Parallel Quantum Computation Approach for Quantum Deep Learning and Classical-Quantum Models

The paradigm of Quantum computing and artificial intelligence has been growing steadily in recent years and given the potential of this technology by recognizing the computer as a physical system that can take advantage of quantum mechanics for solving problems faster, more efficiently, and accurately. We suggest experimentation of this potential through an architecture of different quantum models computed in parallel. In this work, we present encouraging results of how it is possible to use Quantum Processing Units analogically to Graphics Processing Units to accelerate algorithms and improve the performance of machine learning models through three experiments. The first experiment was a reproduction of a parity function, allowing us to see how the convergence of a given Quantum model is influenced significantly by computing it in parallel. For the second and third experiments, we implemented an image classification problem by training quantum neural networks and using pre-trained models to compare their performances with the same experiments carried out with parallel quantum computations. We obtained very similar results in the accuracies, which were close to 100% and significantly improved the execution time, approximately 15 times faster in the best-case scenario. We also propose an alternative as a proof of concept to address emotion recognition problems using optimization algorithms and how execution times can be positively affected by parallel quantum computation. To do this, we use tools such as the cross-platform software library PennyLane and Amazon Web Services to access high-end simulators with Amazon Braket and IBM quantum experience.

Congruences modulo powers of 5 for the rank parity function

International audience It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo powers of 5 for the crank parity function. The generating function for the rank parity function is f (q), which is the first example of a mock theta function that Ramanujan mentioned in his last letter to Hardy. We prove congruences modulo powers of 5 for the rank parity function.

Covariance and Spinorial Statistical Description of Simple Relativistic Stochastic Kinematics

It is shown that Generalized Poisson–Kac processes are closed with respect to Lorentz transformations, providing a class of covariant kinematic processes. The transformation properties of the associated partial probability densities (waves) display spinorial character in a probability space, and their spinorial character is intrinsically related to the parametrization of the internal degrees of freedom of the process. Parity function analysis associated with the bias induced in the partial-wave recombination process by a Lorentz boost, indicates a symmetry breaking in the recombination dynamics. In an inertial reference frame moving with constant velocity [Formula: see text] with respect to the rest frame of the process, stochastic fluctuations are progressively damped out till complete suppression in the limit for [Formula: see text].

Strategy of Fuzzy Mapping using Fixed Point Theorem

To overcome the problems obtained due to non linearity, fixed point theorem. The main intent of this paper is to study the strategy of the fuzzy mapping using fixed point theorem. This fixed point theorem is mainly based on the topological vector space under the fixed selection. This fixed point theorem has convex structure which is in generalized way. This is used in various application fields. In this unity parity function is used to select the spaces available in fuzzy mapping process. The fixed point theorem using fuzzy mapping will improve and extend the classical results.

N-bit Parity Neural Networks with minimum number of threshold neurons

In this paper ordered neural networks for the Nbit parity function containing [log2(N + 1)] threshold elements are constructed. The minimality of this network is proved. The connection between minimum perceptrons of Gamb for the N-bit parity function and one combinatorial problems is established.

Circuit complexity of symmetric Boolean functions in antichain basis

We study the circuit complexity of Boolean functions in an infinite basis consisting of all characteristic functions of antichains over the Boolean cube. For an arbitrary symmetric function we obtain the exact value of its circuit complexity in this basis. In particular, we prove that the circuit complexities of the parity function and the majority function ofThe research is supported by the Russian Foundation for Basic Research, project 14–01–00598.

Complexity of implementation of parity functions in the implication–negation basis

The paper is concerned with circuits in the basis {x →y ,x̅}. The exact value of the complexity of implementation of an even parity function is obtained and the minimal circuits implementing an odd parity function are described

ON THE HARDNESS AGAINST CONSTANT-DEPTH LINEAR-SIZE CIRCUITS

The notion of average-case hardness is a fundamental one in complexity theory. In particular, it plays an important role in the research on derandomization, as there are general derandomization results which are based on the assumption that average-case hard functions exist. However, to achieve a complete derandomization, one usually needs a function which is extremely hard against a complexity class, in the sense that any algorithm in the class fails to compute the function on 1/2 - 2-Ω(n) fraction of its n-bit inputs. Unfortunately, lower bound results are very rare and they are only known for very restricted complexity classes, and achieving such extreme hardness seems even more difficult. Motivated by this, we study the hardness against linear-size circuits of constant depth in this paper. We show that the parity function is extremely hard for them: any such circuit must fail to compute the parity function on at least 1/2 - 2-Ω(n) fraction of inputs.

The Fractional Meta-Trigonometry Based on the R-Function: Part II—Parity Function Graphics, Laplace Transforms, Fractional Derivatives, Meta-Properties

The current fractional trigonometries and hyperboletry are based on three forms of the fractional exponential R-function, Rq,v(a,t), Rq,v(ai,t), and Rq,v(a,it). The fractional meta-trigonometry extends this to an infinite number of bases using the form Rq,v(aiα,iβt). Meta-definitions, meta-Laplace transforms, and meta-identities are developed for these generalized fractional trigonometric functions. Graphic results are presented. Extensions of the fractional trigonometries to the negative time domain and complementary fractional trigonometries are considered. Part II continues from the definition set and graphics given in Part I. It provides a minimal set of graphic results for the parity meta-fractional trigonometry and develops the meta-properties described above.