We study the exact ground states of the Su-Schrieffer-Heeger open chain and of the Kitaev open chain, using the variational quantum eigensolver (VQE) algorithm. These models host symmetry-protected topological phases, characterized by edge modes with vanishing single-particle energy in the thermodynamic limit. The same fact prevents the standard VQE algorithm from converging to the correct ground state for finite chains, since it is quasidegenerate in energy with other many-body states. Notably, this quasidegeneracy cannot be removed by small perturbations, as in typical spin systems. We address this issue by imposing appropriate constraints on the VQE evolution and constructing appropriate variational circuits, to restrict the probed portion of the Hilbert space along the same evolution. These constraints stem from general properties both of the topological phases and of the studied Hamiltonians. In this way, the improved VQE algorithm achieves an accurate convergence to the exact ground states in each phase. The present approach promises large applicability, also to realistic systems with different topologies and/or not easily removable degeneracies, thanks to the very high fidelity achievable also on systems with a relatively high number of qubits.

One of the fundamental tenets of quantum mechanics is that nonorthogonal states cannot be distinguished perfectly. When distinguishing multiple copies of a mixed quantum state, a collective measurement, which generates entanglement between the different copies of the unknown state, can achieve a lower error probability than nonentangling measurements. The error probability that can be attained using a collective measurement on a finite number of copies of the unknown state is given by the Helstrom bound. In the limit where we can perform a collective measurement on asymptotically many copies of the quantum state, the quantum Chernoff bound gives the attainable error probability. It is natural to ask, then, what strategies can be employed to reach these two bounds—is entanglement across all available modes always necessary or can other, experimentally more simple measurements saturate these bounds? In this work we address this question. We find analytic expressions for the Helstrom bound for arbitrarily many copies of the unknown state in simple qubit examples. Using these analytic expressions, we investigate whether the quantum Chernoff bound can be saturated by repeatedly implementing the $M$-copy Helstrom measurement. We also investigate the necessary conditions to saturate the $M$-copy Helstrom bound. It is known that a collective measurement on all $M$ copies of the unknown state is always sufficient to saturate the $M$-copy Helstrom bound. However, general conditions for when such a measurement is necessary to saturate the Helstrom bound remain unknown. We investigate specific measurement strategies which involve entangling operations on fewer than all $M$ copies of the unknown state. For many regimes we find that a collective measurement on all $M$ copies of the unknown state is necessary to saturate the $M$-copy Helstrom bound.

Distributed quantum entanglement plays a crucial role in realizing networks that connect quantum devices. However, sharing entanglement between distant nodes by means of photons is a challenging process primary due to unavoidable losses in the linking channels. In this paper, we propose a simple loss-tolerant protocol for the Greenberger-Horne-Zeilinger-state distribution. We analyze the distribution rate under feasible experimental conditions and demonstrate the advantages of rate-loss scaling with respect to direct transmission. Our protocol does not use quantum repeaters and is achievable with current quantum optics technology. The result has direct application to tasks such as conference key agreement or distributed sensing. Moreover, it reduces the requirements for implementing distributed quantum error correction codes such as the surface code.

In this paper we derive a numerical tensor method to solve the many-body Schrödinger equation for three-particle systems. The Schrödinger equation is first represented in a canonical tensor format using a triple orthogonal Laguerre-based wave function in scaled perimetric coordinates. We demonstrate that the antisymmetry of the wave function can be explicitly included in the tensor method formulation by coupling the indices associated with the coordinates representing the identical fermions, e.g., electrons or muons. It is shown that energies accurate to the picohartree can be achieved in full tensor format in less than 3300 s for atomic and muonic molecular systems. Furthermore, this CPU time is reduced to less than 300 s, without compromising the accuracy of the energy or quality of the wave function, using a low-rank tensor-train decomposition.

In this work, the $4D_{3/2}|3,\pm 2\rangle \to 4D_{5/2}|3,\pm 2\rangle$ transition in the ${\mathrm{Nb}}^{4+}$ ion is identified as a promising candidate for a terahertz (THz) atomic clock, with the transition frequency occurring at 56.022 4 THz. This transition is primarily driven by the magnetic dipole decay channel, which can easily be accessed by a laser. We focus on the stable ${}^{93}\mathrm{Nb}$ isotope, which has 100% natural abundance and a nuclear spin of $I=9/2$ for experimental advantage. Our data analysis allows us to estimate potential systematic shifts in the proposed clock system, including those due to blackbody radiation, electric quadrupole, second-order Zeeman, and second-order Doppler shifts. The scheme presented in this study can help suppress the ac Stark and electric quadrupole shifts in the clock-frequency measurement. All these analyses suggest that the proposed THz atomic clock using ${\mathrm{Nb}}^{4+}$ could be valuable in both quantum thermometry and frequency metrology.

