When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in the system
size. A class of algorithms, exemplified by the Time-Evolving Block-Decimation (TEBD) algorithm, make use of this observation by selecting the relevant subspace through a decimation technique relying on the Singular Value Decomposition (SVD). In these algorithms, the complexity of each time-evolution step is dominated by the SVD. Here we show that, by applying a randomized version of the SVD routine (RRSVD), the power law governing the computational complexity of TEBD is lowered by one degree, resulting in a considerable speed-up. We exemplify the potential gains in efficiency at the hand of some real world examples to which TEBD can be successfully applied to and demonstrate that for those system RRSVD delivers results as accurate as state-of-the-art deterministic SVD routines.
Recent observations of beating signals in the excitation energy transfer dynamics of photosynthetic complexes have been interpreted as evidence for sustained coherences that are sufficiently long-lived for energy transport and coherence to coexist. T
he possibility that coherence may be exploited in biological processes has opened up new avenues of exploration at the interface of physics and biology. The microscopic origin of these long-lived coherences, however, remains to be uncovered. Here we present such a mechanism and verify it by numerically exact simulations of system-environment dynamics. Crucially, the non-trivial spectral structures of the environmental fluctuations and particularly discrete vibrational modes can lead to the generation and sustenance of both oscillatory energy transport and electronic coherence on timescales that are comparable to excitation energy transport. This suggests that the non-trivial structure of protein environments plays a more significant role for coherence in biological processes than previously believed.
