Optimal Twirling Depth for Classical Shadows in the Presence of Noise.

The classical shadows protocol is an efficient strategy for estimating properties of an unknown state ρ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from some ensemble and measuring the twirled state in a fixed basis. It was recently shown that for computing local properties, optimal sample complexity (copies of the state required) is remarkably achieved for unitaries drawn from shallow depth circuits composed of local entangling gates, as opposed to purely local (zero depth) or global twirling (infinite depth) ensembles. Here, we consider the sample complexity as a function of the depth of the circuit, in the presence of noise. We find that this noise has important implications for determining the optimal twirling ensemble. Under fairly general conditions, we (i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter f, (ii) compute thresholds f_{th} at which optimal twirling reduces to local twirling for Pauli operators, (iii) nth order Renyi entropies (n≥2), and (iv) provide a meaningful upper bound t_{max} on the optimal circuit depth for any finite noise strength f, which applies to observables and entanglement entropy measurements. These thresholds strongly constrain the search for optimal strategies to implement shadow tomography and are easily tailored to the experimental system at hand.

Anomalous electronic transport in high-mobility Corbino rings.

We report low-temperature electronic transport measurements performed in two multi-terminal Corbino samples formed in GaAs/Al-GaAs two-dimensional electron gases (2DEG) with both ultra-high electron mobility ( ≳ 20 × 106 cm2/ Vs) and with distinct electron density of 1.7 and 3.6 × 1011 cm-2. In both Corbino samples, a non-monotonic behavior is observed in the temperature dependence of the resistance below 1 K. Surprisingly, a sharp decrease in resistance is observed with increasing temperature in the sample with lower electron density, whereas an opposite behavior is observed in the sample with higher density. To investigate further, transport measurements were performed in large van der Pauw samples having identical heterostructures, and as expected they exhibit resistivity that is monotonic with temperature. Finally, we discuss the results in terms of various lengthscales leading to ballistic and hydrodynamic electronic transport, as well as a possible Gurzhi effect.

Dynamical Enhancement of Symmetries in Many-Body Systems.

We construct a dynamical decoupling protocol for accurately generating local and global symmetries in general many-body systems. Multiple commuting and noncommuting symmetries can be created by means of a self-similar-in-time ("polyfractal") drive. The result is an effective Floquet Hamiltonian that remains local and avoids heating over exponentially long times. This approach can be used to realize a wide variety of quantum models, and nonequilibrium quantum phases.

Electron-phonon instability in graphene revealed by global and local noise probes.

Understanding and controlling nonequilibrium electronic phenomena is an outstanding challenge in science and engineering. By electrically driving ultraclean graphene devices out of equilibrium, we observe an instability that is manifested as substantially enhanced current fluctuations and suppressed conductivity at microwave frequencies. Spatial mapping of the nonequilibrium current fluctuations using nanoscale magnetic field sensors reveals that the fluctuations grow exponentially along the direction of carrier flow. Our observations, including the dependence on density and temperature, are consistently explained by the emergence of an electron-phonon Cerenkov instability at supersonic drift velocities. These results offer the opportunity for tunable terahertz generation and active phononic devices based on two-dimensional materials.

Interacting multi-channel topological boundary modes in a quantum Hall valley system.

Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3-8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires. QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.

Fast Preparation of Critical Ground States Using Superluminal Fronts.

We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼L^{d} (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L^{2}) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.

Anomalous diffusion and griffiths effects near the many-body localization transition.

We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.

Chiral prethermalization in supersonically split condensates.

We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a supersonic unzipping of a single condensate. We use the Lorentz invariance of the low energy sector of such systems to show that dephasing results in an unusual prethermal state, in which right- and left-moving excitations have different, Doppler-shifted temperatures. The chirality of these modes can be probed experimentally by measuring the interference fringe contrasts with the release point of the split condensates moving at another supersonic velocity. Further, an accelerated motion of the release point can be used to observe a spacelike analog of the Unruh effect. A concrete experimental realization of the quantum zipper for a BEC of trapped atoms on an atom chip is outlined.