Related papers: Numerical approaches to time evolution of complex …
Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the…
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used…
With growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schr\"odinger equation is of keen interest in modern electronic structure…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
Most numerical methods for time integration use real-valued time steps. Complex time steps, however, can provide an additional degree of freedom, as we can select the magnitude of the time step in both the real and imaginary directions. We…
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.,…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…
We propose a new concept for the dynamics of a quantum bath, the Chebyshev space, and a new method based on this concept, the Chebyshev space method. The Chebyshev space is an abstract vector space that exactly represents the fermionic or…
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the…
Time-integration for lumped parameter systems obeying implicit Bingham-Kelvin constitutive models is studied. The governing system of equations describing the lumped parameter system is a non-linear differential-algebraic equation and needs…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
One of the unitary forms of the quantum mechanical time evolution operator is given by Cayley's approximation. A numerical implementation of the same involves the replacement of second derivatives in Hamiltonian with the three-point…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…