Periodic Reporting for period 1 - QUANTLATTICE (Ground states, symmetries and dynamics of quantum many-body lattice systems)
Reporting period: 2021-08-01 to 2023-07-31
Quantum technology has the potential to revolutionize all aspects of computation and communication. The societal impact would be broad in scope, given that, for example, computing devices and Internet applications are ubiquitous in everyday life, all around the world. Quantum devices would also offer new insights into the basic sciences, accelerating our understanding of physics, chemistry and biology. Realizing this potential will require scientific achievements in both implementation and theory.
Increasingly mature schemes for quantum computation require better understanding of the relevant physical objects. One such object is the quantum mechanical state, which is a probabilistic description of possible outcomes of a quantum system. A special type of state is called the ground state, describing the lowest energy configuration of a system. Ground states have long been identified to play a special role in both statistical mechanics and quantum computing theory. In this project, we investigated properties of ground states, proving new results about their organization and structure. We focused on systems which fit onto a flat plane, the natural setting of quantum computation, with an overall objective of proving mathematical statements about stable properties of their ground states.
Increasingly mature schemes for quantum computation require better understanding of the relevant physical objects. One such object is the quantum mechanical state, which is a probabilistic description of possible outcomes of a quantum system. A special type of state is called the ground state, describing the lowest energy configuration of a system. Ground states have long been identified to play a special role in both statistical mechanics and quantum computing theory. In this project, we investigated properties of ground states, proving new results about their organization and structure. We focused on systems which fit onto a flat plane, the natural setting of quantum computation, with an overall objective of proving mathematical statements about stable properties of their ground states.
During this project, we demonstrated a rigorous proof of a stable gapped phase of ground states for a non-commuting, two-dimensional many-body Hamiltonian. Our results apply to the decorated Affleck-Kennedy-Lieb-Tasaki models. These models are characterized by the presence of two species of spins arranged on a lattice, such as the hexagonal lattice. The outcome of our work is, to the best of our knowledge, the first of its kind and strengthens our understanding of how quantum systems react to perturbations such as noise.
Our results extend state of the art knowledge about decorated Affleck-Kennedy-Lieb-Tasaki ground states, leaving open the possibility of continued analysis to potentially bridge gaps between statistical mechanical models and quantum computation.