We derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of $d$ field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most $k$-partite entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancillas. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.

We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state through an adaptively constructed quantum circuit, where each adaptive step is informed by feedback from gradient measurements in which the associated tangent space directions are randomized. We provide theoretical arguments and numerical evidence that convergence to the target state can be achieved for almost all initial states. We investigate different randomization procedures and develop lower bounds on the expected cost function change, which allows for drawing connections to barren plateaus and for assessing the applicability of the algorithm to large-scale problems.

The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver algorithm aims to prepare the ground state of a Hamiltonian exploiting parametrized quantum circuits that may offer an advantage compared to classical trial states used, for instance, in quantum Monte Carlo or tensor network calculations. While, traditionally, the main focus has been on developing better trial circuits, we show that the algorithm's success, if optimized within stochastic gradient descent (SGD) or quantum natural gradient descent (QNGD), crucially depends on other parameters such as the learning rate, the number $N_s$ of measurements to estimate the gradient components, and the Hamiltonian gap $\mathrm{\Delta }$. Within the standard SGD or QNGD, we first observe the existence of a finite $N_s$ value below which the optimization is impossible, and the energy variance resembles the behavior of the specific heat in second-order phase transitions. Second, when $N_s$ is above such threshold level, and learning is possible, we develop a phenomenological model that relates the fidelity of the state preparation with the optimization hyperparameters and $\mathrm{\Delta }$. More specifically, we observe that the computational resources scale as $1/{\mathrm{\Delta }}^2$, and we propose a symmetry enhancement of the variational ansatz as a way to increase the closing gap. We test our understanding on several instances of two-dimensional frustrated quantum magnets, which are believed to be the most promising candidates for near-term quantum advantage through variational quantum simulations.

We propose a variational quantum algorithm for estimating microcanonical expectation values in models obeying the eigenstate thermalization hypothesis. Using a relaxed criterion for convergence of the variational optimization loop, the algorithm generates weakly entangled superpositions of eigenstates at a given target energy density. An ensemble of these variational states is then used to estimate microcanonical averages of local operators, with an error whose dominant contribution decreases initially as a power law in the size of the ensemble and is ultimately limited by a small bias. We apply the algorithm to the one-dimensional mixed-field Ising model, where it converges for ansatz circuits of depth roughly linear in system size. The most accurate thermal estimates are produced for intermediate energy densities. In our error analysis, we find connections with recent works investigating the underpinnings of the eigenstate thermalization hypothesis. In particular, the failure of energy-basis matrix elements of local operators to behave as independent random variables is a potential source of error that the algorithm can overcome by averaging over an ensemble of variational states.

Straintronics is an emerging field enabling novel tuneable functionalities of electronic, optical, magnetic, or spin devices with advances being fuelled by new developments in van der Walls (vdW) heterostructure engineering and materials design. Here we show, using state-of-the-art quantum Monte Carlo (QMC) methods, that a single phosphorene monolayer exhibits outstanding straintronics functionalities due to discovered colossal strain tunability of its semiconducting electronic gap. First, we determine the equilibrium atomic structure that differs appreciably from available bulk phosphorene experimental data. That enables us to precisely analyze the quasiparticle band gaps for any uniaxial (armchair and zigzag) and biaxial strains which we describe by a quadrivariate paraboloid function of lattice and internal structure parameters. Using the fixed-node QMC calculations fitted by analytical formulas we localize the following excited state crossings: (i) between the direct ($\mathrm{\Gamma }\to \mathrm{\Gamma }$) and direct but reordered ($\mathrm{\Gamma }\to {\mathrm{\Gamma }}^{\prime }$) excitations that also imply substantial differences of corresponding transport properties; and (ii) between the direct $\mathrm{\Gamma }\to \mathrm{\Gamma }$ and indirect $\mathrm{\Gamma }\to \mathrm{X}$ excitations. Based on this highly accurate many-body treatment, we predict the gauge factor $\approx 100$ meV/% and an unusual behavior with the band gap remaining direct even if strained by several percent. Consequently, we suggest there is a colossal band gap tunability window, larger by an order of magnitude when compared to quintessential straintronic materials such as ${\mathrm{MoS}}_2$. In addition, we ascertain that the ground state deformation energies exhibit an out-of plane negative Poisson's ratio and auxetic behavior.

Multipartite entanglement enables secure and anonymous key exchange between multiple parties in a network. Greenberger-Horne-Zeilinger states have been introduced as resource states for anonymous key exchange protocols, in which an anonymous subset of parties within a larger network establishes a secret key. However, the use of other types of multipartite entanglement for such protocols remains relatively unexplored. Here, we demonstrate that linear cluster states can serve as a versatile and potentially scalable resource in such applications. We implemented an anonymous key exchange protocol with four photons in a linear cluster state and established a shared key between three parties in our network. We show how to optimize the protocol parameters to account for noise and to maximize the finite key rate under realistic conditions. As cluster states have been established as a flexible resource in quantum computation, we expect that our demonstration provides a first step towards their hybrid use for networked computing and communication.

We investigate the topological defect populations for superconducting vortices and magnetic skyrmions on random pinning substrates under driving amplitudes that are swept at different rates or suddenly quenched. When the substrate pinning is sufficiently strong, the system exhibits a nonequilibrium phase transition at a critical drive into a more topologically ordered state where there are few non-sixfold coordinated particles. We examine the number of topological defects that remain as we cross the ordering transition at different rates. In the vortex case, the system dynamically orders into a moving smectic, and the Kibble-Zurek scaling hypothesis gives exponents consistent with directed percolation. Due to their strong Magnus force, the skyrmions dynamically order into an isotropic crystal, producing different Kibble-Zurek scaling exponents that are more consistent with coarsening. We argue that, in the skyrmion crystal, the topological defects can both climb and glide, facilitating coarsening, whereas in the vortex smectic state, the defects cannot climb and coarsening is suppressed. We also examine pulsed driving across the ordering transition and find that the defect population on the ordered side of the transition decreases with time as a power law, indicating that coarsening can occur across nonequilibrium phase transitions. Our results should be general to a wide class of nonequilibrium systems driven over random disorder where there are well-defined topological defects.

