Tensor network for high dimensional systems (M1 – M24; responsible: UPV/EHU; involved: INFN, UIBK, DESY/MPQ, IJS)

We will develop approaches to model higher dimensional systems.

Examples of models of interest are CP(1) model with a topological term at D = 2 + 1 dimensions, U(1) -Higgs and QED and non-abelian theories in D = 2 + 1 dimensions and eventually even D = 3 + 1 dimensions with topological and chemical potential terms, and Hubbard models.

We will utilize the tensor renormalization group and the recently proposed augmented tree TN and tree tensor operator structure to complement and describe high-dimensional quantum simulators.

UPV/EHU will lead in close collaboration with INFN, IJS, UIBK, DESY/MPQ.

Real-time evolution in presence of noise (M7 – M36; responsible IJS; involved: INFN, UPV/EHU, UIBK, DESY/MPQ)

We will develop the means to characterize the precision of simulators, such as gauge theory simulators or those performing some quantum algorithms with a real-time evolution.

We will estimate the impact of the most relevant noise sources, with a particular focus on simulators from WP2 and WP3.

We investigated how quantum gate imperfections in a digital processor or noise and errors in analogue protocols are reflected in modifications to target Hamiltonians and what forms of imperfections, noise, and errors are most damaging.

Then we will develop strategies and protocols to suppress noise in such a way that we push digital and analogue quantum simulations beyond current limitations.

We will also explore alternative approaches in which designed dissipation is exploited to reveal new physics or protect coherence.

IJS will handle close collaboration with all the other nodes.