Hybrid optomechanical systems are emerging as a fruitful architecture for quantum technologies. Hence determining the relevant atom-light and light-mechanics couplings is an essential task in such systems. The fingerprint of these couplings is left in the global state of the system during nonequilibrium dynamics. However, in practice, performing measurements on the entire system is not feasible, and thus one has to rely on partial access to one of the subsystems, namely, the atom, the light, or the mechanics. Here we perform a comprehensive analysis to determine the optimal subsystem for probing the couplings. We find that if the light-mechanics coupling is known or irrelevant, depending on the range of the qubit-light coupling, then the optimal subsystem can be either the light or the qubit. In other scenarios, e.g., simultaneous estimation of the couplings, the light is usually the optimal subsystem. This can be explained as light is the mediator between the other two subsystems. Finally, we show that the widely used homodyne detection can extract a fair fraction of the information about the couplings from the light degrees of freedom.

We show that geometric frustration in a broad class of deformable and naturally curved, shell-like colloidal particles gives rise to self-limiting assembly of finite-sized stacks that far exceed particle dimensions. When interparticle adhesions favor conformal stacking, particle shape requires curvature focusing in the stack, leading to a superextensive accumulation of bending costs that ultimately limit the ground-state stack size to a finite value. Using a combination of continuum theory and particle-based simulation, we demonstrate that the self-limiting size is controlled by the ratio of the intraparticle stiffness to interparticle adhesion, ultimately achieving assembly sizes that are tuned from a few, up to several tens of, particles. The range of self-limiting assembly is delimited by the two structural modes of “frustration escape” which evade the thermodynamic costs of curvature focusing. Crucially, each of these modes can be suppressed through suitable choice of adhesive range and patchiness of adhesion, providing feasible strategies to program finite assembly size via the interplay between shape frustration, binding, and deformability of colloidal building blocks.

Amplitude estimation (AE) is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. Recent works have succeeded in somewhat reducing the necessary resources for AE by trading off some of the speedup for lower depth circuits, but high quality qubits are still needed for demonstrating such algorithms. Here, we report the results of an experimental demonstration of AE on a state-of-the-art trapped ion quantum computer. AE was used to estimate the inner product of randomly chosen four-dimensional unit vectors, and the low-depth AE algorithms were based on the maximum likelihood estimation (MLE) and the Chinese remainder theorem (CRT) techniques. Significant improvements in accuracy were observed for the MLE based approach when deeper quantum circuits were taken into account, including circuits with more than 90 two-qubit gates and depth 60, achieving a mean additive estimation error on the order of ${10}^{-2}$. The CRT based approach was found to provided accurate estimates for many of the data points but was less robust against noise on average. Last, we analyze two more AE algorithms that take into account the specifics of the hardware noise to further improve the results.

In this paper, we study the modification of coherent scattering processes in dense ensembles. Using absorption imaging, we experimentally demonstrate that the absorption cross section in dense ${}^{87}\mathrm{Rb}$ cold atom ensembles is reduced, with respect to the single-particle response. This reduction is linearly dependent on the optical density and well reproduced by a one-dimensional model of coherent field propagation in an ensemble of quantum two-level systems that self-consistently incorporates multiple scattering contribution. Our model shines light upon the key role of incoherent scattering on the modification of the optical response of dense ensembles and leads to a generalization of the Beer-Lambert law. Our result applies to any effective two-level system ensemble and allows for quantitative and absolute in situ absorption imaging.

Dynamical quantum phase transitions are at the forefront of current efforts to understand quantum matter out of equilibrium. Except for a few exactly solvable models, predictions of these critical phenomena typically rely on advanced numerical methods. However, those approaches are mostly restricted to one dimension, making investigations of two-dimensional systems highly challenging. Here, we present evidence of dynamical quantum phase transitions in strongly correlated spin lattices in two dimensions. To this end, we apply our recently developed cumulant method [Phys. Rev. X 11, 041018 (2021)] to determine the zeros of the Loschmidt amplitude in the complex plane of time, and we predict the crossing points of the thermodynamic lines of zeros with the real-time axis, where dynamical quantum phase transitions occur. We find the critical times of a two-dimensional quantum Ising lattice and the XYZ model with ferromagnetic or antiferromagnetic couplings. We also show how dynamical quantum phase transitions can be predicted by measuring the initial energy fluctuations, for example in quantum simulators or other engineered quantum systems.

In the past, the ionization of atoms and molecules by strong, mid-infrared (IR) laser fields has attracted recurrent interest. Measurements with different IR pulses have demonstrated the crucial role of the magnetic field on the electron dynamics, classically known as the Lorentz force ${\mathbf{F}}_L=q(\mathcal{E}+\mathbf{v}\times \mathcal{B})$, that acts upon all particles with charge $q$ in motion. These measurements also require the advancement of theory beyond the presently applied methods. In particular, the strong-field approximation (SFA) is typically based on the dipole approximation alone and neglects both the magnetic field and the spatial dependence of the driving electric field. Here we show and discuss that several, if not most, observations from strong-field ionization experiments with mid-IR fields can be quantitatively explained within the framework of SFA, if the Lorentz force is taken into account by nondipole Volkov states in the formalism. The details of such a treatment are analyzed for the (peak) shifts of the polar-angle distribution of above-threshold ionization photoelectrons along the laser propagation, the steering of electron momenta by two not quite collinear laser beams, or the enhanced momentum transfer to photoelectrons in standing-light fields. Moreover, the same formalism promises to explain the generation of high harmonics and other strong-field rescattering phenomena when driven by mid-IR laser fields. All these results show how strong-field processes can be understood on equal footings within the SFA, if one goes beyond the commonly applied dipole approximation.

