Related papers: Strong and Weak Optimizations in Classical and Qua…
Error mitigation has been one of the recently sought after methods to reduce the effects of noise when computation is performed on a noisy near-term quantum computer. Interest in simulating stochastic processes with quantum models gained…
Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a…
Classical simulation is important because it sets a benchmark for quantum computer performance. Classical simulation is currently the only way to exercise larger numbers of qubits. To achieve larger simulations, sparse matrix processing is…
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
Arguably, the largest class of stochastic processes generated by means of a finite memory consists of those that are sequences of observations produced by sequential measurements in a suitable generalized probabilistic theory (GPT). These…
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…
We investigate the nature of memory effects in the non-Markovian dynamics of spin boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its…
Artificial intelligence and machine learning have been widely adopted both in the industry and in everyday life, but at the cost of high compute demands. Recent studies show that implementing machine learning in physical systems in the deep…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…
Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from…
The crucial feature of a memoryless stochastic process is that any information about its state can only decrease as the system evolves. Here we show that such a decrease of information is equivalent to the underlying stochastic evolution…
Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between…