Beating The House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation (ERT)

We introduce a new technique for the simulation of dissipative quantum systems. This method is
composed of an approximate decomposition of the Lindblad equation into a Kraus map, from which
one can define an ensemble of wavefunctions. Using principal component analysis, this ensemble
can be truncated to a manageable size without sacrificing numerical accuracy. We term this method
Ensemble Rank Truncation (ERT), and find that in the regime of weak coupling, this method is
able to outperform existing wavefunction Monte-Carlo methods by an order of magnitude in both
accuracy and speed. We also explore the possibility of combining ERT with approximate techniques
for simulating large systems (such as Matrix Product States (MPS)), and show that in many cases
this approach will be more efficient than directly expressing the density matrix in its MPS form. We
expect the ERT technique to provide a significant advantage across a broad range of applications
in physics and chemistry, including quantum information, metrology and thermodynamics.