15,929 research outputs found
Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine Learning Approach
Three-qubit quantum gates are key ingredients for quantum error correction
and quantum information processing. We generate quantum-control procedures to
design three types of three-qubit gates, namely Toffoli, Controlled-Not-Not and
Fredkin gates. The design procedures are applicable to a system comprising
three nearest-neighbor-coupled superconducting artificial atoms. For each
three-qubit gate, the numerical simulation of the proposed scheme achieves
99.9% fidelity, which is an accepted threshold fidelity for fault-tolerant
quantum computing. We test our procedure in the presence of decoherence-induced
noise as well as show its robustness against random external noise generated by
the control electronics. The three-qubit gates are designed via the machine
learning algorithm called Subspace-Selective Self-Adaptive Differential
Evolution (SuSSADE).Comment: 18 pages, 13 figures. Accepted for publication in Phys. Rev. Applie
Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks
We study diffusion and consensus based optimization of a sum of unknown
convex objective functions over distributed networks. The only access to these
functions is through stochastic gradient oracles, each of which is only
available at a different node, and a limited number of gradient oracle calls is
allowed at each node. In this framework, we introduce a convex optimization
algorithm based on the stochastic gradient descent (SGD) updates. Particularly,
we use a carefully designed time-dependent weighted averaging of the SGD
iterates, which yields a convergence rate of
after gradient updates for each node on
a network of nodes. We then show that after gradient oracle calls, the
average SGD iterate achieves a mean square deviation (MSD) of
. This rate of convergence is optimal as it
matches the performance lower bound up to constant terms. Similar to the SGD
algorithm, the computational complexity of the proposed algorithm also scales
linearly with the dimensionality of the data. Furthermore, the communication
load of the proposed method is the same as the communication load of the SGD
algorithm. Thus, the proposed algorithm is highly efficient in terms of
complexity and communication load. We illustrate the merits of the algorithm
with respect to the state-of-art methods over benchmark real life data sets and
widely studied network topologies
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Robust Online Hamiltonian Learning
In this work we combine two distinct machine learning methodologies,
sequential Monte Carlo and Bayesian experimental design, and apply them to the
problem of inferring the dynamical parameters of a quantum system. We design
the algorithm with practicality in mind by including parameters that control
trade-offs between the requirements on computational and experimental
resources. The algorithm can be implemented online (during experimental data
collection), avoiding the need for storage and post-processing. Most
importantly, our algorithm is capable of learning Hamiltonian parameters even
when the parameters change from experiment-to-experiment, and also when
additional noise processes are present and unknown. The algorithm also
numerically estimates the Cramer-Rao lower bound, certifying its own
performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
Quantum algorithms have the potential to outperform their classical
counterparts in a variety of tasks. The realization of the advantage often
requires the ability to load classical data efficiently into quantum states.
However, the best known methods require gates to
load an exact representation of a generic data structure into an -qubit
state. This scaling can easily predominate the complexity of a quantum
algorithm and, thereby, impair potential quantum advantage. Our work presents a
hybrid quantum-classical algorithm for efficient, approximate quantum state
loading. More precisely, we use quantum Generative Adversarial Networks (qGANs)
to facilitate efficient learning and loading of generic probability
distributions -- implicitly given by data samples -- into quantum states.
Through the interplay of a quantum channel, such as a variational quantum
circuit, and a classical neural network, the qGAN can learn a representation of
the probability distribution underlying the data samples and load it into a
quantum state. The loading requires
gates and can, thus, enable the
use of potentially advantageous quantum algorithms, such as Quantum Amplitude
Estimation. We implement the qGAN distribution learning and loading method with
Qiskit and test it using a quantum simulation as well as actual quantum
processors provided by the IBM Q Experience. Furthermore, we employ quantum
simulation to demonstrate the use of the trained quantum channel in a quantum
finance application.Comment: 14 pages, 13 figure
Quantum Model Averaging
Standard tomographic analyses ignore model uncertainty. It is assumed that a
given model generated the data and the task is to estimate the quantum state,
or a subset of parameters within that model. Here we apply a model averaging
technique to mitigate the risk of overconfident estimates of model parameters
in two examples: (1) selecting the rank of the state in tomography and (2)
selecting the model for the fidelity decay curve in randomized benchmarking.Comment: For a summary, see http://i.imgur.com/nMJxANo.pn
Neuromorphic, Digital and Quantum Computation with Memory Circuit Elements
Memory effects are ubiquitous in nature and the class of memory circuit
elements - which includes memristors, memcapacitors and meminductors - shows
great potential to understand and simulate the associated fundamental physical
processes. Here, we show that such elements can also be used in electronic
schemes mimicking biologically-inspired computer architectures, performing
digital logic and arithmetic operations, and can expand the capabilities of
certain quantum computation schemes. In particular, we will discuss few
examples where the concept of memory elements is relevant to the realization of
associative memory in neuronal circuits, spike-timing-dependent plasticity of
synapses, digital and field-programmable quantum computing
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