Deep learning methods with symmetry priors for problems in quantum computing.

• Applicant: Dr. Violeta Nikolaeva Ivanova-Rohling
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 527263720

We propose to develop and adapt deep learning and reinforcement learning methods that use known symmetries as priors, as well as Grassmann manifold priors with the goal to solve specific problems in quantum computing. Finding optimal physical spin exchange gate sequences that make efficient logical two-qubit gates can be of great consequence for the paradigm of spin exchange-only computation. This is one promising platform for quantum computation using the a subspace of three physical qubits as a logical qubit. We aim at developing approaches that are for different logical gates, different connectivities and architectures of the physical qubits, and different definitions of efficiency. Inspired by the research in the field of generalized group convolutional neural networks, we will develop invariance-aware neural networks, as well as reinforcement learning approaches that incorporate known symmetries in the space of possible gate sequences. Moreover, we will research methods that find optimal sets of measurement operators that perform quantum measurements for efficient quantum state tomography, a problem related to finding optimal orthoplex-bound-achieving Grassmannian packing of half-dimensional subspaces for Hilbert space of even non-prime-power dimensions. We already have approximated such a packing for Hilbert space of dimension 6. We want to check for the existence of such a packing for Hilbert spaces of dimensions 10, 12, 14, and above and with the gained insight generalize the necessary conditions for which Grassmannian packing exists for even non-prime power dimensions. From a methodology perspective, we would like to apply deep Grassmann manifold learning and adapt it to fit our problem of finding optimal sets of measurement operators.

• DFG Programme: Research Grants