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In the search for improved computational capabilities, conventional microelectronic computers are facing various problems arising from the miniaturization and concentration of active electronics devices (1-2). Therefore, researchers have…
A variant of the parallel tempering method is proposed in terms of a stochastic switching process for the coupled dynamics of replica configuration and temperature permutation. This formulation is shown to facilitate the analysis of the…
An efficient method of computing power expansions of algebraic functions is the method of Kung and Traub and is based on exact arithmetic. This paper shows a numeric approach is both feasible and accurate while also introducing a…
In some physical implementations of quantum computers, 2-qubit operations can be applied only on certain pairs of qubits. Compilation of a quantum circuit into one compliant to such qubit connectivity constraint results in an increase of…
Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further…
In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential $V(x) = \frac{1}{2} \omega^2 x^2 + g x^4$ is presented. Using a path integral formalism, the exact…
We present tools and methods to generalize parity compilation to digital quantum computing devices with arbitrary connectivity graphs and construct circuit implementations for the constraint Hamiltonian of higher-order constrained binary…
In the past few years, successive improvements of the asymptotic complexity of square matrix multiplication have been obtained by developing novel methods to analyze the powers of the Coppersmith-Winograd tensor, a basic construction…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Quantum computing has shown tremendous promise in addressing complex computational problems, yet its practical realization is hindered by the limited availability of qubits for computation. Recent advancements in quantum hardware have…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
This paper presents the results of studies in elaboration of a mathematical model of the cavity-chain slow wave structures. Considered is the problem of coupling of an infinitely long cylindrical cavity chain coupled through centerholes in…
In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible…
A new kind of dual-band reflection-mode circular polarizers (RMCPs) is introduced with wide bandwidth and wide-view at the operating frequencies. The proposed RMCPs are based on dual-layer rectangular patches on both sides of a substrate,…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
In any ab initio molecular orbital (MO) calculations, the major task involves the computation of the so-called molecular multi-center integrals. Multi-center integral calculations is a very challenging mathematical problem in nature.…
The resistance coefficients in screen Coulomb potential of stellar plasma are evaluated in high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of…
We calculate the vacuum polarization functions on the lattice using the overlap fermion formulation.By matching the lattice data at large momentum scales with the perturbative expansion supplemented by Operator Product Expansion (OPE), we…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…