UC Riverside

I developed a computationally efficient framework for accelerating the quantum optimal control of various multi-qubit systems. This framework decomposes the Hilbert space of the multi-qubit system and enables unitary transformations of the Hamiltonians based on the symmetry of finite groups. The Hamiltonians are block diagonalized after transformation, which features a natural structure for computing these blocks in parallel. Specifically, the size of the Hamiltonians of an n-qubit system is reduced from 2^n × 2^n to O(n × n) or O((2^n / n) × (2^n / n)) under Sn symmetry or Dn symmetry, respectively. This approach reduces the execution time of quantum optimal control by orders of magnitude while the accuracy of the output is not affected. The Lie-Trotter-Suzuki decomposition generalizes this symmetry-based approach to a more general variety of multi-qubit systems. Based on the symmetry-induced decomposition of the Hilbert space, I propose the concept of symmetry-protected subspaces, which are potential platforms for preparing commonly used symmetric states, realizing simultaneous gate operations, quantum error suppression, and simulation of other quantum systems. A perspective on ladder operators and selection rules is provided to facilitate the understanding of the transformation of the Hamiltonians. I provide the Python source code for the quantum optimal control framework and the symmetry-based methods.