An angular correlation function (ACF) of a pair of Lyman-$\alpha$ photons produced in photodissociation of ${\mathrm{H}}_2$ with linearly polarized incident light is measured on a whole sphere at a 33.66-eV photon energy so that we may distinctly substantiate that the $2p$ atom pairs are in the state previously identified by Torizuka et al. as the $2p$ atom-pair state [Phys. Rev. A 99, 063426 (2019)], who measured the ACF only on a circle in the plane perpendicular to the incident light beam. The $2p$ atom-pair state determined with much less uncertainty than before is investigated in terms of whether or not the state is entangled. We discover that the pair of fragment $\mathrm{H}\left(2p\right)$ atoms is certainly entangled in terms of the electron-electron entanglement, and obtain the entanglement entropy of the $2p$ atom-pair state. The similar discussion is made in terms of the electronic spatial-spin entanglement too, where the spatial motion and spin motion of electrons are considered nonidentical partial systems at variance with the former electron-electron entanglement. It turns out that the pair of fragment H($2p$) atoms is entangled in terms of the electronic spatial-spin entanglement as well as the electron-electron entanglement.

We study the matter-wave solitons in Bose-Einstein condensate (BEC) trapped on a Möbius st rip (MS), based on the respective Gross-Pitaevskii (GP) equation with the mean-field theory. In the linear regime, vortex states are characterized by quantum numbers, $n$ and $m$, corresponding to the transverse and circumferential directions, with the phase structure determined by the winding number (WN) $m$. Odd and even values of $n$ must associate, respectively, with integer and half-integer values of $m$, the latter ones requiring two cycles of motion around MS for returning to the initial phase. Using variational and numerical methods, we solve the GP equation with the attractive nonlinearity, producing a family of ground-state (GS) solitons for values of the norm below the critical one, above which the collapse sets in. Vortex solitons with $n=1,m=1$ and $n=2,m=1/2$ are obtained in a numerical form. The vortex solitons with $n=1,m=1$ are almost uniformly distributed in the azimuthal direction, while ones with $n=2,m=1/2$ form localized states. The Vakhitov-Kolokolov criterion and linear-stability analysis for the GS soliton solutions and vortices with $n=1,m=1$ demonstrates that they are completely stable, while the localized states with $n=2,m=1/2$ are completely unstable. Finally, the motion of solitons on the MS and the collision of two solitons are discussed.

The origin of the second harmonic generation (SHG) from plasmonic structures remains a subject of debate. Here, we investigate SHG from gold plasmonic nanostructures by scanning nanostructures at the single-particle level to acquire two-dimensional (2D) SHG maps which are qualitatively and quantitatively compared with numerically simulated SHG maps. This approach allows us to discriminate the role played by the surface and bulk contributions to SHG. Our findings reveal that the tangential surface source contribution, often neglected in the literature, plays a dominant role and is affected by surface roughness. This is evident when comparing the SHG maps obtained from identically sized gold nanoparticles that are fabricated using physical and chemical techniques. Additionally, the normal surface source is not found to significantly impact SHG in these configurations.

A practical approach is proposed for efficiently generating ultrashort attosecond pulses from realistic solid-state materials, aiming to optimize pulse width effectively. By adjusting the photon energy while maintaining a constant peak electric field, this strategy modulates the peak vector potential and laser field period, thereby controlling the high harmonic cutoff energy and the time-domain emission characteristics of the harmonics. The field-driven electronic dynamics lead to a nonmonotonic variation in both the intensity and the duration of the generated attosecond pulses. The light field frequency can be adjusted to yield the optimal pulse. Beyond the primary demonstration with hexagonal boron nitride as a prototypical material, significant pulse width optimization has been achieved across a range of different materials. This straightforward and versatile strategy shows promise for application in solid-state materials, offering new pathways to promote high harmonic performance.

