The broad efforts of this research group will be theoretical aspects related to quantum computing. We primarily focus on quantum error-correcting codes (methods to protect information in quantum systems) and certain Hamiltonian simulation reduction methods (methods for determining properties of a system using a quantum computer).
The primary thrust is around going beyond the traditional framework of qubit based quantum computing. For certain problems there are direct group theoretic extensions which can provide a modest improvement, but we aim to exceed this in ways leveraging broader insights into the structures beyond the qubit case. Below we provide some more specialized examples to illustrate this idea.
Quantum error-correcting codes
The qubit case can naturally be extended to the qudit case through methods like group theory. In the infinite limit unfortunately this breaks down. Instead we take an invariant approach. While this allows us to generate codes for qudits, we can also generate codes for continuous and infinite systems. Different metrics for protection permit protection of continuous systems against differing noises.
Maximal reduction of Hamiltonian simulations using easy resources
This reduction does not require going beyond qubits, however, taking the larger perspective of symplectic spaces, which is clearer in the cases beyond qubits, makes this maximal reduction far clearer. Additionally, we can observe differing savings depending on the number of levels in the system. Further exploration of this will be needed.