In this paper, we propose three physical images, namely, asymmetric external inputs, discretization of the low rate region, and secondary outbreak, to understand the mystery of the relative timescales in the coevolution dynamics on multiplex networks. We carry out our analysis on an irreversible information-epidemic coevolution dynamics. In this dynamics, we found five kinds of anomalous behaviors, which are that with the increase of relative information processing speed, the final epidemic size may be monotonically increasing, monotonically decreasing, first decreasing and then increasing, first increasing and then decreasing but increasing again, and suddenly increasing with large fluctuation. Such complex behavior can be fully explained by our three physical images. Moreover, these five behaviors may transform into one another, which is far more complex than cyclic dynamics. Of course, our physical images easily provide an explanation for the results of cyclic coevolution dynamics. Since our discussion does not rely on specific dynamics and networks, our research may readily be extended to a broader field, rather than the network epidemiology in this paper.

The filiform corrosion of Mg in NaCl solution was characterized by acoustic emission spectroscopy, measurements of the free-corrosion potential, and optical observations under in situ conditions. Three stages of corrosion were identified: an incubation period, localized attack, and filament propagation. The corrosion mechanisms include the Mg dissolution, the breakdown of hydroxide/oxide surface films, and the burst of gas bubbles. Localized attack and filament propagation are distinguished by a gradual transition from correlated avalanches (wild events) to predominantly stochastic processes (mild events), which still contain some weak avalanche signals. Our approach provides a way to monitor corrosion under in situ conditions.

The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and the approximate degeneracy of the Landau levels are known to also survive on crystalline lattices with discrete translation symmetry when the magnetic flux through a primitive cell is small compared to the flux quantum. Here we show that the notion of Landau levels and the quantum Hall effect can be generalized to two-dimensional (2D) noncrystalline lattices without spatial long-range order. Remarkably, even when the spatial correlations decay over microscopic distances, 2D systems can exhibit a number of well-resolved Landau-like bands. The existence of these bands imply that noncrystalline systems in magnetic fields can support the hallmark quantum effects which have been typically associated with crystalline solids.

The ability to control levitated nanoparticles allows one to explore various fields of physics, including quantum optics, quantum metrology, and nonequilibrium physics. It has been recently demonstrated that the arrangement of two levitated nanoparticles naturally realizes the tunable nonreciprocal dipole-dipole interaction. Motivated by this development, we here propose and analyze an array of levitated nanoparticles as an ideal platform to study non-Hermitian physics in a highly controlled manner. We employ the non-Bloch band theory to determine the continuum bands of the proposed setup and investigate the non-Hermitian skin effect therein. In particular, we point out that the levitated nanoparticle array exhibits rich dynamical phases, including the dynamically unstable phase and the unconventional critical phase where the spectral singularity persists over a broad region of the controllable parameters. We also show that the long-range nature of the dipole-dipole interaction gives rise to the unique self-crossing point of the continuum band.

Recently, topologically nontrivial polarization textures have been predicted and observed in nanoscale systems. While these polarization textures are interesting and promising in terms of applications, their topology in general is yet to be fully understood. For example, the relation between topological polarization structures and band topology has not been explored, and polar domain structures are typically considered in topologically trivial systems. In particular, the local polarization in a crystal supercell is not well-defined, and typically calculated using approximations that do not satisfy gauge invariance. Furthermore, local polarization in supercells is typically approximated using calculations involving smaller unit cells, meaning the connection to the electronic structure of the supercell is lost. In this work, we propose a definition of local polarization which is gauge invariant and can be calculated directly from a supercell without approximations. We show using first-principles calculations for commensurate bilayer hexagonal boron nitride that our expressions for local polarization give the correct result at the unit cell level, which is a first approximation to the local polarization in a moiré superlattice. We also illustrate using an effective model that the local polarization can be directly calculated in real space. Finally, we discuss the relation between polarization and band topology, for which it is essential to have a correct definition of polarization textures.

The spin phenomena observed at a clean metal-insulator interface are typically reduced to the Rashba-Edelstein effect, which leads to spin accumulation over a few monolayers. We demonstrate that the presence of interface disorder significantly expands the range of potential phenomena. Specifically, the skew scattering at the metal-insulator boundary gives rise to the “kinetic Rashba-Edelstein effect,” where spin accumulation occurs on a much larger length scale comparable to the mean free path. Moreover, at higher orders of spin-orbit interaction, skew scattering is accompanied with spin relaxation resulting in the interface spin-Hall effect—a conversion of electrical current to spin current at the metal surface. Unlike the conventional spin-Hall effect, this phenomenon persists even within the Born approximation. These two predicted phenomena can dominate the spin density and spin current in devices of intermediate thickness.

Networks of quantum devices with coherent control over their configuration offer promising advantages in quantum information processing, including quantum communication, computation, and sensing. So far, the investigation of these advantages assumed that the control system was initially uncorrelated with the data processed by the network. Here, we explore the power of quantum correlations between data and control, showing two communication tasks that can be accomplished with information-erasing channels if and only if the sender shares prior entanglement with a third party (the “controller”) controlling the network configuration. The first task is to transmit classical messages without leaking information to the controller. The second task is to establish bipartite entanglement with a receiver, or, more generally, to establish multipartite entanglement with a number of spatially separated receivers.