In this Reply, we set out a discussion on the strength as well as the plausible shortcomings of generalized Lorenz-Mie theory in estimating the trapping force on a particle with an emphasis on the implications of ultrashort pulsed excitation.

In a comprehensive, important, and innovative paper devoted to the evaluation of nonlinear optical force exerted on particles trapped in optical tweezers, imprecise statements have, however, been made which may be misleading to newcomers. The present Comment aims to correct these statements in order to avoid the propagation of incorrect beliefs.

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA Ansatz is not optimal, there is no systematic approach for finding better Ansätze. We address this problem by developing an iterative version of QAOA that is problem tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity.

The SWAP network is a qubit routing sequence that can be used to efficiently execute the Quantum Approximate Optimization Algorithm (QAOA). Even with a minimally connected topology on an $n$-qubit processor, this routing sequence enables $\mathcal{O}\left(n^2\right)$ operations to execute in $\mathcal{O}\left(n\right)$ steps. In this work, we optimize the execution of SWAP networks for QAOA through two techniques. First, we take advantage of an overcomplete set of native hardware operations [including 150-ns controlled-$\frac{\pi }{2}$ phase gates with up to 99.67(1)% fidelity] to decompose the relevant quantum gates and SWAP networks in a manner which minimizes circuit depth and maximizes gate cancellation. Second, we introduce equivalent circuit averaging, which randomizes over degrees of freedom in the quantum circuit compilation to reduce the impact of systematic coherent errors. Our techniques are experimentally validated at the Advanced Quantum Testbed through the execution of QAOA circuits for finding the ground state of two- and four-node Sherrington-Kirkpatrick spin-glass models with various randomly sampled parameters. We observe a $\sim 60\%$ average reduction in error (total variation distance) for QAOA of depth $p=1$ on four transmon qubits on a superconducting quantum processor.

Informationally complete (IC) positive operator-valued measures (POVMs) are generalized quantum measurements that offer advantages over the standard computational basis readout of qubits. For instance, IC-POVMs enable efficient extraction of operator expectation values, a crucial step in many quantum algorithms. POVM measurements are typically implemented by coupling one additional ancilla qubit to each logical qubit, thus imposing high demands on the device size and connectivity. Here, we show how to implement a general class of IC-POVMs without ancilla qubits. We exploit the higher-dimensional Hilbert space of a qudit in which qubits are often encoded. POVMs can then be realized by coupling each qubit to two of the available qudit states, followed by a projective measurement. We develop the required control pulse sequences and numerically establish their feasibility for superconducting transmon qubits through pulse-level simulations. Finally, we present an experimental demonstration of a qudit-space POVM measurement on IBM Quantum hardware. This paves the way to making POVM measurements broadly available to quantum computing applications.

The study of high-harmonic generation in confined quantum systems is vital to establishing a complete physical picture of harmonic generation from atoms and molecules to bulk solids. Based on a multilevel approach, we demonstrate how intraband resonances significantly influence the harmonic spectra via charge pumping to the higher subbands and thus redefine the cutoff laws. As a proof of principle, we consider the interaction of graphene nanoribbons, with zigzag as well as armchair terminations, and resonant fields polarized along the cross-ribbon direction. Here, this effect is particularly prominent due to many nearly equiseparated energy levels. In such a scenario, a cascade resonance effect can take place in high-harmonic generation when the field strength is above a critical threshold, which is completely different from the harmonic generation mechanism of atoms, molecules, and bulk solids. We further discuss the implications not only for other systems in a nanoribbon geometry, but also systems where only a few subbands (energy levels) meet this frequency-matching condition by considering a generalized multilevel Hamiltonian. Our study highlights that cascade resonance has a fundamentally distinct influence on the laws of harmonic generation, specifically the cutoff laws based on laser duration, field strength, and wavelength, thus unraveling additional insights in solid-state high-harmonic generation.

The recently synthesized ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ has been proposed as a Kitaev magnet in proximity to the quantum spin liquid phase. We explore its microscopic Hamiltonian and magnetic ground state using many-body quantum chemistry methods and exact diagonalization techniques. Our calculations establish a dominant bond dependent ferromagnetic Kitaev exchange between Ir sites and find that the inclusion of Ag $4d$ orbitals in the configuration interaction calculations strikingly enhances the Kitaev exchange. Furthermore, using exact diagonalization of the nearest-neighbor fully anisotropic $J\text{−}K\text{−}\mathrm{\Gamma }$ Hamiltonian, we obtain the magnetic phase diagram as a function of further neighbor couplings. We find that the antiferromagnetic off-diagonal coupling stabilizes long range order, but the structure factor calculations suggest that the material is very close to the quantum spin liquid phase and the ordered state can easily collapse into a liquid by small perturbations such as structural distortion or bond disorder.

