Bipartite Quantum Systems

In this semester research project at the Trapped Ion Quantum Physics group (ETH), we studied computational methods for analysing ensembles of two level systems coupled to a bosonic mode in an open system setting, which is highly relevant for simulating such systems and verifying hypothesis. When all two-level systems are assumed to be identical, the permutational symmetry allows to exponentially reduce the computational resources needed and lead to efficient computational solutions - which are implemented in the library Permutational Invariant Quantum Solver PIQS. However, as soon as one two-level system can be distinguished from the others, the permutational symmetry is broken and the exponential complexity is recovered. In this project we showed that, in the case of bipartite system composed of two level systems belonging to two different species, the speedup is still exponential and allows to estimate the complexity for a more general mixed-species scenario, which is of great scientific interest.