Related papers: Quantum Mechanics Simulated as Branching Process
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the…
This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum…
The simple algorithm for the simulation and visualization of non relativistic quantum dynamics is proposed that is based on a collective behavior of classical particles. Any quantum particle is represented as the swarm of its classical…
A branching random walk algorithm for the many-body Wigner equation and its numerical applications for quantum dynamics in phase space are proposed and analyzed. After introducing an auxiliary function, the (truncated) Wigner equation is…
Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured,…
We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system.…
Our understanding of the physics of biological molecules, such as proteins and DNA, is limited because the approximations we usually apply to model inert materials are not in general applicable to soft, chemically inhomogeneous systems. The…
Classical simulation of quantum computers is an irreplaceable step in the design of quantum algorithms. Exponential simulation costs demand the use of high-performance computing techniques, and in particular distribution, whereby the…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…
Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
The resources required to characterise the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce…
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an…
The introduction of quantum concepts is increasingly making its way into generative machine learning models. However, while there are various implementations of quantum Generative Adversarial Networks, the integration of quantum elements…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…