Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

By A. Strathearn, P. Kirton, D. Kilda, Jonathan Keeling, Brendon W. Lovett. Nature Communications, 2017

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In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system–bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment. In general the computational requirements for simulating quantum systems scale exponentially but in some cases it is possible to formulate more efficient schemes. Here the authors present an efficient approach to calculate non-Markovian quantum dynamics using matrix product operator methods.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9a46a837129ee8bd96d0359b5df24f7a72572654