We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in $1+1$ dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive $E_8$ theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the $E_8$ point in detail. Close to both the free fermion and $E_8$ theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in $1+1$ dimensions.

Materials with a kagome lattice naturally host topological electronic structures, giving rise to many intriguing quantum states within this family. In this study, we performed calculations of the electronic structure and Fermi surface, and measured the longitudinal resistivity ${\rho }_{xx}(\mathit{T},\mathit{B})$, Hall resistivity ${\rho }_{yx}(\mathit{T},\mathit{B})$, and quantum oscillations of the magnetization as a function of temperature and magnetic field for ${\mathrm{Pd}}_3{\mathrm{Tl}}_2{\mathrm{S}}_2$, a kagome-lattice material. We observed an unsaturated extremely large magnetoresistance of 14 500% at 2 K and 9 T, the highest reported in kagome lattice materials, which was attributed to the carrier compensation supported by the Hall resistivity measurements. The band structure calculations, along with the observation of nontrivial Berry phases in the de Haas–van Alphen oscillations, demonstrate that ${\mathrm{Pd}}_3{\mathrm{Tl}}_2{\mathrm{S}}_2$ is a topological nodal-net (Hopf link) semimetal.

We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of a Hermitian matrix $H$, thus suggesting the use of quantum phase estimation. Our proposed quantum algorithm operates in the standard $s$-sparse, oracle-based query access model. For a network of $N$ oscillators with maximum norm ${\parallel H\parallel }_{\max }$, and when the eigenvalue tolerance $\varepsilon$ is much smaller than the minimum eigenvalue gap, we use ${\mathcal{O}(log(Ns\parallel H\parallel }_{\max }/\varepsilon )$ algorithmic qubits and obtain a rigorous worst-case query complexity upper bound $\mathcal{O}(s\parallel H{\parallel }_{\max }/\left({\delta }^2\varepsilon \right))$ up to logarithmic factors, where $\delta$ denotes the desired precision on the coefficients appearing in the response functions. Crucially, our proposal does not suffer from the infamous state preparation bottleneck and can as such potentially achieve large quantum speedups compared to relevant classical methods. As a proof-of-principle of exponential quantum speedup, we show that a simple adaptation of our algorithm solves the random glued-trees problem in polynomial time. We discuss practical limitations as well as potential improvements for quantifying finite-size, end-to-end complexities for application to relevant instances.

A body immersed in a nematic liquid crystal disturbs the fluid's preferred molecular configuration and increases its stored elastic energy. In an active nematic, the fluid components also generate a stress in the bulk fluid. By introducing either an immersed body or boundary, a large scale flow can be triggered due to anchoring boundary conditions alone—a global pressure built by active stresses at equilibrium is instantly released everywhere. The fluid then imposes viscous, elastic, and active stresses on such surfaces which, if compliant, may result in a surface deformation. We study the deformations and stresses of a linearly elastic body placed in an active nematic in two dimensions. Using complex variable techniques, exact expressions for the fluid flow, director field, surface tractions, and body deformation are derived. Qualitative differences between elastic and active stress-driven deformations are identified, depending on an active Ericksen number, anchoring conditions, and body material properties, thereby suggesting a new method for measuring mechanical stresses in active anisotropic environments. Flow profiles, external confinement, and anchoring-induced stirring are also addressed.

Many claims of computational advantages have been made for quantum computing over classical but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference to fluid equations. We build on an idea based on a linear combination of unitaries to simulate nonunitary, non-Hermitian quantum systems, and generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations. These algorithms are end-to-end, with relatively low-depth quantum circuits that demonstrate quantum advantage, with the best-case asymptotic complexities, which we show are near optimal. We demonstrate the performance of the algorithms by conducting: (a) fully gate level, state-vector simulations using an in-house, high-performance, quantum simulator called qflows; (b) experiments on a real quantum device; and (c) noisy simulations using qiskit aer. We also provide device specifications such as error rates (noise) and state sampling (measurement) to accurately perform convergent flow simulations on noisy devices. The results offer evidence that the proposed algorithm is amenable for use on near-term quantum devices.

