Probing Antiferromagnetic Hysteresis on Programmable Quantum Annealers

Abstract

Using programmable analog quantum annealing processors, we implement a sampling-based magnetic hysteresis protocol to probe the counterintuitive notion of magnetic memory of antiferromagnets. A key component of this protocol responsible for the hysteresis is a transverse field, which enables state transitions, while the magnetic field sweep is done via a longitudinal control field. We present evidence of full saturation and reversal of the hysteresis curve, as well as emergent magnetic domain mediated by quantum fluctuations that give rise to the magnetic memory effect in antiferromagnets.

Figures (26)

• Figure 1: Schematic of the magnetic hysteresis protocol. Panel a shows the field ramps over time, as schematics (not actual energy scales or timescales) where we begin recording magnetization at the maximum-polarization longitudinal field denoted by the dashed purple vertical line, and panel b shows the conceptual tracing of the average magnetization response to the applied longitudinal field $H_z$. Panels c and d show the programmed D-Wave hardware waveforms for the final simulation time of $11.2 \mu$s, where $s$ is the "anneal-schedule" control parameter, and the h-gain field is $H_z$. Adapted from ref. pelofske2025magnetichysteresisexperimentsperformed.
• Figure 2: Magnetic hysteresis on 1D odd antiferromagnetic rings. Average magnetization (y-axis) as a function of the applied longitudinal field $H$ (x-axis). The overlaid black arrows on the average magnetization lines sampled from the QPUs simultaneously denote the time-progression of the experiment, as well as the direction of the longitudinal field sweeps. The $H$ field units are in normalized hardware programmable units, see Appendix \ref{['section:A_s_B_s_functions']}. The different lines correspond to D-Wave experiments performed at different anneal-schedule-pauses, defined by $s$, which corresponds to a particular physical field ratio of $\Gamma/J$ (denoted in the legend).
• Figure 3: Selected example 1D antiferromagnet spin configurations measured during the hysteresis cycle run on Advantage2_prototype2.6 (at $s=0.7$), comprised of $1131$ spins. Each spin configuration is from a different applied longitudinal field value in the non-saturated region of the hysteresis cycle. The spin configurations are shown as a circular annular wedge plot where black slice denote spin down qubit measurements and cyan slices denote spin up qubit measurements. The net magnetization for each sample is shown in the center of each plot.
• Figure 4: Domain wall density (y-axis) on the 1D antiferromagnetic rings during the hysteresis cycles as a function of applied longitudinal field $H$. Left hand column shows the total, average, domain wall wall density, regardless of the sign of the domain wall. Right hand column shows the spin down ($\downarrow \downarrow$) domain wall density. Like in the prior hysteresis result plots, each line that is plotted corresponds to a paused $\Gamma/J$ value on the D-Wave processor. Each row corresponds to the different system size embedded on a different quantum annealing processor. Note that because these rings have an odd number of spins, we are always guaranteed to have at least one pinned domain wall somewhere on the ring.
• Figure 5: Magnetic hysteresis on 2D antiferromagnetic square lattices, on four different D-Wave quantum annealers. Average magnetization (y-axis) as a function of the applied longitudinal field (x-axis). The overlaid black arrows on the average magnetization lines sampled from the QPUs simultaneously denote the time-progression of the analog simulations, as well as the direction of the longitudinal field sweeps.