Related papers: Quantum Simulation of Markov Chains
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 concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Stochastic processes underlie a vast range of natural and social phenomena. Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g. traffic congestion, are effectively probabilistic because we…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear…
We study how generators of Markovian dynamics of a qubit can be simulated using a programmable quantum processor.
We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research…
We study the structure of quantum Markov Processes from the point of view of product systems and their representations.
A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving…
Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle…
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…