Preserving symmetries in NISQ algorithms

ORAL

Abstract

Many classical optimization problems display local or global symmetries. In the Quantum Alternating Operator Ansatz (QAOA), these symmetries can be used to design mixers which restrict the evolution of the system to a subspace which is exponentially smaller than the full Hilbert space [1,2]. However, in realistic scenarios, errors can break the symmetry and yield invalid solutions to the optimization problem. In this talk, we show an analysis of the probability of staying in the correct subspace under the influence of realistic noise models. Moreover, for the example of 3-coloring, we show that it is possible to exploit the natural redundancy of the qubit encoding to bring back the evolution into the correct subspace.
[1] From QAOA to QAOA, Hadfield, Wang, O'Gorman, Rieffel, Venturelli, Biswas, Algorithms, 2019.
[2] XY-mixers: analytical and numerical results for QAOA, Wang, Rubin, Dominy, Rieffel, arXiv:1904.09314

*We appreciate support from NASA Ames Research Center, NASA Advanced Exploration systems (AES) program, NASA Transformative Aeronautic Concepts Program (TACP), and the AFRL Information Directorate under grant F4HBKC4162G001. ZW is also supported by NASA Academic Mission Services (NAMS), contract number NNA16BD14C, and MS by USRA NAMS R&D Student program.

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Presenters

  • Michael Streif

    • Quantum AI Lab, USRA; NASA Ames Research Center
    • Quantum AI Lab, USRA and NASA Ames

Authors

  • Michael Streif

    • Quantum AI Lab, USRA; NASA Ames Research Center
    • Quantum AI Lab, USRA and NASA Ames

  • Eleanor Rieffel

    • Quantum AI Lab, NASA Ames Research Center
    • QuAIL, NASA Ames Research Center
    • NASA Ames Research Center, Quantum AI Lab (QuAIL)
    • NASA Ames Research Center
    • QuAIL, NASA

  • Zhihui Wang

    • Quantum AI Lab, USRA; NASA Ames Research Center
    • NASA Quantum Artificial Intelligence Laboratory (QuAIL) - USRA Research Institute for Advanced Computer Science (RIACS)
    • Quantum AI Lab, USRA and NASA Ames