Unsharp measurement is a unique type of measurement which provides a tradeoff between information gain and state disturbance. Such measurement is a crucial method in quantum theory and shows potential in various applications. We propose a device-independent scheme for certifying unsharp measurements with binary outcome in an efficient manner. Our scheme has low consumption of measurement resources and is robust against noise. In experiment, we demonstrate the certification of a typical kind of unsharp measurements. We achieve high fidelities above 0.9 when the strength of the unsharp measurement is less than 0.6 and get near unity fidelities in the low measurement strength range. Our scheme can be applied to enhance the feasibility and practicability of device-independent quantum information processing tasks.

We introduce a solvable model of a measurement-induced phase transition (MIPT) in a deterministic but chaotic dynamical system with a positive Lyapunov exponent. In this setup, an observer only has a probabilistic description of the system but mitigates chaos-induced uncertainty through repeated measurements. Using a minimal representation via a branching tree, we map this problem to the directed polymer (DP) model on the Cayley tree, although in a regime dominated by rare events. By studying the Shannon entropy of the probability distribution estimated by the observer, we demonstrate a phase transition distinguishing a chaotic phase with a reduced Lyapunov exponent from a strong-measurement phase where uncertainty remains bounded. Remarkably, the location of the MIPT transition coincides with the freezing transition of the DP, although the critical properties differ. We provide an exact, universal scaling function describing the entropy growth in the critical regime. Numerical simulations confirm our theoretical predictions, highlighting a simple yet powerful framework to explore measurement-induced transitions in classical chaotic systems.

In the Aharonov-Bohm effect, charged particles accumulate a phase as they travel in space, encircling a source of magnetic flux. We develop a temporal analog of the Aharonov-Bohm effect, where the photons' path is in the time-domain instead of the spatial domain, and moreover demonstrate it experimentally with entangled photon pairs rather than single, uncorrelated quanta. Relying on the temporal SU(1,1) interferometer, the constructed interferometric scheme excels in its temporal resolution and sensitivity. This system can be applied for quantum-enhanced measurements, metrology at GHz frequencies, advanced sensing of dispersion properties, and high-precision temporal measurements.

Many systems, classical or quantum, closed or open, exhibit universal statistical properties. Exciton–polariton condensates, being intrinsically driven-dissipative, offer a promising platform for observing nonequilibrium universal features. By conducting extensive numerical simulations of an incoherently pumped and interacting condensate coupled to an exciton reservoir we show that the effective nonlinearity of the condensate phase dynamics can be finely adjusted across a broad range, by varying the exciton–polariton interaction strength, allowing one to probe three main universal regimes with parameters accessible in current experiments: the weakly nonlinear Edwards-Wilkinson (EW) regime, where the phase fluctuations dominate, but the phase profile does not become rough, the strongly nonlinear Kardar-Parisi-Zhang regime, where the condensate phase fluctuations grow in a superdiffusive manner leading to roughening of the phase, and a vortex-dominated phase emerging at stronger interactions, where both density and phase dynamics play significant roles. Our results provide a unified picture of the phase diagram of two-dimensional exciton–polariton condensates under incoherent pumping, and shed light on recent experimental and numerical observations.

Innovation and its complement exnovation describe the progression of realized possibilities from the past to the future, and the process depends on the structure of the underlying graph. For example, the phylogenetic tree represents the unique path of mutations to a single species. To a technology, paths are manifold, like a “truss.” We solve for the phase diagram of a model, where a population innovates while outrunning exnovation. The dynamics progress on random graphs that capture the degree of historical contingency. Higher connectivity speeds innovation but also increases the risk of system collapse. We show how dynamics and structural connectivity conspire to unleash innovative diversity or to drive it extinct.

We develop a suitable technique to design zero-energy graphene models with radial electrostatic potentials capable of achieving electrostatic confinement. Using the Gaussian law for electrostatics, we derive the charge density associated with these potentials that correspond to concentric electrostatic rings. The technique is based on a modified supersymmetric transformation that allows us to design time-reversal invariant interaction terms and to find the corresponding zero-energy bound states in analytical form. Consequently, solutions with the same probability density but different angular momentum are characterized by circular probability currents flowing in opposite directions. The energies of the systems defined in two Dirac valleys (one-valley) have a fourfold (twofold) degeneracy. As an example of the technique, we construct a ring-decorated Coulomb potential that exhibits zero-energy collapse and bound states together.

One of the most promising applications of quantum computers is solving partial differential equations (PDEs). By using the Schrödingerization technique—which converts nonconservative PDEs into Schrödinger equations—the problem can be reduced to Hamiltonian simulations. The particular class of Hamiltonians we consider is shown to be sufficient for simulating almost any linear PDE. In particular, these Hamiltonians consist of discretizations of polynomial products and sums of position and momentum operators. This paper addresses an important gap by efficiently loading these Hamiltonians into the quantum computer through block-encoding. The construction is explicit and efficient in terms of one- and two-qubit operations, forming a fundamental building block for constructing the unitary evolution operator for that class of Hamiltonians. The proposed algorithm demonstrates a squared logarithmic scaling with respect to the spatial partitioning size, offering a polynomial speedup over classical finite-difference methods in the context of spatial partitioning for solving PDEs. Furthermore, the algorithm is extended to the multidimensional case, achieving an exponential acceleration with respect to the number of dimensions, alleviating the curse of dimensionality problem. This work provides an essential foundation for developing explicit and efficient quantum circuits for PDEs, Hamiltonian simulations, and ground state and thermal state preparation.