As quantum computing advances, the complexity of quantum circuits is rapidly increasing, driving the need for robust methods to aid in their design. Equivalence checking plays a vital role in identifying errors that may arise during compilation and optimization of these circuits and is a critical step in quantum circuit verification. In this work, we introduce a method based on matrix product operators (MPOs) for determining the equivalence of quantum circuits. Our approach contracts tensorized quantum gates from two circuits into an intermediary MPO, exploiting their reversibility to determine their equivalence or nonequivalence. Our results show that this method offers significant scalability improvements over existing methods, with polynomial scaling in circuit width and depth for the practical use cases we explore. We expect that this work to set a standard for scalable equivalence checking of quantum circuits and will become a crucial tool for the validation of increasingly complex quantum systems.

For a fluid of convex hard particles, characterized by a length scale ${\sigma }_{\text{min}}$ and an anisotropy parameter $\epsilon$, we develop a formalism allowing one to relate thermodynamic quantities to the body's shape. In a first step, its thermodynamics is reduced to that of spherical particles. The latter have a hard core of diameter ${\sigma }_{\text{min}}$ and a soft shell with a thickness $\epsilon {\sigma }_{\text{min}}/2$. Besides their hard core repulsion at ${\sigma }_{\text{min}}$, they interact by effective entropic forces which will be calculated. Based on this mapping, a second step provides a perturbative method for the systematic calculation of thermodynamic quantities with the shape anisotropy $\epsilon$ as a smallness parameter. In leading order in $\epsilon$, the equation of state is derived as a functional of the particle's shape. To illustrate these findings, they are applied to a one- and two-dimensional fluid of ellipses and compared with results from different analytical approaches and our computer simulations. The mapping to spherical particles also implies that any phase transition of spherical particles, e.g., the liquid-hexatic transition, also exists for the nonspherical ones, and shifts linearly with $\epsilon$ for weak shape anisotropy. This is supported by our Monte Carlo simulation.

Ultracold quantum-gas mixtures of fermionic atoms with resonant control of interactions offer a unique test-bed to explore few- and many-body quantum states with unconventional properties. The emergence of such strongly correlated systems, for instance, symmetry-broken superfluids, is usually accompanied by hydrodynamic collective behavior. Thus experimental progress in this field naturally requires a deep understanding of hydrodynamic regimes. Here, we report on experiments employing a tunable Fermi-Fermi mixture of ${}^{161}\mathrm{Dy}$ and ${}^{40}\mathrm{K}$ near quantum degeneracy. We investigate the full spectrum of dipole modes across a Feshbach resonance and characterize the crossover from collisionless to deep hydrodynamic behavior in measurements of frequencies and damping rates. We compare our results with a theoretical model that considers the motion of the mass centers of the two species, and we identify the contributions of friction and mean-field interaction. We show that one oscillating mode exists over the whole range of interactions, exhibiting striking changes of frequency and damping in the deep hydrodynamic regime. We observe the second oscillating mode to split into two purely exponential damping modes. One of these exponential modes shows very fast damping, faster than any other relevant timescale, and is largely insensitive to experimental imperfections. It provides an accurate measure for the interspecies drag effect, which generalizes the concept of spin drag explored in other experiments. We finally characterize the interspecies drag in terms of a microscopic friction coefficient, and we discuss its unitarity-limited universal behavior on top of the resonance.

Chemical shifts and J-couplings are fundamental parameters in NMR spectroscopy, they provide structural information about molecules. Extracting these quantities from isotopes such as carbon or nitrogen results in reduced sensitivity due to their low gyromagnetic ratios. In this paper, we present a method for detecting chemical shifts and J-couplings at the microscale in low-gyromagnetic-ratio nuclei using NV centers. By leveraging hydrogen nuclei, we achieve strong coupling with NVs and fast signal emission that aligns with NV coherence times. In addition, the technique is well suited for implementations under high magnetic fields. We demonstrate that our protocol achieves a sensitivity enhancement of more than one order of magnitude for scenarios involving ${}^{13}\mathrm{C}$, with even greater improvements for nuclei with lower gyromagnetic ratios.

In polarization experiments at storage rings, one of the challenges is to maintain the spin-resonance condition of a radio-frequency spin rotator with the spin precessions of the orbiting particles. Time-dependent variations of the magnetic fields of ring elements lead to unwanted variations of the spin-precession frequency. We report here on a solution to this problem by shielding (or masking) one of the bunches stored in the ring from the high-frequency fields of the spin rotator, so that the masked pilot bunch acts as a comagnetometer for the other signal bunch, tracking fluctuations in the ring on a time scale of about one second. While the new method was developed primarily for searches of electric dipole moments of charged particles, it may have far-reaching implications for future spin physics facilities, such as the EIC and NICA.

