Related papers: Gillespie algorithm for quantum jump trajectories
Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical…
The Lindblad master equation (LME) describing the Markovian dynamics of the quantum open system can be understood as the evolution of the effective non-Hermitian Hamiltonian balanced with random quantum jumps. Here we investigate the…
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution…
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…
Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…
Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body…
Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in…
Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework…
We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the…
Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating non-unitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics,…
Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo Wave…
We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed…
We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension $N$ instead of a complex density matrix of dimension $N^2$,…
Simulated quantum annealing based on the path-integral Monte Carlo is one of the most common tools to simulate quantum annealing on classical hardware. Nevertheless, it is in principle highly non-trivial whether or not this classical…
The rapid development of quantum computers has enabled demonstrations of quantum advantages on various tasks. However, real quantum systems are always dissipative due to their inevitable interaction with the environment, and the resulting…
We discuss mapping the Bloch-Redfield master-equation to Lindblad form and then unravelling the resulting evolution into a stochastic Schr\"odinger equation according to the quantum-jump method. We give two approximations under which this…
The irreversible motion of an open quantum system can be represented through an ensemble of state vectors following a stochastic dynamics with piecewise deterministic paths. It is shown that this representation leads to a natural definition…