Path-independent (PI) quantum control has recently been proposed to integrate quantum error correction and quantum control [W.-L. Ma, M. Zhang, Y. Wong, K. Noh, S. Rosenblum, P. Reinhold, R. J. Schoelkopf, and L. Jiang, Phys. Rev. Lett. 125, 110503 (2020)], achieving fault-tolerant quantum gates against ancilla errors. Here we reveal the underlying algebraic structure of PI quantum control. The PI Hamiltonians and propagators turn out to lie in an algebra isomorphic to the ordinary matrix algebra, which we call the PI matrix algebra. The PI matrix algebra, defined on the Hilbert space of a composite system (including an ancilla system and a central system), is isomorphic to the matrix algebra defined on the Hilbert space of the ancilla system. By extending the PI matrix algebra to the Hilbert-Schmidt space of the composite system, we provide an exact and unifying condition for PI quantum control against ancilla noise.

We study the effect of spontaneous emission and incoherent atomic pumping on the nonlinear semiclassical dynamics of the unbalanced Dicke model—a generalization of the Dicke model that features independent coupling strengths for the co- and counter-rotating interaction terms. As well as the ubiquitous superradiant behavior the Dicke model is well-known for, the addition of spontaneous emission combined with the presence of strong counter-rotating terms creates a laserlike behavior termed counter-lasing. These states appear in the semiclassical model as stable periodic orbits. We perform a comprehensive dynamical analysis of the appearance of counter-lasing in the unbalanced Dicke model subject to strong cavity dissipation, such that the cavity field can be adiabatically eliminated to yield an effective Lipkin-Meshkov-Glick (LMG) model. If the coupling strength of the corotating interactions is small, then the counter-lasing phase appears via a Hopf bifurcation of the deexcited state. We find that if the rate of spontaneous emission is small, this can lead to resurgent superradiant pulses. However, if the corotating coupling is larger, then the counter-lasing phase must emerge via the steady-state superradiant phase. Such a transition is the result of the competition of the coherent and incoherent processes that drive superradiance and counter-lasing, respectively. We observe a surprisingly complex transition between the two, associated with the formation of a chaotic attractor over a thin transitional parameter region.

The anomalous Hall effect (AHE) is a key transport signature revealing the topological properties of magnetic compounds. In quantum materials, the classical linear dependence of the AHE on magnetization often breaks down, which is typically ascribed to the presence of topological magnetic or electronic textures. However, the complex electronic structure of these compounds may offer alternative, unexplored mechanisms. Here, we show that a giant nonlinear AHE can originate from a series of magnetic-field-induced Lifshitz transitions in the spin-dependent band structure. In our experiments on ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ the AHE contributes to 97% of the total Hall response, corresponding to a record anomalous Hall angle of 21%. Our scaling analysis and first-principles calculations demonstrate that the electronic structure is extremely sensitive to spin canting, with the magnetic field causing band crossing and band inversion and introducing a band gap when oriented along specific directions. Our results not only provide an ideal platform for Berry curvature engineering but reveal a general effect that may be applied to other material systems.

We investigate wave-vortex interaction emerging from an expanding compact vortex cluster in a two-dimensional Bose-Einstein condensate. We adapt techniques developed for compact gravitational objects to derive the characteristic modes of the wave-vortex interaction perturbatively around an effective vortex flow field. We demonstrate the existence of orbits or sound rings, in analogy to gravitational light rings, and compute the characteristic spectrum for the out-of-equilibrium vortex cluster. The spectrum obtained from numerical simulations of a stochastic Gross-Pitaevskii equation exhibiting an expanding vortex cluster is in excellent agreement with analytical predictions. Our findings are relevant for two-dimensional quantum turbulence, the semiclassical limit around fluid flows, and rotating compact objects exhibiting discrete circulation.

We demonstrate a postquench dynamics simulation of a Heisenberg model on present-day IBM quantum hardware that extends beyond the coherence time of the device. This is achieved using a hybrid quantum-classical algorithm that propagates a state using Trotter evolution and then performs a classical optimization that effectively compresses the time-evolved state into a variational form. When iterated, this procedure enables simulations to arbitrary times with an error controlled by the compression fidelity and a fixed Trotter step size. We show how to measure the required cost function, the overlap between the time-evolved and variational states, on present-day hardware, making use of several error mitigation methods. In addition to carrying out simulations on real hardware, we investigate the performance and scaling behavior of the algorithm with noiseless and noisy classical simulations. We find the main bottleneck in going to larger system sizes to be the difficulty of carrying out the optimization of the noisy cost function.

