Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7200 random MaxCut instances, with $n=14–23$ qubits and depth parameter $p\le 12$, and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. We describe the rate of exponential scaling or effective temperature in terms of a series with a leading-order term $T\sim C_{\min }/n\sqrt{p}$, with $C_{\min }$ the optimal solution energy. Using this scaling, we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.

In this paper we analyze entanglement-based (EB) continuous-variable (CV) quantum-key distribution (QKD) with bright multimode non-Gaussian light. Our analysis is centered around the role of non-Gaussianity in mitigating the excess noise arising due to the mismatch between the signal modes and the local oscillators used for measurements. To be specific, we consider the non-Gaussian resources generated by single-photon subtraction and zero-photon catalysis applied on a two-mode squeezed vacuum (TMSV) state. We show that, at a given strength of the mode-mismatch noise, zero-photon catalysis leads to the maximum transmission distance, compared to the TMSV. However, considering the unavoidable issue of photon loss in the linear optical scheme for implementing zero-photon catalysis, our results hints at the single-photon-subtracted TMSV being the optimal choice for maximizing the transmission distance in EB CV QKD.

We present tools and methods to generalize parity compilation to digital quantum computing devices with arbitrary connectivity graphs and construct circuit implementations for the constraint Hamiltonian of higher-order constrained binary optimization problems. In particular, we show how even nonlocal constraints can be efficiently implemented without expensive SWAP gates. We show how the presented tools can be used to optimize the total circuit depth and CNOT count of the quantum approximate optimization algorithm in the parity architecture and highlight the advantages of the flexible compilation using various examples. We derive the relation between the developed gate sequences and the traditional approach that uses SWAP gates. The result can be applied to improve the implementation of many other nonlocal operators.

Quantum walks have been shown to be important for quantum metrological tasks, in particular for the estimation of the evolution parameters of the walk. In this work, we address the enhancement of this parameter estimation using the driven discrete-time quantum walk (DDTQW), which is a variant of the discrete-time quantum walk with multiple walkers. DDTQW has two regimes based on the interference between the walker number, i.e., phase matched and phase mismatched. We derive an expression for the quantum Fisher information (QFI) in the phase-matched regime of DDTQW driven using the squeezing operator, demonstrating an exponential increase in QFI. In the phase-mismatched regime, QFI varies as $t^2$, consistent with previous studies. Our analysis shows that parameter estimation can be improved by driving the walk using squeezing operators.

Relying on the redefined vacuum state approach and based on one-particle three-loop Feynman diagrams, partial third-order interelectronic corrections to the valence electron energy shift are investigated in Li-like ions. The idea is to begin with simple one-particle gauge-invariant subsets composed of Feynman diagrams and to keep track of them in the many-electron frame, which is a strong asset of the formalism. An independent derivation is undertaken with the help of perturbation theory to cross-check the expressions. This two-method scheme helps to resolve how the different terms are distributed among three- and four-electron contributions. Furthermore, it provides a tool to overcome the difficulties related to the derivation of reducible terms, which are tricky to deal with. These two independent derivations and the comparison of the resulting expressions are fully consistent, except for two expressions. In these cases, the discrepancy can be traced back to a different topology of the poles.

The hadronic vacuum polarization correction to the $g$ factor of a bound electron is investigated theoretically. An effective hadronic Uehling potential obtained from measured cross sections of $e^{-}{e}^{+}$ annihilation into hadrons is employed to calculate $g$-factor corrections for low-lying hydrogenic levels. Analytical Dirac-Coulomb wave functions, as well as bound wave functions accounting for the finite nuclear radius are used. Closed formulas for the $g$-factor shift in the case of a point-like nucleus are derived. In heavy ions, such effects are found to be much larger than for the free-electron $g$ factor.

At present, the nearest-neighbor tight-binding model is often used to study the high-order harmonic generation (HHG) in solids, but its defects are little known. We theoretically investigate the defects of the nearest-neighbor tight-binding model in the study of solid HHG by developing the semiconductor Bloch equations with the accelerated Bloch-like basis consisting of the maximally localized Wannier functions. To achieve this goal, we calculate the harmonic spectra, orientation and ellipticity dependence of harmonic yield in monolayer black phosphorus using the nearest-neighbor tight-binding model, and the ab initio model, respectively. It is found that there are obvious differences between the calculation results of the two models. This indicates the limitations of the nearest-neighbor tight-binding approximation in the study of solid HHG. Furthermore, we study the role of the matrix elements of the position operator under the Wannier basis in solid HHG, which are often discarded in many previous works. It is found that these matrix elements have an important influence on the orientation and ellipticity dependence of higher-order harmonic yield. This work remedies some defects of previous theories and will greatly promote the accurate calculation of strong-field nonlinear responses in solids.

