Related papers: On hyperbolic interferences in the quantum--like r…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
Building on the work [18], where some standard basis for the queer $q$-Schur superalgebra $\mathcal{Q}_q(n,r;R)$ is defined by a labelling set of matrices and their associated double coset representatives, we investigate the matrix…
We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
Precision measurements of molecules offer an unparalleled paradigm to probe physics beyond the Standard Model. The rich internal structure within these molecules makes them exquisite sensors for detecting fundamental symmetry violations,…
Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <->…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the…
Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…
Quantum neural networks (QNNs) have shown remarkable potential due to their capability of representing complex functions within exponentially large Hilbert spaces. However, their application to multivariate regression tasks has been…
The notion of a $U$-statistic for an $n$-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a selfadjoint `kernel' $K$ acting on $(\mathbb{C}^{d})^{\otimes r}$ with $r<n$, we define the…
In previous publications I have proposed a geometrical framework underpinning the local, realistic, and deterministic origins of the strong quantum correlations observed in Nature, without resorting to superdeterminism, retrocausality, or…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
Generalized quantum statistics will be presented in the context of representation theory of Lie (super)algebras. This approach provides a natural mathematical framework, as is illustrated by the relation between para-Bose and para-Fermi…