Related papers: Open systems dynamics: Simulating master equations…
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…
A generalization of the stochastic wave function method is presented which allows the unravelling of arbitrary linear quantum master equations which are not necessarily in Lindblad form and, moreover, the explicit treatment of memory…
The Kraus representation of quantum channels allows for a precise emulation of the complex dynamics that take place on quantum processors, whether for benchmarking algorithms, predicting the performance of error correction and mitigation,…
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically…
In this paper we consider a quantum open system and treat the master equation with some restricted dissipator which consists of a set of projection operators (projectors). The exact solution is given under the commutable approximation (in…
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We derive the master equation that governs the evolution of the measured state backwards in time in an open system. This allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements,…
We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e.,…
The paper is devoted to a new idea of simulation of accounting by quantum computing. We expose the actual accounting principles in a pure mathematics language. After that we simulated the accounting principles on quantum computers. We show…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
We present our ongoing work aimed at accelerating a particle-resolved direct numerical simulation model designed to study aerosol-cloud-turbulence interactions. The dynamical model consists of two main components - a set of fluid dynamics…
An efficient numerical algorithm for the laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
Finding better solutions to combinatorial optimization problems could have a large positive impact on many real-world application areas, such as logistics. For this reason, significant efforts have been made to design novel optimisation…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…