For a particle undergoing a Lévy flight of index $s\in (0,1)$ in the unit square, we analyze the first hitting time to a set of small targets of radius $\mathcal{O}\left(\varepsilon \right)$ for $0<\varepsilon \ll 1$. In particular, we show how boundary interactions and the configuration of targets within the unit square impact the expected first hitting time. Furthermore, we illustrate how a target can be “shielded” by absorbing obstacles, and how a Lévy flight search can be significantly superior in navigating these obstacles versus Brownian motion. As part of this analysis, we introduce a method for accurately computing source-neutral Green's functions of the fractional Laplacian operator on the unit square with either periodic or homogeneous Neumann boundary conditions, the latter of which we formulate and interpret using a method of images-type argument. Our approach involves analytically constructing the singular behavior of the Green's function in a neighborhood around the location of the singularity, and then formulating a “smooth” problem for the remainder term. This smooth problem can be solved for numerically using a basic finite difference scheme and leads directly to accurate extraction of the regular part of the Green's function (and its gradient, if so desired). Incorporating this new method for computing Green's functions into a matched asymptotic analysis framework enables us to provide new insights into the 2-D Lévy flight narrow capture problem beyond those of leading order theory. All asymptotic predictions are confirmed by full numerical solutions.

Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time hypothesis, its computational complexity was proven to be no less than $2^{N^{2/3}}$, where $N$ is the total number of spins. Here, we report results of extensive experimentation with D-Wave 3D annealer with $N\le 5627$. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, which scales as $2^{N/\beta }$ with $\beta \approx {10}^3$. Based on statistical analysis of low-energy states, we argue that with an improvement of annealing protocols and device noise reduction, $\beta$ can be increased even further. This suggests that, for $N<{\beta }^3$, annealing devices provide most efficient way to find an exact ground state.

We propose a resource-efficient shadow-tomography scheme using equatorial-stabilizer measurements generated from subsets of Clifford unitaries. For $n$-qubit systems, equatorial-stabilizer-based shadow-tomography schemes can estimate $M$ observables (up to an additive error $\varepsilon$) using $\mathcal{O}(log\left(M\right),\mathrm{poly}\left(n\right),1/{\varepsilon }^2)$ sampling copies for a large class of observables, including those with traceless parts possessing polynomially bounded Frobenius norms. For arbitrary quantum-state observables with a constant Frobenius norm, sampling complexity becomes $n$ independent. Our scheme only requires an $n$-depth controlled-$Z$ (CZ) circuit [$\mathcal{O}\left(n^2\right)$ CZ gates] and Pauli measurements per sampling copy. Alternatively, our scheme is realizable with $2n$-depth circuits comprising $n^2$ nearest-neighboring cnot gates, exhibiting a smaller maximal gate count relative to previously known randomized-Clifford-based proposals. We numerically confirm our theoretically derived shadow-tomographic sampling complexities with random pure states and multiqubit graph states. Finally, we demonstrate that equatorial-stabilizer-based shadow tomography is more noise tolerant than randomized-Clifford-based schemes in terms of fidelity estimation for the Greenberger–Horne–Zeilinger state and W state.

Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the energy-time degree of freedom, this challenge is exacerbated because realistic high-resolution frequency measurements are obtained as a function of light passing through arbitrary filters positioned at uneven intervals. In this work, we show how the data gathered from these kinds of measurements can be used to fully certify the degree of energy and timing correlations needed to certify energy-time entanglement without having to make special assumptions about the state or the measurement device. We accomplish this by showing how to construct a continuous-variable probability density from the data that can closely estimate, but never overestimate the correlations (and entanglement) actually present in the system, and note that these methods are applicable to all continuous-variable degrees of freedom (e.g., spatial, field quadratures, etc.). We illustrate the feasibility of these methods using frequency and timing correlations obtainable from photon pairs in spontaneous parametric down-conversion.

Drops on a vibrating substrate can experience a variety of motion regimes, including directional motion and climbing. The key ingredient to elicit these regimes is simultaneously activating the in-plane and out-of-plane degrees of freedom of the substrate with the proper phase difference. This is typically achieved by imposing a prescribed rigid-body motion of the entire substrate. However, this framework is unable to establish different motion conditions in different regions of the substrate, thus lacking the precious spatial selectivity necessary to elicit complex drop control patterns. Challenging this paradigm, we leverage the inherent elasticity of the substrate to provide the required in-plane and out-of-plane modal characteristics and spatial diversity. To this end, we design architected substrates exhibiting a rich landscape of deformation modes, and we exploit their multimodal response to switch between drop motion regimes and select desired spatial patterns, using the excitation frequency as our tuning parameter.

