5,035 research outputs found
Generating Interpretable Fuzzy Controllers using Particle Swarm Optimization and Genetic Programming
Autonomously training interpretable control strategies, called policies,
using pre-existing plant trajectory data is of great interest in industrial
applications. Fuzzy controllers have been used in industry for decades as
interpretable and efficient system controllers. In this study, we introduce a
fuzzy genetic programming (GP) approach called fuzzy GP reinforcement learning
(FGPRL) that can select the relevant state features, determine the size of the
required fuzzy rule set, and automatically adjust all the controller parameters
simultaneously. Each GP individual's fitness is computed using model-based
batch reinforcement learning (RL), which first trains a model using available
system samples and subsequently performs Monte Carlo rollouts to predict each
policy candidate's performance. We compare FGPRL to an extended version of a
related method called fuzzy particle swarm reinforcement learning (FPSRL),
which uses swarm intelligence to tune the fuzzy policy parameters. Experiments
using an industrial benchmark show that FGPRL is able to autonomously learn
interpretable fuzzy policies with high control performance.Comment: Accepted at Genetic and Evolutionary Computation Conference 2018
(GECCO '18
Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
If we distribute n qubits between two parties, which quantum pure states and
distributions of qubits would allow all-versus-nothing (or
Greenberger-Horne-Zeilinger-like) proofs of Bell's theorem using only
single-qubit measurements? We show a necessary and sufficient condition for the
existence of these proofs for any number of qubits, and provide all distinct
proofs up to n=7 qubits. Remarkably, there is only one distribution of a state
of n=4 qubits, and six distributions, each for a different state of n=6 qubits,
which allow these proofs.Comment: REVTeX4, 4 pages, 2 figure
Graphical description of the action of Clifford operators on stabilizer states
We introduce a graphical representation of stabilizer states and translate
the action of Clifford operators on stabilizer states into graph operations on
the corresponding stabilizer-state graphs. Our stabilizer graphs are
constructed of solid and hollow nodes, with (undirected) edges between nodes
and with loops and signs attached to individual nodes. We find that local
Clifford transformations are completely described in terms of local
complementation on nodes and along edges, loop complementation, and change of
node type or sign. Additionally, we show that a small set of equivalence rules
generates all graphs corresponding to a given stabilizer state; we do this by
constructing an efficient procedure for testing the equality of any two
stabilizer graphs.Comment: 14 pages, 8 figures. Version 2 contains significant changes.
Submitted to PR
Completeness of the classical 2D Ising model and universal quantum computation
We prove that the 2D Ising model is complete in the sense that the partition
function of any classical q-state spin model (on an arbitrary graph) can be
expressed as a special instance of the partition function of a 2D Ising model
with complex inhomogeneous couplings and external fields. In the case where the
original model is an Ising or Potts-type model, we find that the corresponding
2D square lattice requires only polynomially more spins w.r.t the original one,
and we give a constructive method to map such models to the 2D Ising model. For
more general models the overhead in system size may be exponential. The results
are established by connecting classical spin models with measurement-based
quantum computation and invoking the universality of the 2D cluster states.Comment: 4 pages, 1 figure. Minor change
Graphical calculus for Gaussian pure states
We provide a unified graphical calculus for all Gaussian pure states,
including graph transformation rules for all local and semi-local Gaussian
unitary operations, as well as local quadrature measurements. We then use this
graphical calculus to analyze continuous-variable (CV) cluster states, the
essential resource for one-way quantum computing with CV systems. Current
graphical approaches to CV cluster states are only valid in the unphysical
limit of infinite squeezing, and the associated graph transformation rules only
apply when the initial and final states are of this form. Our formalism applies
to all Gaussian pure states and subsumes these rules in a natural way. In
addition, the term "CV graph state" currently has several inequivalent
definitions in use. Using this formalism we provide a single unifying
definition that encompasses all of them. We provide many examples of how the
formalism may be used in the context of CV cluster states: defining the
"closest" CV cluster state to a given Gaussian pure state and quantifying the
error in the approximation due to finite squeezing; analyzing the optimality of
certain methods of generating CV cluster states; drawing connections between
this new graphical formalism and bosonic Hamiltonians with Gaussian ground
states, including those useful for CV one-way quantum computing; and deriving a
graphical measure of bipartite entanglement for certain classes of CV cluster
states. We mention other possible applications of this formalism and conclude
with a brief note on fault tolerance in CV one-way quantum computing.Comment: (v3) shortened title, very minor corrections (v2) minor corrections,
reference added, new figures for CZ gate and beamsplitter graph rules; (v1)
25 pages, 11 figures (made with TikZ
Graph Concatenation for Quantum Codes
Graphs are closely related to quantum error-correcting codes: every
stabilizer code is locally equivalent to a graph code, and every codeword
stabilized code can be described by a graph and a classical code. For the
construction of good quantum codes of relatively large block length,
concatenated quantum codes and their generalizations play an important role. We
develop a systematic method for constructing concatenated quantum codes based
on "graph concatenation", where graphs representing the inner and outer codes
are concatenated via a simple graph operation called "generalized local
complementation." Our method applies to both binary and non-binary concatenated
quantum codes as well as their generalizations.Comment: 26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]]
are added. Submitted to JM
A monomial matrix formalism to describe quantum many-body states
We propose a framework to describe and simulate a class of many-body quantum
states. We do so by considering joint eigenspaces of sets of monomial unitary
matrices, called here "M-spaces"; a unitary matrix is monomial if precisely one
entry per row and column is nonzero. We show that M-spaces encompass various
important state families, such as all Pauli stabilizer states and codes, the
AKLT model, Kitaev's (abelian and non-abelian) anyon models, group coset
states, W states and the locally maximally entanglable states. We furthermore
show how basic properties of M-spaces can transparently be understood by
manipulating their monomial stabilizer groups. In particular we derive a
unified procedure to construct an eigenbasis of any M-space, yielding an
explicit formula for each of the eigenstates. We also discuss the computational
complexity of M-spaces and show that basic problems, such as estimating local
expectation values, are NP-hard. Finally we prove that a large subclass of
M-spaces---containing in particular most of the aforementioned examples---can
be simulated efficiently classically with a unified method.Comment: 11 pages + appendice
Universal quantum computer from a quantum magnet
We show that a local Hamiltonian of spin-3/2 particles with only two-body
nearest-neighbor Affleck-Kennedy-Lieb-Tasaki and exchange-type interactions has
an unique ground state, which can be used to implement universal quantum
computation merely with single-spin measurements. We prove that the Hamiltonian
is gapped, independent of the system size. Our result provides a further step
towards utilizing systems with condensed matter-type interactions for
measurement-based quantum computation.Comment: 5 pages, 3 figure
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