We study the influence of single-atom dissipation and dephasing noise on the performance of Dicke and Tavis-Cummings quantum batteries, where the electromagnetic field of the cavity hosting the system acts as a charger. For these models a genuine charging process can only occur in the transient regime. Indeed, unless the interaction with the environment is cut off, the asymptotic energy of the battery is solely determined by the environment and does not depend on the initial energy of the electromagnetic field. We numerically estimate the fundamental figures of merit for the model, including the time at which the battery reaches its maximum ergotropy, the average energy, and the energy that needs to be used to switch the battery-charger interaction on and off. Depending on the scaling of the coupling between the battery and the charger, we show that the model can still exhibit a subextensive charging time. However, for the Dicke battery, this effect comes with a higher cost when switching the battery-charger interaction on and off. We also show that as the number of battery constituents increases, both the Dicke and Tavis-Cummings models become asymptotically free, meaning the amount of energy that is not unitarily extractable becomes negligible. We obtain this result numerically and demonstrate analytically that it is a consequence of the symmetry under permutations of the model. Finally, we perform simulations for different values of the detuning, showing that the optimal regime for the Dicke battery is off-resonance, in contrast with what is observed in the Tavis-Cummings case.

We present a comprehensive quantum many-body theory for $q$-deformed fermions and bosons, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters $k$ and $q$, these particles exhibit statistical behaviors that interpolate between conventional bosonic and fermionic systems, enabling us to model complex interactions via statistical modifications. We develop a generalized Wick theorem and extended Feynman diagrammatics tailored to $kq$ particles, allowing us to calculate two types of Green's functions. Explicit expressions for these Green's functions are derived in both direct and momentum spaces, providing key insights into the collective properties of $q$-fermionic and bosonic systems. Using a random-phase approximation, we estimate the dielectric function for $q$-fermion gas ($k=-1$) and analyze the Friedel oscillations, the plasmon excitations, and the energy-loss function. Our results demonstrate that the effective interaction is tuned by the value of $q$ so that a noninteracting limit is obtained as $q\to 0$, where the Friedel and the plasma oscillations disappear. An optimal value of $q$, namely, $q^{*}$, the plasma frequency, and the energy-loss function show an absolute maximum and the effective interaction changes behavior.

The ability to generate bipartite entanglement in quantum computing technologies is widely regarded as pivotal. However, the role of genuinely multipartite entanglement is much less understood than bipartite entanglement, particularly in the context of solving complicated optimization problems using quantum devices. It is thus crucial from both the algorithmic and hardware standpoints to understand whether multipartite entanglement contributes to achieving a good solution. Here we tackle this challenge by analyzing genuine multipartite entanglement—quantified by the generalized geometric measure—generated in Trotterized quantum annealing and the quantum approximate optimization algorithm. Using numerical benchmarks, we analyze its occurrence in the annealing schedule in detail. We observe a multipartite-entanglement barrier, and we explore how it correlates to the algorithm's success. We also prove how multipartite entanglement provides an upper bound to the overlap of the instantaneous state with an exact solution. Vice versa, the overlaps to the initial and final product states, which can be easily measured experimentally, offer upper bounds for the multipartite entanglement during the entire schedule. Our results help to shed light on how complex quantum correlations come to bear as a resource in quantum optimization.

The efficiency of a quantum metrology protocol can be significantly diminished by the interaction of the system with its environment, leading to a loss of purity and, as a result, a mixed state for the probing system. An example is the measurement of a magnetic field through the rotation of a spin that is subject to decoherence due to its coupling to a surrounding spin or bosonic bath. In this work we define mixed optimal quantum rotosensors (OQRs) as mixed spin-$j$ states that achieve maximum sensitivity to estimate infinitesimal rotations, when the rotation axis is unknown. We study two scenarios, where the probe states saturate the averaged fidelity or the averaged quantum Cramér-Rao bound, the latter giving the ultimate sensitivity. We find that mixed OQRs can achieve sensitivity equal to that of pure states and are obtained by mixing states from linear subspaces of anticoherent states. We present several examples of mixed OQRs and their associated anticoherent subspaces. We also show that OQRs maximize entanglement in a specific sense, preserving the known relation between entanglement and optimal rotation sensitivity for pure states, even in the context of mixed states. Our results highlight the interconnection between quantum metrology of rotations, anticoherence, and entanglement in mixed spin states.

Quantum measurement plays a crucial role in quantum metrology. Due to the limitations of experimental capabilities, collectively measuring multiple copies of probing systems can present significant challenges. Therefore, the concept of locality in quantum measurements must be considered. In this work, we investigate the possibility of achieving the quantum Cramér-Rao bound (QCRB) through local measurements (LMs). We first demonstrate that if there exists a LM to saturate the QCRB for qubit systems, then we can construct another rank-1 local projective measurement to saturate the QCRB. In this sense, rank-1 local projective measurements are sufficient to analyze the problem of saturating the QCRB. For pure qubits, we propose two necessary and sufficient methods to determine whether and how a given parameter estimation model can achieve the QCRB through LMs. The first method, dubbed the iterative matrix partition method and based on unitary transformations that render the diagonal entries of a traceless matrix vanish, elucidates the underlying mathematical structure of LMs as well as the local measurements with classical communications (LMCC), generalizing the result by Zhou et al. [Quantum Sci. Technol. 5, 025005 (2020)], which only holds for the later case. We clarify that the saturation of the QCRB through LMs for the Greenberger–Horne–Zeilinger-encoded states is actually due to the self-similar structure in this approach. The second method, dubbed the hierarchy of orthogonality conditions and based on the parametrization of rank-1 measurements for qubit systems, allows us to construct several examples of saturating QCRBs, including the three-qubit $W$ states and the $N$-qubit $W$ states ($N\ge 3$). Our findings offer insights into achieving optimal performance in quantum metrology when measurement resources are limited.

Dynamical decoupling represents an active approach towards the protection of quantum memories and quantum gates. Because dynamical decoupling operations can interfere with a system's own time evolution, the protection of quantum gates is more challenging than that of quantum states. In this work, we put forward a simple but general approach towards the realization of higher-order protection of quantum gates and further execute the first cloud-based demonstration of dynamical-decoupling-protected quantum gates at the first order and the second order. The central idea of our approach is to engineer (hence regain the control of) the gate Hamiltonian in coordination with higher-order dynamical decoupling sequences originally proposed for the protection of quantum memories. The physical demonstration on an IBM quantum processor indicates the effectiveness and potential of our approach on noisy intermediate scale quantum computers.

Two-qubit gates are a fundamental constituent of a quantum computer and typically its most challenging operation. In a trapped-ion quantum computer, this is typically implemented with laser beams which are modulated in amplitude, frequency, phase, or a combination of these. The required modulation becomes increasingly more complex as the quantum computer becomes larger, complicating the control hardware design. Here we develop a simple method to essentially remove the pulse-modulation complexity by engineering the normal modes of the ion chain. We experimentally test the feasibility of the method in a three-ion chain. This opens up the possibility to trade off complexity between the design of the trapping fields and the optical control system, which will help scale the ion-trap quantum computing platform.

Quantum transducers are essential for connecting hybrid quantum systems with distinct frequencies, pivotal for hybrid quantum networks. A deterministic quantum transducer protocol is proposed for the upconversion of single phonons in the microwave domain to optical photons. Utilizing a hybrid optomechanical crystal coupled to a three-level emitter, the protocol deterministically upconverts an itinerant phonon into an optical photon, when an auxiliary optical cavity mode is driven by a single photon. Furthermore, the deterministic upconversion transducer can also be achieved by driving the emitter with a classical laser pulse, rather than driving the optical cavity with a single photon. The intracavity photon numbers in both protocols are significantly less than one during the operation, thus overcoming the problem of parasitic heating within radiation-pressure coupling of hybrid optomechanical systems. These outstanding features make the protocols particularly useful for the realization of large-scale distributed hybrid quantum networks.

We propose to realize a mechanical dynamical Casimir effect (MDCE) in a hybrid optomechanical system consisting of a cavity mode, a low-frequency mechanical oscillator, and a two-level atomic system. Described by the effective Hamiltonian, the mechanical energy is directly converted to the photons through a three-wave-mixing mechanism. It is not a quantum simulation of a parametric DCE such as in superconducting circuits. Using a master-equation approach, we analyze the system dynamics in various regimes with respect to the ratio of the effective coupling strength and the loss rate of the system. The dynamics under the strong-coupling regime confirms various three-wave-mixing processes for creating photons by annihilation of mechanical and atomic excitations. Under the weak-coupling regime, a continuous production of photons can be demonstrated by driving both the mechanical oscillator and atom. By virtue of an atom of tunable frequency, our method avoids using the high-frequency mechanical oscillator, which is required for the conventional DCE in optomechanical systems under the double-photon resonance yet is out of reach of experiment. It is found that the mechanical frequency can be about two orders smaller than the cavity mode in yielding a remarkable flux of DCE photons.