We investigate the dynamics of an atomtronic superconducting quantum interference device (SQUID) created by two mobile barriers, moving at two different, constant velocities in a quasi-one-dimensional toroidal condensate. We implement a multiband truncated Wigner approximation numerically to demonstrate the functionality of a SQUID reflected in the oscillatory voltage-flux dependence. The relative velocity of the two barriers results in a chemical potential imbalance analogous to a voltage in an electronic system. The average velocity of the two barriers corresponds to a rotation of the condensate, analogous to a magnetic flux. We demonstrate that the voltage equivalent shows characteristic flux-dependent oscillations. We point out the parameter regime of barrier heights and relaxation times for the phase slip dynamics, resulting in a realistic protocol for atomtronic SQUID operation.

We show that pairing in an ultracold Fermi gas under spin-orbital-angular-momentum coupling (SOAMC) can acquire topological characters encoded in the quantized angular degrees of freedom. The resulting topological superfluid is the angular analog of its counterpart in a one-dimensional Fermi gas with spin-orbit coupling, but characterized by a Zak phase defined in the angular-momentum space. Upon tuning the SOAMC parameters, a topological phase transition occurs, which is accompanied by the closing of the quasiparticle excitation gap. Remarkably, a topological vortex state can also be stabilized by deforming the Fermi surface, which is topologically nontrivial in both the coordinate and angular-momentum space, offering interesting potentials for applications in quantum information and quantum control. We discuss how the topological phase transition and the exotic vortex state can be detected experimentally.

In the past years, many efforts have been made to study various noteworthy phenomena in both parity-time $\left(\mathcal{PT}\right)$ and anti-parity-time $\left(\mathcal{APT}\right)$ symmetric systems. However, entanglement dynamics in $\mathcal{APT}$-symmetric systems has not previously been investigated in both theory and experiments. Here, we investigate the entanglement evolution of two qubits in an $\mathcal{APT}$-symmetric system. In the $\mathcal{APT}$-symmetric unbroken regime, our theoretical simulations demonstrate the periodic oscillations of entanglement when each qubit evolves identically, while the nonperiodic oscillations of entanglement when each qubit evolves differently. In particular, when each qubit evolves near the exceptional point in the $\mathcal{APT}$-symmetric unbroken regime, there exist entanglement sudden vanishing and revival. Moreover, our simulations demonstrate rapid decay and delayed death of entanglement provided one qubit evolves in the $\mathcal{APT}$-symmetric broken regime. In this work, we also perform an experiment with a linear optical setup. The experimental results agree well with our theoretical simulation results. Our findings reveal novel phenomena of entanglement evolution in the $\mathcal{APT}$-symmetric system and opens a new direction for future studies on the dynamics of quantum entanglement in multiqubit $\mathcal{APT}$-symmetric systems or other non-Hermitian quantum systems.

We present an inexpensive first-principles approach for describing quantum paraelectricity that combines density functional theory (DFT) treatment of the electronic subsystem with quantum mechanical treatment of the ions through solution of the single-particle Schrödinger equation with the DFT-calculated potential. Using ${\mathrm{BaTiO}}_3$, ${\mathrm{SrTiO}}_3$, and ${\mathrm{KTaO}}_3$ as model systems, we show that the approach can straightforwardly distinguish between ferroelectric, paraelectric, and quantum paraelectric materials, based on simple quantities extracted from standard density functional and density functional perturbation theories. We calculate the influence of isotope substitution and strain on quantum paraelectric behavior and find that, while complete replacement of oxygen-16 by oxygen-18 has a surprisingly small effect, experimentally accessible strains can induce large changes. Finally, we collect the various choices for the phonon mass that have been introduced in the literature. We identify those that are most physically meaningful by comparing them with our results that avoid such a choice through the use of mass-weighted coordinates.

We study the implementation of a high fidelity controlled-phase gate in a Rydberg quantum computer. The protocol is based on a symmetric gate with respect to the two qubits as experimentally realized by Levine et al. [Phys. Rev. Lett. 123, 170503 (2019)], but allows for arbitrary pulse shapes with time-dependent detuning. Optimizing the pulse shapes, we introduce laser pulses which shorten the time spent in the Rydberg state by 10% and reduce the leading contribution to the gate infidelity, i.e., the decay from the Rydberg state. Remarkably, this reduction can be achieved for smooth pulses in detuning and smooth turning on of the Rabi frequency as required in any experimental realization. We carefully analyze the influence of fundamental error sources such as the photon recoil and the microscopic interaction potential, as well as the harmonic trapping of the atoms for an experimentally realistic setup based on strontium-88 atoms. We find that an average gate fidelity above 99.9% is possible for a very conservative estimation of experimental parameters.