Quantum spin glasses and quantum annealing

7 problems

• Does quantum annealing outscale classical algorithms on 3D spin glasses?

  Contested

  Whether quantum annealers reach good low-energy states faster, as problems grow, than the best ordinary computer methods is still argued. The answer depends on which classical methods are used for the comparison.

• Asymptotic scaling of coherent quantum annealing in 3D spin glasses

  Partially resolved

  A quantum annealer slowly removes a sideways field so that the spins settle into a low-energy arrangement, and the leftover energy falls as a power of the anneal time. Whether that power keeps the value predicted from the critical point, and what happens at long anneal times, is not known.

• How the energy gap closes at the 3D quantum spin-glass transition

  Open

  At the critical sideways field the energy needed to create the first excitation (the gap) shrinks as the sample grows. In two dimensions this shrinking has been measured separately for excitations that keep and that flip the global spin-reversal symmetry; in three dimensions it is unsettled.

• Exponentially small gaps inside the quantum spin-glass phase

  Open

  Below the critical sideways field, the two lowest energy levels of a spin glass can approach each other and swap order as the field is reduced, and each near-crossing forces a quantum annealer to slow down. Whether such near-crossings occur in typical large samples, and how small their gaps become, decides whether annealing is exponentially slow even after the critical point is passed.

• Does the random SU(2) Heisenberg magnet freeze at zero temperature?

  Partially resolved

  When quantum spins free to point in any direction interact with random couplings of both signs, they may freeze into a glass or stay in a liquid-like state with no frozen moments. For spin $1/2$ with all-to-all random couplings, calculations suggest weak freezing, but its size and the liquid-like behavior above it are unsettled, and short-range versions are open.

• Is the 2D quantum spin-glass transition controlled by infinite randomness?

  Partially resolved

  In some disordered quantum magnets the transition is controlled by rare, strongly coupled regions, so time scales grow exponentially with length instead of as a power. In two dimensions simulations find that one kind of excitation behaves this way while another does not, and how the two fit into one critical theory is unsettled.

• Does LiHo_xY_1-xF4 have a true spin-glass phase and quantum transition?

  Contested

  $\mathrm{LiHoYF_4}$ is a crystal in which magnetic holmium ions are diluted by nonmagnetic yttrium, and a sideways field adds quantum fluctuations. Experiments disagree on whether its low-temperature state is a genuine spin glass, so it is unclear whether it realizes a quantum spin-glass transition.