2019/02/22 by Albert T. Schmitz, Schmitz, Albert T., Sonika Johri +1 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Data Storage Technologies #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Parallel Computing and Optimization Techniques #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1902.08625
openalex publication_date 2019/02/22 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
A many-body Hamiltonian can be block-diagonalized by expressing it in terms\nof symmetry-adapted basis states. Finding the group orbit representatives of\nthese basis states and their corresponding symmetries is currently a\nmemory/computational bottleneck on classical computers during exact\ndiagonalization. We apply Grover's search in the form of a minimization\nprocedure to solve this problem. Our quantum solution provides an exponential\nreduction in memory, and a quadratic speedup in time over classical methods. We\ndiscuss explicitly the full circuit implementation of Grover minimization as\napplied to this problem, finding that the oracle only scales as polylog in the\nsize of the group, which acts as the search space. Further, we design an error\nmitigation scheme that, with no additional qubits, reduces the impact of\nbit-flip errors on the computation, with the magnitude of mitigation directly\ncorrelated with the error rate, improving the utility of the algorithm in the\nNoisy Intermediate Scale Quantum era.\n