Microscopics of Quantum Annealing in the Disordered Dipolar Ising Ferromagnet LiHo${}_x$Y${}_{1-x}$F${}_4$

Abstract

Quantum annealing (QA) refers to an optimization process that uses quantum fluctuations to find the global minimum of a rugged energy landscape with many local minima. Conceptually, QA is often framed in the context of the disordered transverse field Ising model, in which a magnetic field applied perpendicular to the Ising axis tunes the quantum fluctuations and enables the system to tunnel through energy barriers, and hence reach the ground state more quickly. A solid state material closely related to this model, LiHo${}_{0.45}$Y${}_{0.55}$F${}_4$, was shown to exhibit faster dynamics after a QA protocol, compared to thermal annealing (TA), but little is known about the actual process of optimization involved or the nature of the spin correlations in the state that is reached. Here, we report on the microscopics of QA in this material using diffuse magnetic neutron scattering. Comparing a QA to a TA protocol that reach the same end-point, we find very similar final diffuse scattering which consists of pinch-point scattering, largely consistent with critical scattering near a phase boundary in the dipolar Ising ferromagnetic model. However, comparing the time evolution at the end of the protocols, we find that the spin correlations evolve more significantly after TA, suggesting that QA produces a state closer to equilibrium. We also observe experimental evidence that the transverse field produces random fields, which had been previously predicted for this material and studied in other contexts. Thus, while the material does exhibit a quantum speedup under quantum annealing conditions, it is not a simple annealing problem; the energy landscape being optimized is changing as the optimization proceeds.

References in corpus (20)

• Quantum Annealing in the Transverse Ising Model
• Mantid - Data Analysis and Visualization Package for Neutron Scattering and $\mu SR$ Experiments
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Annealing and Analog Quantum Computation
• Quantum annealing of the Traveling Salesman Problem
• Theory of the [111] magnetization plateau in spin ice
• Quantum Phase Transition of a Magnet in a Spin Bath
• Pinch Points and Kasteleyn Transitions: How Spin Ice Changes its Entropy
• Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
• Induced Random Fields in the LiHo${}_x$Y${}_{1-x}$F${}_4$ Quantum Ising Magnet in a Transverse Magnetic Field
• Quantum and Classical Glass Transitions in $LiH{o}_x{Y}_{1-x}{F}_4$
• Ferromagnet in a continuously tuneable random field
• $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ as a random field Ising ferromagnet
• Significance of the Hyperfine Interactions in the Phase Diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Quantum spin glass and the dipolar interaction
• Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo_xY_{1-x}F_4
• Phase diagram with enhanced spin-glass region of mixed Ising / XY magnets LiHo${}_x$Er${}_{1-x}$F${}_4$
• Effective Spin-1/2 Description of Transverse-Field-Induced Random Fields in Dipolar Spin Glasses with Strong Single-Ion Anisotropy
• Quantum spin glass in anisotropic dipolar systems
• Screening and the Pinch Point Paradox in Spin Ice