46,351 research outputs found
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
Quantum Random Self-Modifiable Computation
Among the fundamental questions in computer science, at least two have a deep
impact on mathematics. What can computation compute? How many steps does a
computation require to solve an instance of the 3-SAT problem? Our work
addresses the first question, by introducing a new model called the ex-machine.
The ex-machine executes Turing machine instructions and two special types of
instructions. Quantum random instructions are physically realizable with a
quantum random number generator. Meta instructions can add new states and add
new instructions to the ex-machine. A countable set of ex-machines is
constructed, each with a finite number of states and instructions; each
ex-machine can compute a Turing incomputable language, whenever the quantum
randomness measurements behave like unbiased Bernoulli trials. In 1936, Alan
Turing posed the halting problem for Turing machines and proved that this
problem is unsolvable for Turing machines. Consider an enumeration E_a(i) =
(M_i, T_i) of all Turing machines M_i and initial tapes T_i. Does there exist
an ex-machine X that has at least one evolutionary path X --> X_1 --> X_2 --> .
. . --> X_m, so at the mth stage ex-machine X_m can correctly determine for 0
<= i <= m whether M_i's execution on tape T_i eventually halts? We demonstrate
an ex-machine Q(x) that has one such evolutionary path. The existence of this
evolutionary path suggests that David Hilbert was not misguided to propose in
1900 that mathematicians search for finite processes to help construct
mathematical proofs. Our refinement is that we cannot use a fixed computer
program that behaves according to a fixed set of mechanical rules. We must
pursue methods that exploit randomness and self-modification so that the
complexity of the program can increase as it computes.Comment: 50 pages, 3 figure
Prediction of Atomization Energy Using Graph Kernel and Active Learning
Data-driven prediction of molecular properties presents unique challenges to
the design of machine learning methods concerning data
structure/dimensionality, symmetry adaption, and confidence management. In this
paper, we present a kernel-based pipeline that can learn and predict the
atomization energy of molecules with high accuracy. The framework employs
Gaussian process regression to perform predictions based on the similarity
between molecules, which is computed using the marginalized graph kernel. To
apply the marginalized graph kernel, a spatial adjacency rule is first employed
to convert molecules into graphs whose vertices and edges are labeled by
elements and interatomic distances, respectively. We then derive formulas for
the efficient evaluation of the kernel. Specific functional components for the
marginalized graph kernel are proposed, while the effect of the associated
hyperparameters on accuracy and predictive confidence are examined. We show
that the graph kernel is particularly suitable for predicting extensive
properties because its convolutional structure coincides with that of the
covariance formula between sums of random variables. Using an active learning
procedure, we demonstrate that the proposed method can achieve a mean absolute
error of 0.62 +- 0.01 kcal/mol using as few as 2000 training samples on the QM7
data set
Isogeny-based post-quantum key exchange protocols
The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented
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