We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator $e^{-\beta H}$ for infinite $\beta$. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature $\beta$, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically.

We present models where ${\gamma }_{+}$ and ${\gamma }_{-}$, the exponents of the susceptibility in the high- and low-temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The ${\mathbb{Z}}_q$-invariant models are the simplest examples for two-component order parameters ($N=2$) and the model with icosahedral symmetry for $N=3$. We accurately compute ${\gamma }_{+}-{\gamma }_{-}$ as well as the ratio $\nu /{\nu }^{\prime }$ of the exponents of the two correlation lengths present for $T<T_c$.

When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful way to complement usual refocusing techniques. Relaxation imposes a fundamental limit on the sensitivity of state of the art quantum sensors which cannot be overcome by dynamical decoupling. The only way to overcome this is to utilize quantum error correcting codes. We present a superconducting magnetometry design that incorporates approximate quantum error correction, in which the signal is generated by a two qubit Hamiltonian term. This two-qubit term is provided by the dynamics of a tunable coupler between two transmon qubits. For fast enough correction, it is possible to lengthen the coherence time of the device beyond the relaxation limit.

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.

We experimentally demonstrate a simple yet versatile optimal quantum control technique that achieves tailored robustness against qubit inhomogeneities and control errors while requiring minimal bandwidth. We apply the technique to nitrogen-vacancy (NV) centers in diamond and verify its performance using quantum process tomography. In a wide-field NV center magnetometry scenario, we achieve a homogeneous sensitivity across a 33% drop in control amplitude, and we improve the sensitivity by up to 2 orders of magnitude for a normalized detuning as large as 40%, achieving a value of $20\mathrm{nT}{\mathrm{Hz}}^{-1/2}\mu {\mathrm{m}}^{3/2}$ in sensitivity times square root volume.

Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of nonhydrodynamic modes. We review nonhydrodynamic modes in kinetic theory and gauge-gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data we find hints of nonhydrodynamic modes in cold Fermi gases in two and three dimensions.

Replica exchange (RE) is one of the most popular enhanced-sampling simulations technique in use today. Despite widespread successes, RE simulations can sometimes fail to converge in practical amounts of time, e.g., when sampling around phase transitions, or when a few hard-to-find configurations dominate the statistical averages. We introduce a generalized RE scheme, density-of-states-informed RE, that addresses some of these challenges. The key feature of our approach is to inform the simulation with readily available, but commonly unused, information on the density of states of the system as the RE simulation proceeds. This enables two improvements, namely, the introduction of resampling moves that actively move the system towards equilibrium and the continual adaptation of the optimal temperature set. As a consequence of these two innovations, we show that the configuration flow in temperature space is optimized and that the overall convergence of RE simulations can be dramatically accelerated.

We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov–de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.

The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While noninteracting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system’s boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.

The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While post-quantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.

A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.

Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both earlier and later) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state “quantum trajectory.” Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unraveling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.

We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.

We study the effects of integrability-breaking perturbations on the nonequilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalizations of quantum Boltzmann equations. We benchmark our method against time-dependent density matrix renormalization group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalization plateaux for local observables on all accessible time scales. Increasing the strength of the integrability-breaking term induces a “drift” away from the prethermalization plateaux towards thermal behavior. We identify a time scale characterizing this crossover.

The dynamics of wave packets in the fractional Schrödinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in the fractional Schrödinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional input chirped Gaussian beams is not harmonic. In one dimension, the beam propagates along a zigzag trajectory in real space, which corresponds to a modulated anharmonic oscillation in momentum space. In two dimensions, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display an increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.