397 research outputs found
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
Quantum Computation, Markov Chains and Combinatorial Optimisation
This thesis addresses two questions related to the title, Quantum Computation, Markov Chains and Combinatorial Optimisation. The first question involves an algorithmic primitive of quantum computation, quantum walks on graphs, and its relation to Markov Chains. Quantum walks have been shown in certain cases to mix faster than their classical counterparts. Lifted Markov chains, consisting of a Markov chain on an extended state space which is projected back down to the original state space, also show considerable speedups in mixing time. We design a lifted Markov chain that in some sense simulates any quantum walk. Concretely, we construct a lifted Markov chain on a connected graph G with n vertices that mixes exactly to the average mixing distribution of a quantum walk on G. Moreover, the mixing time of this chain is the diameter of G. We then consider practical consequences of this result. In the second part of this thesis we address a classic unsolved problem in combinatorial optimisation, graph isomorphism. A theorem of Kozen states that two graphs on n vertices are isomorphic if and only if there is a clique of size n in the weak modular product of the two graphs. Furthermore, a straightforward corollary of this theorem and LovaÌszâs sandwich theorem is if the weak modular product between two graphs is perfect, then checking if the graphs are isomorphic is polynomial in n. We enumerate the necessary and sufficient conditions for the weak modular product of two simple graphs to be perfect. Interesting cases include complete multipartite graphs and disjoint unions of cliques. We find that all perfect weak modular products have factors that fall into classes of graphs for which testing isomorphism is already known to be polynomial in the number of vertices. Open questions and further research directions are discussed
QuOp_MPI: a framework for parallel simulation of quantum variational algorithms
QuOp_MPI is a Python package designed for parallel simulation of quantum
variational algorithms. It presents an object-orientated approach to quantum
variational algorithm design and utilises MPI-parallelised sparse-matrix
exponentiation, the fast Fourier transform and parallel gradient evaluation to
achieve the highly efficient simulation of the fundamental unitary dynamics on
massively parallel systems. In this article, we introduce QuOp_MPI and explore
its application to the simulation of quantum algorithms designed to solve
combinatorial optimisation algorithms including the Quantum Approximation
Optimisation Algorithm, the Quantum Alternating Operator Ansatz, and the
Quantum Walk-assisted Optimisation Algorithm.Comment: Software available at: https://github.com/Edric-Matwiejew/QuOp_MP
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
The next few years will be exciting as prototype universal quantum processors
emerge, enabling implementation of a wider variety of algorithms. Of particular
interest are quantum heuristics, which require experimentation on quantum
hardware for their evaluation, and which have the potential to significantly
expand the breadth of quantum computing applications. A leading candidate is
Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates
between applying a cost-function-based Hamiltonian and a mixing Hamiltonian.
Here, we extend this framework to allow alternation between more general
families of operators. The essence of this extension, the Quantum Alternating
Operator Ansatz, is the consideration of general parametrized families of
unitaries rather than only those corresponding to the time-evolution under a
fixed local Hamiltonian for a time specified by the parameter. This ansatz
supports the representation of a larger, and potentially more useful, set of
states than the original formulation, with potential long-term impact on a
broad array of application areas. For cases that call for mixing only within a
desired subspace, refocusing on unitaries rather than Hamiltonians enables more
efficiently implementable mixers than was possible in the original framework.
Such mixers are particularly useful for optimization problems with hard
constraints that must always be satisfied, defining a feasible subspace, and
soft constraints whose violation we wish to minimize. More efficient
implementation enables earlier experimental exploration of an alternating
operator approach to a wide variety of approximate optimization, exact
optimization, and sampling problems. Here, we introduce the Quantum Alternating
Operator Ansatz, lay out design criteria for mixing operators, detail mappings
for eight problems, and provide brief descriptions of mappings for diverse
problems.Comment: 51 pages, 2 figures. Revised to match journal pape
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Hybrid quantum-classical heuristic for the bin packing problem
Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum resources. Up to now, many problems of different nature have been addressed through the perspective of this revolutionary computation paradigm, but there are still many open questions. In this work, a hybrid classical-quantum approach is presented for dealing with the one-dimensional Bin Packing Problem (1dBPP). The algorithm comprises two modules, each one designed for being executed in different computational ecosystems. First, a quantum subroutine seeks a set of feasible bin configurations of the problem at hand. Secondly, a classical computation subroutine builds complete solutions to the problem from the subsets given by the quantum subroutine. Being a hybrid solver, we have called our method H-BPP. To test our algorithm, we have built 18 different 1dBPP instances as a benchmarking set, in which we analyse the fitness, the number of solutions and the performance of the QC subroutine. Based on these figures of merit we verify that H-BPP is a valid technique to address the 1dBPP.QUANTEK project (ELKARTEK program from the Basque Government, expedient no. KK-2021/00070)
Spanish RamĂłn y Cajal Grant RYC-2020-030503- I
QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies
EU FET Open project Quromorphic (828826) and EPIQUS (899368
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