Quantifying information scrambling via classical shadow tomography on programmable quantum simulators
Physical Review A: Atomic, Molecular and Optical Physics American Physical Society 106 (2022) 012441
Abstract:
We develop techniques to probe the dynamics of quantum information, and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time evolution channels rather than of quantum states, and rely only on single-qubit operations and measurements. We identify two unambiguous signatures of quantum information scrambling, neither of which can be mimicked by dissipative processes, and relate these to many-body teleportation. By realizing quantum chaotic dynamics in experiment, we measure both signatures, and support our results with numerical simulations of the quantum system. We additionally investigate operator growth under this dynamics, and observe behaviour characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators.Excitonic fractional quantum Hall hierarchy in Moiré heterostructures
Physical Review B American Physical Society 105:23 (2022) 231521
Abstract:
We consider fractional quantum Hall states in systems where two flat Chern number C=±1 bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor ν = 1 this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized 'orbital ferromagnet’ parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for moir'e heterostructures of bilayer graphene on a hexagonal boron nitride substrate.Global phase diagram of the normal state of twisted bilayer graphene
Physical Review Letters American Physical Society 128:15 (2022) 156401
Abstract:
We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the “cascade” physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.Excitonic fractional quantum Hall hierarchy in moire heterostructures
PHYSICAL REVIEW B 105:23 (2022) ARTN 235121
Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene
Physical Review X American Physical Society 11:4 (2021) 041063