We investigate the quasiparticle excitations in the Fulde-Ferrell–type helical state of a superconductor with inversion symmetry breaking and strong Rashba spin-orbit coupling. We restrict to a state with single finite momentum of Cooper pairs in the helical phase that is determined by minimization of the condensation energy. We derive the dependence of quasiparticle dispersions on the Rashba coupling strength and external field. It leads to a peculiar momentum-space segmentation of the corresponding Rashba Fermi surface sheets. We show that it may be directly visualized by the method of quasiparticle interference that identifies the critical points of the segmented sheets and can map their evolution with field strength, bias voltage, and Rashba coupling. We also indicate a strategy for how to determine the finite Cooper-pair momentum from experimental quantities. This investigation has the potential for a more detailed microscopic understanding of the helical superconducting state under the influence of Rashba spin-orbit coupling.

Quantum many-body scarred systems host special nonthermal eigenstates that support periodic revival dynamics and weakly break the ergodicity. Here, we study the quantum information scrambling dynamics in quantum many-body scarred systems, with a focus on the “PXP” model. We use the out-of-time-ordered correlator (OTOC) and Holevo information as measures of the information scrambling and apply an efficient numerical method based on matrix product operators to compute them up to 41 spins. We find that both the OTOC and Holevo information exhibit a linear light cone and periodic oscillations inside the light cone for initial states within the scarred subspace, which is in sharp contrast to thermal or many-body localized systems. The periodic revivals of OTOCs and Holevo information signify unusual breakdown of quantum chaos and are not equivalent to the revival dynamics of state fidelity or local observables studied in the previous literature. To explain the formation of the linear light-cone structure, we provide a perturbation-type calculation based on a phenomenological model. In addition, we demonstrate that the OTOC and Holevo information dynamics of the PXP model can be measured using the Rydberg-atom quantum simulators with current experimental technologies and numerically identify the measurable signatures using experimental parameters.

Marine plankton are usually modeled as settling elongated microswimmers. We consider the torque induced by fluid inertia on such swimmers, and we discover that they spontaneously swim in the direction opposite to gravity. We analyze the equilibrium orientation of swimmers in quiescent fluid and the mean orientation in turbulent flows using direct numerical simulations. Similar to well-known gyrotaxis mechanisms, the effect of fluid inertial torque can be quantified by an effective reorientation timescale. We show that the orientation of swimmers strongly depends on the reorientation timescale, and swimmers exhibit strong preferential alignment in an upward direction when the timescale is of the same order of the Kolmogorov timescale. Our findings suggest that the fluid inertial torque is a different mechanism of gyrotaxis that stabilizes the upward orientation of microswimmers such as plankton.

We report a comprehensive study of magnetic correlations in ${\mathrm{LaNiO}}_2$, a parent compound of the recently discovered family of infinite-layer (IL) nickelate superconductors, using multiple experimental and theoretical methods. Our specific heat, muon-spin rotation ($\mu \mathrm{SR}$), and magnetic susceptibility measurements on polycrystalline ${\mathrm{LaNiO}}_2$ show that long-range magnetic order remains absent down to 2 K. Nevertheless, we detect residual entropy in the low-temperature specific heat, which is compatible with a model fit that includes paramagnon excitations. The $\mu \mathrm{SR}$ and low-field static and dynamic magnetic susceptibility measurements indicate the presence of short-range magnetic correlations and glassy spin dynamics, which we attribute to local oxygen nonstoichiometry in the average infinite-layer crystal structure. This glassy behavior can be suppressed in strong external fields, allowing us to extract the intrinsic paramagnetic susceptibility. Remarkably, we find that the intrinsic susceptibility shows non-Curie-Weiss behavior at high temperatures, in analogy to doped cuprates that possess robust nonlocal spin fluctuations. The distinct temperature dependence of the intrinsic susceptibility of ${\mathrm{LaNiO}}_2$ can be theoretically understood by a multimethod study of the single-band Hubbard model in which we apply complementary cutting-edge quantum many-body techniques (dynamical mean-field theory, cellular dynamical mean-field theory, and the dynamical vertex approximation) to investigate the influence of both short- and long-ranged correlations. Our results suggest a profound analogy between the magnetic correlations in parent (undoped) IL nickelates and doped cuprates.

