modes -- focusing on quantum
Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional
topological insulators -- and describe striking experimental fingerprints that
they provide. Finally, we discuss how coupled parafermion arrays in quantum
Hall architectures yield topological phases that potentially furnish hardware
for a universal, intrinsically decoherence-free quantum computer.Comment: 14 pages, 4 figures; slated for Annual Reviews of Condensed Matter
Physic
Variational neural network ansatz for steady states in open quantum systems
We present a general variational approach to determine the steady state of
open quantum lattice systems via a neural network approach. The steady-state
density matrix of the lattice system is constructed via a purified neural
network ansatz in an extended Hilbert space with ancillary degrees of freedom.
The variational minimization of cost functions associated to the master
equation can be performed using a Markov chain Monte Carlo sampling. As a first
application and proof-of-principle, we apply the method to the dissipative
quantum transverse Ising model.Comment: 6 pages, 4 figures, 54 references, 5 pages of Supplemental
Information
Valence Bond Solids for Quantum Computation
Cluster states are entangled multipartite states which enable to do universal
quantum computation with local measurements only. We show that these states
have a very simple interpretation in terms of valence bond solids, which allows
to understand their entanglement properties in a transparent way. This allows
to bridge the gap between the differences of the measurement-based proposals
for quantum computing, and we will discuss several features and possible
extensions
Quantum-assisted finite-element design optimization
Quantum annealing devices such as the ones produced by D-Wave systems are
typically used for solving optimization and sampling tasks, and in both
academia and industry the characterization of their usefulness is subject to
active research. Any problem that can naturally be described as a weighted,
undirected graph may be a particularly interesting candidate, since such a
problem may be formulated a as quadratic unconstrained binary optimization
(QUBO) instance, which is solvable on D-Wave's Chimera graph architecture. In
this paper, we introduce a quantum-assisted finite-element method for design
optimization. We show that we can minimize a shape-specific quantity, in our
case a ray approximation of sound pressure at a specific position around an
object, by manipulating the shape of this object. Our algorithm belongs to the
class of quantum-assisted algorithms, as the optimization task runs iteratively
on a D-Wave 2000Q quantum processing unit (QPU), whereby the evaluation and
interpretation of the results happens classically. Our first and foremost aim
is to explain how to represent and solve parts of these problems with the help
of a QPU, and not to prove supremacy over existing classical finite-element
algorithms for design optimization.Comment: 17 pages, 5 figure
A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms
Recent years have seen significant advances in quantum/quantum-inspired
technologies capable of approximately searching for the ground state of Ising
spin Hamiltonians. The promise of leveraging such technologies to accelerate
the solution of difficult optimization problems has spurred an increased
interest in exploring methods to integrate Ising problems as part of their
solution process, with existing approaches ranging from direct transcription to
hybrid quantum-classical approaches rooted in existing optimization algorithms.
While it is widely acknowledged that quantum computers should augment classical
computers, rather than replace them entirely, comparatively little attention
has been directed toward deriving analytical characterizations of their
interactions. In this paper, we present a formal analysis of hybrid algorithms
in the context of solving mixed-binary quadratic programs (MBQP) via Ising
solvers. We show the exactness of a convex copositive reformulation of MBQPs,
allowing the resulting reformulation to inherit the straightforward analysis of
convex optimization. We propose to solve this reformulation with a hybrid
quantum-classical cutting-plane algorithm. Using existing complexity results
for convex cutting-plane algorithms, we deduce that the classical portion of
this hybrid framework is guaranteed to be polynomial time. This suggests that
when applied to NP-hard problems, the complexity of the solution is shifted
onto the subroutine handled by the Ising solver
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