As quantum devices scale to larger numbers of qubits, entangling gates between distant stationary qubits will help provide flexible, long-range connectivity in modular architectures. In this work, we present protocols for implementing long-range two-qubit gates mediated by either Fock-state or time-bin qubits—photonic encodings that are both compatible with the coplanar waveguide resonators commonly used in circuit quantum electrodynamics (QED). These protocols become deterministic in the limit of vanishing photon loss. Additionally, photon loss can be heralded, signaling a failed two-qubit gate attempt. We model the loss of a time-bin qubit to a dielectric environment consisting of an ensemble of two-level systems, which are believed to be the dominant mechanism for dielectric loss in circuit QED architectures. The backaction (on the stationary qubits) associated with the loss of the time-bin qubit is strongly suppressed in a non-Markovian regime where the temporal separation of the time bins is short compared to the dielectric environment's correlation time. This result suggests strategies based on a combination of materials-fabrication and time-bin-qubit optimization for ensuring that the loss of a time-bin qubit is not only heralded but also approximately backaction-free.

Computational fluid dynamics (CFD) is a specialized branch of fluid mechanics that utilizes numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing, which has the potential to resolve nonlinear differential equations more efficiently than classical computers. Here, we try to answer the question of which regimes of nonlinear partial differential equations for fluid dynamics can have an efficient quantum algorithm. We propose a connection between the numerical parameter $R$, which guarantees efficiency in the truncation of the Carleman linearization, and the physical parameters that describe the fluid flow. This link can be made thanks to the Kolmogorov scale, which determines the minimum size of the grid needed to properly resolve the energy cascade induced by the nonlinear term. Additionally, we introduce the formalism for vector field simulation in different spatial dimensions, providing the discretization of the operators and the boundary conditions.

We present a protocol to create entangled coherent states by engineering cross-Kerr interactions between bosonic systems endowed with (externally driven) internal spin-like degrees of freedom. With slight modifications, the protocol is also able to produce N00N states through nonlinear beam-splitter interactions. Each bosonic system interacts locally with its spin and by suitably tuning the model parameters, various classes of effective bosonic interaction Hamiltonians, mediated by the coupled spins, can be engineered. Our approach is benchmarked by numerical simulations aimed at studying the entanglement within a bosonic register and comparing it with the expected one resulting from the target Hamiltonians.

Efficient generation of arbitrary superposed quantum states in high-dimensional systems is crucial for various quantum technologies but remains fundamentally challenging because of the intricate and extensive parameter control. In this work, we propose a generalized discrete one-dimensional quantum walk model with time- and position-dependent coin operations, and varied shift lengths. This approach enables deterministic and direct preparation of any qudit state $|\varphi \rangle ={\sum }_{k=0}^{d-1}{a}_k|k\rangle$ using binary or ternary tree structures, without solving quadratic equations. Our method requires only $O(logd)$ steps and $O\left(d\right)$ coin operations, significantly reducing the resource requirements compared to the previous approach of $O\left(d\right)$ steps and $O\left(d^2\right)$ coin operations. Additionally, we propose an experimental scheme based on successive interferometers, demonstrating that our method is compatible with current state-of-the-art experimental technologies. This efficient method for preparing quantum superposition states lays a foundation for advancing quantum technologies, with broad applications in quantum information processing.

Quantum algorithms for scientific computing and their applications have been actively studied. In this paper, we propose a quantum algorithm for estimating the first eigenvalue of a differential operator $\mathcal{L}$ on ${\mathbb{R}}^d$ and its application to cosmic inflation theory. A common approach for this eigenvalue problem involves applying the finite-difference discretization to $\mathcal{L}$ and computing the eigenvalues of the resulting matrix, but this method suffers from the curse of dimensionality, namely, the exponential complexity with respect to $d$. Our first contribution is the development of a quantum algorithm for this task, leveraging recent quantum singular value transformation-based methods. Given a trial function that overlaps well with the eigenfunction, our method runs with query complexity scaling as $\tilde{O}(d^3/{\epsilon }^2)$ with $d$ and estimation accuracy $\epsilon$, which is polynomial in $d$ and shows improvement over existing quantum algorithms. Then, we consider the application of our method to a problem in a theoretical framework for cosmic inflation known as stochastic inflation, specifically calculating the eigenvalue of the adjoint Fokker–Planck operator, which is related to the decay rate of the tail of the probability distribution for the primordial density perturbation. We numerically see that, in some cases, simple trial functions overlap well with the first eigenfunction, indicating our method is promising for this problem.