The ongoing COVID-19 pandemic is the first epidemic in human history in which digital contact tracing has been deployed at a global scale. Tracking and quarantining all the contacts of individuals who test positive for a virus can help slow down an epidemic, but the impact of contact tracing is severely limited by the generally low adoption of contact-tracing apps in the population. We derive here an analytical expression for the effectiveness of contact-tracing app installation strategies in a susceptible-infected-recovered (SIR) model on a given contact graph. We propose a decentralized heuristic to improve the effectiveness of contact tracing under fixed adoption rates, which targets a set of individuals to install contact-tracing apps and can be easily implemented. Simulations on a large number of real-world contact networks confirm that this heuristic represents a feasible alternative to the current state of the art.

There is a growing interest in applying different external potentials other than the conventional uniform disorder for inhibiting thermalization and realizing the many-body localization (MBL) phase. Various types of external potentials have been explored, e.g., linear/quasiperiodic potentials and discrete disorder, but what type of potentials is the most “effective” for inducing MBL remains elusive. In this work, we formally introduce the problem of the optimal randomized potential from two aspects, which is to find the optimal on-site energy distribution so that (1) the required random field strength for the onset of MBL (i.e., $W_c$ in the literature) is the minimal, and (2) the thermalization occurs the slowest after the system is prepared in an out-of-equilibrium state. We choose the spinless fermionic chain to study the problem using two complementary methods. For short chains ($L<20$), we employ exact numerical approaches for (1) diagnosing MBL transitions and (2) simulating the dynamics of the entanglement entropy. For longer chains [$L\sim O\left(100\right)$], we employ a modified real-space renormalization group (RSRG) approach to trade off accuracy for simulation sizes and scaling properties. Both methods predict that random potentials with a certain degree of polarization towards binary disorder will favor the MBL more than the uniform distribution. For some studied cases, the optimal random distribution lies in between the uniform and binary disorder. We attribute that to the competition between increased on-site energy fluctuation and enhanced degeneracy near the distribution edge ($\pm W$). While precisely determining the functional form of the optimal random distribution is not feasible at present, our results could be useful for engineering more efficient potentials for realizing MBL in mesoscopic systems.

Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist defects. However, implementing twist-based lattice surgery may require additional resources, such as extra device connectivity, and could lower the threshold and overall performance for the surface code. Here we provide an explicit twist-based lattice surgery protocol and its requisite connectivity layout. We also provide new stabilizer measurement circuits for measuring twist defects which are compatible with our chosen gate scheduling. We undertake the first circuit-level error correction simulations during twist-based lattice surgery using a biased depolarizing noise model. Our results indicate a slight decrease in the threshold for timelike logical failures compared to lattice surgery protocols with no twist defects in the bulk. However, comfortably below threshold (i.e., with CNOT infidelities below $5\times {10}^{-3}$), the performance degradation is mild and in fact preferable over proposed alternative twist-free schemes. Lastly, we provide an efficient scheme for measuring $Y$ operators along boundaries of surface codes, which bypasses certain steps that were required in previous schemes.

In some non-Hermitian systems, the eigenstates in the bulk are localized at the boundaries of the systems. This is called the non-Hermitian skin effect, and it has been studied mostly in discrete systems. In the present work, we study the non-Hermitian skin effect in a continuous periodic model. In a one-dimensional system, we show that the localization lengths are equal for all the eigenstates. Moreover, the localization length and the eigenspectra in a large system are independent of the types of open boundary conditions. These properties are also found in a non-Hermitian photonic crystal. Such remarkable behaviors in a continuous periodic model can be explained in terms of the non-Bloch band theory. By constructing the generalized Brillouin zone for a complex Bloch wave number, we derive the localization length and the eigenspectra under an open boundary condition. Furthermore, we show that the generalized Brillouin zone also has various physical properties, such as bulk-edge correspondence.