Simulating Heavy-Hex Transverse Field Ising Model Magnetization Dynamics Using Programmable Quantum Annealers

Abstract

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.