Engineering topics

Friedman, Aaron J.

Publications and source records attributed to Friedman, Aaron J..

4 records

DOE OSTI2024

Quantum teleportation implies symmetry-protected topological order

We constrain a broad class of teleportation protocols using insights from locality. In the ``standard'' teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a ``resource state'' exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry G k = ( Z 2 × Z 2 ) k . The k logical states are teleported between the edges of the chain by measuring the corresponding 2 k string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of k qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.

Hong, Yifan↗

DOE OSTI2023

Hydrodynamics of higher-rank gauge theories

We extend recent work on hydrodynamics with global multipolar symmetries — known as “fracton hydrodynamics” — to systems in which the multipolar symmetries are gauged. We refer to the latter as “fracton magnetohydrodynamics”, in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell’s equations and in systems with one-form symmetries obeying certain constraints; while we focus on “minimal” higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Topological edge modes without symmetry in quasiperiodically driven spin chains

Here we construct an example of a 1d quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. In a sharp departure from topological phases in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this emergent dynamical symmetry-protected topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long timescales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a type of boundary critical with no known static or Floquet analogue, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Diffusive hydrodynamics from integrability breaking

We describe here the crossover from generalized to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically, in general. When integrability is broken, only a few of these conserved quantities survive. The remaining conserved quantities are generically transported diffusively; we further derive a compact and general diffusion equation for these. The diffusion constant depends on the matrix elements of the integrability-breaking perturbation; for a certain class of integrability-breaking perturbations, including long-range interactions, the diffusion constant can be expressed entirely in terms of generalized hydrodynamic data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