Freiburg 2019 – scientific programme
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FM: Fall Meeting
FM 75: Quantum Computation: Simulation II
FM 75.2: Talk
Thursday, September 26, 2019, 14:15–14:30, 1010
Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors — •Jan-Michael Reiner1,2, Frank Wilhelm-Mauch3, Gerd Schön1,4, and Michael Marthaler1,2,3 — 1Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany — 2HQS Quantum Simulations, c/o CyberLab, Haid-und-Neu-Straße 20, 76131 Karlsruhe — 3Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany — 4Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76021 Karlsruhe, Germany
A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a time-dependent Hamiltonian, where the -- ideally short -- fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasi-static errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities.