The precision of quantum sensing could be improved by exploiting quantum phase transitions, where the physical quantity tends to diverge when the system approaches the quantum critical point. This critical enhancement phenomenon has been applied to the quantum Rabi model, showing a promising sensing enhancement without the need for complex initial state preparation. In this work, we present a quantum phase transition in the coupling cavity-mechanical oscillator system when the coupling strength crosses a critical point, determined by the effective detuning of the cavity and frequency of the mechanical mode. By utilizing this critical phenomenon, we obtain a prominent enhancement of quantum sensing, such as the position and momentum of the mechanical oscillator. This result provides an alternative method to enhance the quantum sensing of some physical quantities, such as mass, charge, and weak force, in a large mass system.

We investigate the electromagnetic fields produced by the oscillating point electric or magnetic dipole placed in a spherical volume with a nonzero time-independent effective axion field. Our analytical solution shows that the fields outside the volume are a superposition of electric and magnetic dipole fields. Such multipole time-dependent generalization of the Witten effect can be realized in magnetoelectrics, topological insulators, or metamaterials providing a flexible probe of $\mathcal{P}$- and $\mathcal{T}$-symmetry-breaking phenomena in different electromagnetic structures.

We investigate the two-photon scattering processes in a one-dimensional waveguide coupled to either a two-level or three-level giant atom. By manipulating the accumulated phase shift between the two coupling points, we are able to effectively modify the characteristics of these scattering processes. Utilizing the Lippmann-Schwinger formalism, we obtain the exact two-photon interacting scattering wave functions of these two systems. Additionally, analytical expressions for the incoherent power spectra and second-order correlations are derived. The incoherent spectrum, which is defined by the correlation of the bound state, provides valuable insights into photon-photon correlations. It serves as a useful indicator of the degree of photon-photon correlation between scattered photons. Furthermore, the second-order correlation function gives a direct measure of the photon-photon correlation. For photons scattered by the two-level giant atom, manipulating the accumulated phase shift allows for improvement of the photon-photon correlation and adjustment of the evolution of the second-order correlation. In the case of the three-level giant atom, the photon-photon correlation can be substantially increased. The photon-photon interaction and correlation distance of the scattered photons can be further enhanced by tuning the accumulated phase shift. Moreover, the statistical properties can be adjusted by the control field.

Existing lower bounds on redundancy in fault-tolerant quantum circuits are applicable when both the input and the intended output are quantum states. These bounds may not necessarily hold, however, when the intended outputs are classical bits, as in Shor's or Grover's algorithms. Here we show that, indeed, noise thresholds obtained from existing bounds do not apply to a simple fault-tolerant implementation of the quantum phase estimation algorithm where the output quantum state suffers from noise before the measurement. Then we obtain a nonasymptotic lower bound on the minimum required redundancy for fault-tolerant quantum circuits with classical inputs and outputs. Further, recent results show that, due to physical resource constraints in quantum circuits, increasing redundancy can increase noise, which in turn may render many fault-tolerance schemes useless. So it is of both practical and theoretical interest to characterize the effect of resource constraints on the fundamental limits of fault-tolerant quantum circuits. As an application of our lower bound, we characterize the fundamental limit of fault-tolerant quantum circuits with classical inputs and outputs under resource-constraint-induced noise models.

We present an interferometric method for studying the Rabi dynamics in atoms by employing an $\omega \text{−}2\omega$ extreme ultraviolet pulse pair generated from the seeded free-electron laser. By solving the time-dependent Schrödinger equation (TDSE) for hydrogen atoms, we study the photoelectron spectrum that emerges when the $\omega$ pulse triggers Rabi oscillations between the ground state and the first excited state. The interference between the one-photon and two-photon ionization pathways in the photoelectron signal gives access to the phase difference between the one- and two-photon transition amplitudes. Compared to the cases without Rabi oscillations, an additional $\pi$ phase jump is observed in the energy domain. Based on perturbation theory, we demonstrate that this phase jump directly reflects the ultrafast buildup of Rabi oscillations in the time domain. The present $\omega \text{−}2\omega$ scheme can be generalized and applied to other more complex atoms or molecules provided that the populations of bound states can be efficiently and coherently modulated using the free-electron laser.

Quantum chemistry has been identified as one of the most promising areas where quantum computing can have a tremendous impact. For current noisy intermediate-scale quantum (NISQ) devices, one of the best available methods to prepare approximate wave functions on quantum computers is the adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver (ADAPT-VQE). However, ADAPT-VQE suffers from a significant measurement overhead when estimating the importance of operators in the wave function. In this work, we propose fermionic adaptive sampling theory VQE (FAST-VQE), a method for selecting operators based on importance metrics solely derived from the populations of Slater determinants in the wave function. Thus, our method mitigates measurement overheads for ADAPT-VQE as it is only dependent on the populations of Slater determinants which can simply be determined by measurements in the computational basis. We introduce two heuristic importance metrics, one based on selected configuration interaction with perturbation theory and one based on approximate gradients. In state vector and finite shot simulations, FAST-VQE using the heuristic metric based on approximate gradients converges at the same rate or faster than ADAPT-VQE and requires dramatically fewer shots.

In the past years, many quantum algorithms have been proposed to tackle hard combinatorial problems. In particular, the maximum independent set (MIS) is a known NP-hard problem that can be naturally encoded in Rydberg atom arrays. By representing a graph with an ensemble of neutral atoms one can leverage Rydberg dynamics to naturally encode the constraints and the solution to MIS. However, the classes of graphs that can be directly mapped “vertex-to-atom” on standard devices with two-dimensional capabilities are currently limited to Unit-Disk graphs. In this setting, the inherent spatial locality of the graphs can be leveraged by classical polynomial-time approximation schemes (PTAS) that guarantee an $\epsilon$-approximate solution. In this work, we build upon recent progress made for using three-dimensioanl arrangements of atoms to embed more complex classes of graphs. We report experimental and theoretical results which represent important steps towards tackling combinatorial tasks on quantum computers for which no classical efficient $\varepsilon$-approximation scheme exists.

In recent years, supervised and semisupervised machine learning methods such as neural networks, support vector machines (SVMs), and semisupervised support vector machines (S4VMs) have been widely used in quantum entanglement and quantum steering verification problems. However, few studies have focused on detecting genuine multipartite entanglement based on machine learning. Here, we investigate supervised and semisupervised machine learning for detecting genuine multipartite entanglement of three-qubit states. We randomly generate three-qubit density matrices and train an SVM for the detection of genuine multipartite entangled states. Moreover, we improve the S4VM training method, which optimizes the grouping of prediction samples and then performs iterative predictions. Through numerical simulation, it is confirmed that this method can significantly improve the prediction accuracy.

We calculate accurate potential-energy curves for a ground-state ${\mathrm{He}}^{+}$ ion interacting with a He atom in the lowest-energy metastable ${}^{3}S$ electronic state. We employ the full configuration-interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the ${\mathrm{He}}_2^{+}$ molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the ${\mathrm{He}}_2^{+}$ molecular ion in the excited electronic state and collisional studies of ${\mathrm{He}}^{+}$ ions immersed in ultracold gases of metastable He atoms.

Although quantum simulation can give insight into elusive or intractable physical phenomena, many quantum simulators are unavoidably limited in the models they mimic. Such is also the case for atom arrays interacting via Rydberg states, a platform potentially capable of simulating any kind of spin exchange model, albeit with currently unattainable experimental capabilities. Here, we propose a route towards simulating generic spin-exchange Hamiltonians in atom arrays, using Floquet engineering with both global and local control. To demonstrate the versatility and applicability of our approach, we numerically investigate the generation of several spin-exchange models which have yet to be realized in atom arrays, using only previously demonstrated experimental capabilities. Our proposed scheme can be readily explored in many existing setups, providing a path to investigate a large class of exotic quantum spin models.

We focus on the generation and control of simultaneous squeezing for two mechanical oscillators in a cavity optomechanical system. The two mechanical oscillators couple to an optical cavity driven by two-tone lasers, and the phase-dependent phonon-hopping interaction between the two mechanical modes is introduced to create synthetic magnetism. We show that the presence of the synthetic magnetism between the two bare mechanical modes can break the Bogoliubov-dark-mode effect, and enable the strong squeezing (breaking the so-called 3-dB limit) of the two mechanical modes to be achieved simultaneously. Moreover, the asymmetrical squeezing for two mechanical oscillators can be realized by adjusting the phase of the phonon-hopping interaction. We find that the asymmetrical squeezing is caused by nonreciprocal population transfer between the two Bogoliubov modes. The presented scheme has significantly strong robustness against thermal noise, and can be extended to multiple mechanical modes to achieve strong squeezing and control the relative squeezing degree of multiple mechanical oscillators, which may be meaningful for the study of macroscopic quantum effects and quantum precision measurement.

We theoretically propose a magnon-based superconducting qubit hybrid system containing two ferromagnetic yttrium iron garnets (YIGs) and one superconducting qubit, demonstrating that this hybrid quantum system is feasible in achieving the unconventional two-mode magnon blockade and generating the quantum correlated magnon pairs. Through the virtual-photon excitation mediated by the same cavity mode, the effective couplings can be established not only between the Kittel modes and the qubit, but also between the two Kittel modes. We characterize the magnon blockade by utilizing the equal-time second-order correlation functions and impose a constraint on the correlations between the two Kittel modes by introducing the Cauchy-Schwarz inequality (CSI). In the weak qubit-magnon coupling regime, our results indicate the following: (i) Under the scenario of the resonance couplings, the ratio of driving strengths and the ratio of coupling strengths between the two Kittel modes and the cavity mode can be employed to control and regulate the magnon blockade and the violation of the CSI. Not only the two Kittel modes can achieve the unconventional magnon antibunching effects simultaneously, but also the correlations between them violate the classical CSI. It is important to note that when the degrees of both the antibunching effects for the two Kittel modes and the anticorrelation between them reach their highest levels simultaneously, the correlations happen not to violate the CSI. But our proposal offers a feasible route for preparing a high-quality single-magnon source. (ii) Under the scenario of the out-of-resonance couplings, by adjusting the frequency detunings between the first Kittel mode and the second Kittel mode as well as the qubit, the quantum correlated two-mode magnon pairs can be obtained. (iii) Finally, it is found that the magnon antibunching effect of the second Kittel mode is robust against the dissipation ratio between the two Kittel modes. These results illustrate how to optimally choose the parameters to realize nonclassical magnon pair generation and CSI violation. The hybrid YIG quantum system we propose here holds the potential in the development of efficient microwave single-magnon sources and quantum magnon-magnon pairs required in future quantum information processing tasks.

We investigate the two-channel nonreciprocal scattering of a coherent atomic ensemble under the linear spatial Kramers-Kronig modulation, which has potential applications in chiral phase modulation and broadband coherent perfect or asymmetric absorbers that yet are typically unavailable in conventional continuous atomic media. In the regime of electromagnetically induced transparency, we observe the direction-dependent (chiral) phase modulation, which may enrich the burgeoning chiral quantum optics and can be used for implementing photonic filters, unidirectional amplifiers, and coherent asymmetric absorbers. By simplifying the stringent generation condition of coherent perfect absorption (CPA), we demonstrate the possibility of realizing two-channel CPA with broadband and sharp edges. Our proposal may be used to design and integrate some all-optical functional devices at extremely low power levels for quantum information processing and optical communication networks.

We explore special features of quantum light-matter interactions inside structured waveguides due to their finite bandwidth, band edges, and nontrivial topological properties. We model the waveguides as either a tight-binding (TB) chain or a Su-Schrieffer-Heeger (SSH) chain. For unstructured waveguides with infinite bandwidth, the transmission and reflection coefficients of a side-coupled two-level emitter (2LE) are the same as the reflection and transmission coefficients of a direct-coupled 2LE. We show that this analogy breaks down for structured waveguides with finite bandwidth due to the appearance of Lamb shift only for the direct-coupled 2LE. We further predict a robust light-emitter coupling at zero collective decay width of a single giant 2LE (with two couplings at different points) near the band edges of the structured waveguides where topological features can be beneficial. Finally, we study single-photon dynamics in a heterojunction of a long TB and short SSH waveguide connected to a 2LE at the SSH end. We show the propagation of a photon from the excited emitter to the TB waveguide only when the SSH waveguide is in the topological phase. Thus, the heterojunction acts as a conditional propagation channel.

Local unitary operations cannot affect the quantum correlations between two systems sharing an entangled state although they do influence the outcomes of local measurements. By considering local squeezing operations we introduce an extended family of observables allowing violation of the Clauser-Horne-Shimony-Holt Bell inequality for two-mode Gaussian systems. We show that local squeezing can enable or enhance the identification of nonlocal two-mode states. In particular, we show that local squeezing followed by photon–no-photon discrimination can suffice to reveal nonlocality in a broad ensemble of pure and mixed two-mode Gaussian states.

Many quantum speed limits for isolated systems can be generalized to also apply to closed systems. This is, for example, the case with the well-known Mandelstam-Tamm quantum speed limit. Margolus and Levitin derived an equally well-known and ostensibly related quantum speed limit, and it seems to be widely believed that the Margolus-Levitin quantum speed limit can be similarly generalized to closed systems. However, a recent geometrical examination of this limit reveals that it differs significantly from most known quantum speed limits. In this paper, we show that, contrary to the common belief, the Margolus-Levitin quantum speed limit does not extend to closed systems in an obvious way. More precisely, we show that for every hypothetical bound of Margolus-Levitin type, there are closed systems that evolve with a conserved normalized expected energy between states with any given fidelity in a time shorter than the bound. We also show that for isolated systems, the Mandelstam-Tamm quantum speed limit and a slightly weakened version of this limit that we call the Bhatia-Davies quantum speed limit always saturate simultaneously. Both of these evolution time estimates extend straightforwardly to closed systems. We demonstrate that there are closed systems that saturate the Mandelstam-Tamm but not the Bhatia-Davies quantum speed limit.

The general-purpose interactive theorem-proving assistant called prove-it was used to verify the quantum phase estimation (QPE) algorithm, specifically claims about its outcome probabilities. prove-it is unique in its ability to express sophisticated mathematical statements, including statements about quantum circuits, integrated firmly within its formal theorem-proving framework. We demonstrate our ability to follow a textbook proof to produce a formally certified proof, highlighting useful automation features to fill in obvious steps and make formal proving nearly as straightforward as informal theorem proving. Finally, we make comparisons with formal theorem proving in other systems where similar claims about QPE have been proven.