38,353 research outputs found
Efficient Approximation of Quantum Channel Capacities
We propose an iterative method for approximating the capacity of
classical-quantum channels with a discrete input alphabet and a finite
dimensional output, possibly under additional constraints on the input
distribution. Based on duality of convex programming, we derive explicit upper
and lower bounds for the capacity. To provide an -close estimate
to the capacity, the presented algorithm requires , where denotes the input alphabet size and
the output dimension. We then generalize the method for the task of
approximating the capacity of classical-quantum channels with a bounded
continuous input alphabet and a finite dimensional output. For channels with a
finite dimensional quantum mechanical input and output, the idea of a universal
encoder allows us to approximate the Holevo capacity using the same method. In
particular, we show that the problem of approximating the Holevo capacity can
be reduced to a multidimensional integration problem. For families of quantum
channels fulfilling a certain assumption we show that the complexity to derive
an -close solution to the Holevo capacity is subexponential or
even polynomial in the problem size. We provide several examples to illustrate
the performance of the approximation scheme in practice.Comment: 36 pages, 1 figur
Reinforcement Learning in Different Phases of Quantum Control
The ability to prepare a physical system in a desired quantum state is
central to many areas of physics such as nuclear magnetic resonance, cold
atoms, and quantum computing. Yet, preparing states quickly and with high
fidelity remains a formidable challenge. In this work we implement cutting-edge
Reinforcement Learning (RL) techniques and show that their performance is
comparable to optimal control methods in the task of finding short,
high-fidelity driving protocol from an initial to a target state in
non-integrable many-body quantum systems of interacting qubits. RL methods
learn about the underlying physical system solely through a single scalar
reward (the fidelity of the resulting state) calculated from numerical
simulations of the physical system. We further show that quantum state
manipulation, viewed as an optimization problem, exhibits a spin-glass-like
phase transition in the space of protocols as a function of the protocol
duration. Our RL-aided approach helps identify variational protocols with
nearly optimal fidelity, even in the glassy phase, where optimal state
manipulation is exponentially hard. This study highlights the potential
usefulness of RL for applications in out-of-equilibrium quantum physics.Comment: A legend for the videos referred to in the paper is available on
https://mgbukov.github.io/RL_movies
Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces
Quantum annealing algorithms belong to the class of metaheuristic tools,
applicable for solving binary optimization problems. Hardware implementations
of quantum annealing, such as the quantum annealing machines produced by D-Wave
Systems, have been subject to multiple analyses in research, with the aim of
characterizing the technology's usefulness for optimization and sampling tasks.
Here, we present a way to partially embed both Monte Carlo policy iteration for
finding an optimal policy on random observations, as well as how to embed (n)
sub-optimal state-value functions for approximating an improved state-value
function given a policy for finite horizon games with discrete state spaces on
a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can
be expressed as a quadratic unconstrained binary optimization (QUBO) problem,
and show that quantum-enhanced Monte Carlo policy evaluation allows for finding
equivalent or better state-value functions for a given policy with the same
number episodes compared to a purely classical Monte Carlo algorithm.
Additionally, we describe a quantum-classical policy learning algorithm. Our
first and foremost aim is to explain how to represent and solve parts of these
problems with the help of the QPU, and not to prove supremacy over every
existing classical policy evaluation algorithm.Comment: 17 pages, 7 figure
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
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