2015/03/31 by Ryan Sweke, Ilya Sinayskiy, Denis Bernard +1
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Discrete mathematics #Markov process #Mathematics #Open quantum system #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Quantum operation #Quantum process #Quantum system #Semigroup #Set (abstract data type) #Statistical physics #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.91.062308
published as Phys. Rev. A 91, 062308 (2015) · Revised version. Restricted recombination method to first order Suzuki-Lie-Trotter integrators, and added discussion concerning issues with the application of higher order integrators in the open quantum systems setting
openalex publication_date 2015/06/08 · arxiv created 2017/05/28 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the problem of constructing a ``universal set'' of Markovian processes, such that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through sequential simulations of processes from the universal set. In particular, for quantum systems of dimension d, we explicitly construct a universal set of semigroup generators, parametrized by d2\ensuremath-3 continuous parameters, and prove that a necessary and sufficient condition for the dynamical simulation of a d-dimensional Markovian quantum system is the ability to implement (a) quantum channels from the semigroups generated by elements of the universal set of generators, and (b) unitary operations on the system. Furthermore, we provide an explicit algorithm for simulating the dynamics of a Markovian open quantum system using this universal set of generators, and show that it is efficient, with respect to this universal set, when the number of distinct Lindblad operators (representing physical dissipation processes) scales polynomially with respect to the number of subsystems.