Related papers: Simple Algorithm for Factorized Dynamics of g_n-Au…
Quantum theory is based on a mathematical structure totally different from conventional arithmetic. Due to the symmetric nature of bosonic particles, annihilation or creation of single particles translates a quantum state depending on how…
For a given target system and apparatus described by quantum theory, the so-called quantum no-programming theorem indicates that a family of states called programs in the apparatus with a fixed unitary operation on the total system programs…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved…
We propose a method for implementation of an universal set of one- and two-quantum-bit gates for quantum computation in the system of two coupled electrons with constant non-diagonal exchange interaction. Suppression of the exchange…
We introduce a randomized algorithm based on qDrift to compute Hamiltonian dynamics on digital quantum computers. We frame it as physDrift because conservation laws in physics are obeyed during evolution of arbitrary quantum states.…
Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is…
Non-adiabatic dynamics at molecule-metal interfaces govern diverse and technologically important phenomena, from heterogeneous catalysis to dye-sensitized solar energy conversion and charge transport across molecular junctions. Realistic…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We present a quantum averaging theory (QAT) for analytically modeling unitary gate dynamics in driven quantum systems beyond the rotating-wave approximation. QAT addresses the simultaneous presence of distinct timescales by generating a…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
Open Quantum Brownian Motion (OQBM) was introduced as a scaling limit of discrete-time open quantum walks. This limit defines a new class of quantum Brownian motion, which incorporates both the external and internal degrees of freedom of…
In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
In the 1980's Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse…