Simulating Heavy-Hex Transverse Field Ising Model Magnetization Dynamics
  Using Programmable Quantum Annealers
Recently, a Hamiltonian dynamics simulation was performed on a kicked
ferromagnetic 2D transverse field Ising model with a connectivity graph native
to the 127 qubit heavy-hex IBM Quantum architecture using ZNE quantum error
mitigation. We demonstrate that one of the observables in this Trotterized
Hamiltonian dynamics simulation, namely magnetization, can be efficiently
simulated on current superconducting qubit-based programmable quantum annealing
computers. We show this using two distinct methods: reverse quantum annealing
and h-gain state encoding. This simulation is possible because the 127 qubit
heavy-hex connectivity graph can be natively embedded onto the D-Wave Pegasus
quantum annealer hardware graph and because there exists a direct equivalence
between the energy scales of the two types of quantum computers. We derive
equivalent anneal pauses in order to simulate the Trotterized quantum circuit
dynamics for varying Rx rotations $\theta_h \in (0, \frac{\pi}{2}]$, using
quantum annealing processors. Multiple disjoint instances of the Ising model of
interest can be embedded onto the D-Wave Pegasus hardware graph, allowing for
parallel quantum annealing. We report equivalent magnetization dynamics using
quantum annealing for time steps of 20, 50 up to 10,000, which we find are
consistent with exact classical 27 qubit heavy-hex Trotterized circuit
magnetization dynamics, and we observe reasonable, albeit noisy, agreement with
the existing simulations for single site magnetization at 20 Trotter steps. The
quantum annealers are able to simulate equivalent magnetization dynamics for
thousands of time steps, significantly out of the computational reach of the
digital quantum computers on which the original Hamiltonian dynamics
simulations were performed.
Elijah Pelofske Andreas Bärtschi Stephan Eidenbenz