We show that the formalism of Wertheim's first-order thermodynamic perturbation theory can be generalized for the fluid of rotating sticky particles with anisotropic hard core confined to a quasi-one-dimensional channel. Using the transfer-matrix method, we prove that the theory is exact if the hard-body interaction is additive, only the first neighbors interact, and the particles can stick together only along the channel. We show that the most convenient treatment of association in narrow channels is to work in the NPT ensemble, where all structural and thermodynamic quantities can be expressed as a function of pressure and fraction of sites unbonded.

The moiré structure of AB-stacked ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$ represents a natural platform to realize Kondo lattice models due to the discrepancy of the bandwidth between the individual layers. Here, we study this system at the commensurate filling of ${\nu }_{\mathrm{tot}}=2$. Our focus is on the $1+1$ filling setting of ${\nu }_{\mathrm{Mo}}={\nu }_{\mathrm{W}}=1$, which enables a Kondo lattice description. We find a Kondo semimetal due to the sizable intraorbital hopping among the electrons in the ${\mathrm{MoTe}}_2$ layer. The Kondo-driven (emergent) flat band is naturally pinned to the Fermi energy. When combined with the inherent topology of the electronic structure, a topological Kondo semimetal phase ensues. We calculate the valley Hall response, and due to the breaking of inversion symmetry we also identify a spontaneous Hall effect. There is a Berry curvature dodecapole that leads to a fourth-order spontaneous Hall effect in the perturbative regime of the electric field that is further amplified in the nonperturbative regime. As such, the system provides a tunable setting to simulate topological Kondo semimetals. Finally, we discuss the pathways that connect the physics realized here to the Weyl-Kondo semimetals and their proximate phases,which have been advanced in recent years in topological Kondo lattice models and materials.

Inductively shunted superconducting qubits, such as the unimon qubit, combine high anharmonicity with protection from low-frequency charge noise, positioning them as promising candidates for the implementation of fault-tolerant superconducting quantum computers. In this work, we develop accurate closed-form approximations for the frequency and anharmonicity of the unimon qubit that are also applicable to any single-mode superconducting qubits with a single-well potential profile, such as the quarton qubit or the kinemon qubit. We use these results to theoretically explore the single-qubit gate fidelity and coherence times across the parameter space of qubits with a single-well potential. We find that the gate fidelity can be optimized by tuning the Hamiltonian to (1) a high qubit mode impedance of $1–2\mathrm{k}\mathrm{\Omega }$, (2) a low qubit frequency of 1 GHz, (3) and a perfect cancellation of the linear inductance and the Josephson inductance attained at a flux bias of half flux quantum. According to our theoretical analysis, the proposed qubit parameters have the potential to enhance the single-qubit gate fidelity of the unimon beyond 99.99%, even without significant improvements to the dielectric quality factor or the flux noise density measured for the first unimon qubits. Furthermore, we compare unimon, transmon, and fluxonium qubits in terms of their energy spectra and qubit coherence subject to dielectric loss and $1/f$ flux noise in order to highlight the advantages and limitations of each qubit type.

A quantitative first-principles description of complex substitutional materials such as alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum mechanical problem. Therefore, materials properties must be modeled. The cluster expansion (CE) method is widely used for this purpose, but it struggles with properties that exhibit nonlinear dependencies on composition, often failing even in a qualitative description. By looking at CE through the lens of machine learning, we resolve this severe problem and introduce a nonlinear CE approach, yielding extremely accurate and computationally efficient results as demonstrated by distinct examples.

This study explores the feasibility of utilizing quantum error correction to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two lattice surgery-based protocols (local and nonlocal) are introduced to establish logical Bell states between distant nodes using an intermediary node. We simulate the protocols using realistic experimental parameters, including ion trap memories, noisy optical channels, frequency conversion, and nondestructive detection of photonic qubits. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances ($d=3,5$) under depolarizing and physical noise models. Pseudothresholds are identified, with physical error rates above $p_{\mathrm{err}}\sim {10}^{-3}$ offering no advantage over unencoded Bell states under depolarizing noise. Pseudo-thresholds are also reevaluated in terms of gate error rates $p_{{\mathrm{err}}_H}$, $p_{{\mathrm{err}}_{CX}}$, and $p_{{\mathrm{err}}_M}$. For a distance of 1 km between the end node and the intermediary, an advantage over unencoded Bell-state heralded protocols requires reducing gate error rates by an order of magnitude ($0.1p_{{\mathrm{err}}_H}$, $0.1p_{{\mathrm{err}}_{CX}}$, and $0.1p_{{\mathrm{err}}_M}$). These results highlight the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Additionally, the nonlocal protocol rate was analyzed achieving rates up to $(32.53\pm 1.53)\mathrm{Hz}$ over distances of 1 to $80\mathrm{km}$ between the end node and the intermediary node.