Related papers: A quantum stochastic Lie-Trotter product formula
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
We show that the series product, which serves as an algebraic rule for connecting state-based input/output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum…
In this article, we study quantum randomness of stochastic cosmological particle production scenario using quantum corrected higher order Fokker Planck equation. Using the one to one correspondence between particle production in presence of…
The Lie--Trotter product formula is a foundational approximation for the quantum partition function, yet obtaining rigorous error bounds for the unbounded Hamiltonians common in physics remains a significant challenge. This paper provides a…
An extension of Chernoff's product formula for one-parameter functions taking values in the space of bounded linear operators on a Banach space is given. Essentially, the $n$-th one-parameter function in the product formula is mapped by the…
We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
The Lie-Trotter formula has been a fundamental tool in quantum mechanics, quantum computing, and quantum simulations. The error estimations for the Lie-Trotter product formula play a crucial role in achieving scalability and computational…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…
A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
Quantum simulation is a cornerstone application of quantum computing, yet how fundamental quantum resources--entanglement and non-stabilizerness (``magic")--shape simulation fidelity remains an open question. In this work, we establish a…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
We investigate the question of how to compute the cotensor product, and more generally the derived cotensor (i.e., Cotor) groups, of a tensor product of comodules. In particular, we determine the conditions under which there is a…