Accelerating the Quantum Optimal Control of Large Qubit Systems with Symmetry-based Hamiltonian Transformations and Linear Unitary Propagators

We have developed a novel framework for the quantum optimal control (QOC) of multi-qubit systems. A large family of Hamiltonians satisfies the symmetry of finite groups, e.g., the permutation group S_n and the dihedral group D_n. Using the symmetry of a multi-qubit system, we can decompose the Hilbert space of the system and block diagonalize the Hamiltonian, which enables efficient computations when the transition is limited to a specific subspace. We show that the size of the n-qubit Hamiltonian is reduced from 2ⁿ to O(n) under S_n symmetry or O(2ⁿ/n) under D_n symmetry. We show that the computational cost for carrying out quantum control of these transformed Hamiltonians is significantly reduced without affecting the fidelity of the output. We also show that the Lie-Trotter-Suzuki decomposition generalizes the application of this technique to a larger number of varieties of multi-qubit systems.