We investigate coherent single-photon transport in a waveguide quantum electrodynamics structure containing multiple giant atoms. The single-photon scattering amplitudes are solved using a real-space method. The results give rise to a clear picture of the multichannel scattering process. In the case of identical and equally spaced giant atoms in a separate configuration, we also use the transfer-matrix method to express the scattering amplitudes in terms of compact analytical expressions, which allow us to conveniently analyze the properties of the scattering spectra. Based on these theoretical results, we find that the nondipole effects of giant atoms, which are relevant to the design of the setup, can strongly manipulate several types of collective properties of the output fields, including the superradiant phenomenon, the multiple Fano interference, and the photonic band gap. This makes it possible to manipulate the photon transport in a more versatile way than with small atoms. We also make a proposal to probe the topological states of a chain of braided giant atoms by using photon scattering spectra, showing that waveguide quantum electrodynamics systems with giant atoms are ideal platforms to merge topological physics and on-chip quantum optics.

It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e., allowing for the source to be partially correlated with the choices of measurement settings; however, what is the minimal amount of measurement independence needed to observe quantum nonlocality? Here we explore this question and consider models with strong measurement-dependent locality, where measurement choices can be perfectly determined in almost all rounds of the Bell test. Nevertheless, we show that quantum nonlocality can still be observed in this scenario, which we conjecture is minimal within the framework we use. We also discuss potential applications in randomness amplification.

This paper explores an approach to fault-tolerant quantum computing (FTQC), relying on quantum polar codes. We consider quantum polar codes of Calderbank-Shor-Steane type, encoding one logical qubit, which we refer to as ${\mathcal{Q}}_1$ codes. First, we show that a subfamily of ${\mathcal{Q}}_1$ codes is equivalent to the well-known family of Shor codes. Moreover, we show that ${\mathcal{Q}}_1$ codes significantly outperform Shor codes, of the same length and minimum distance. Second, we consider the fault-tolerant preparation of ${\mathcal{Q}}_1$ code states. We give a recursive procedure to prepare a ${\mathcal{Q}}_1$ code state, based on two-qubit Pauli measurements only. The procedure is not by itself fault-tolerant; however, the measurement operations therein provide redundant classical bits, which can be advantageously used for error detection. Fault tolerance is then achieved by combining the proposed recursive procedure with an error detection method. Finally, we consider the fault-tolerant error correction of ${\mathcal{Q}}_1$ codes. We use Steane error correction, which incorporates the proposed fault-tolerant code state preparation procedure. We provide numerical estimates of the logical error rates for ${\mathcal{Q}}_1$ and Shor codes of length 16 and 64 qubits, assuming a circuit-level depolarizing noise model. Remarkably, the ${\mathcal{Q}}_1$ code of length 64 qubits achieves a logical error rate very close to ${10}^{-6}$ for the physical error rate $p={10}^{-3}$, therefore demonstrating the potential of the proposed polar-codes-based approach to FTQC.

We study an electromagnetic radiation of a small bunch having a variable charge value and crossing a flat interface between two media. Both media are linear, homogeneous, stationary, and isotropic. They may have frequency dispersion but no spatial dispersion. Cherenkov radiation can be generated in the second medium only. It is assumed that the bunch charge value decreases exponentially starting from a certain time moment after the charge enters the second medium. This means that we take into account the scatter of the particle path lengths connected with the statistical nature of energy losses of particles. It is taken into account that a filamentous “trace” consisting of immobile charges is formed in the second medium. We obtain a general solution of the problem, which is the sum of the forced field, i.e., the charge field in the unbounded medium, and the free field connected with the influence of the boundary. An asymptotic study for the far-field zone is carried out. We obtain expressions for the spherical wave as well as for the cylindrical wave generated in the second medium if the charge velocity is sufficiently high. The spherical wave is radically different from the usual transition radiation, since it consists of two parts: the transition radiation wave and the wave generated due to the bunch decay and the formation of its trace. We describe the main properties of radiation. If the process of the bunch decay starts exactly at the boundary between media, then the angular distribution of the radiation energy has a single maximum in each of two regions. In the second medium, the radiation, as a rule, is greater than in the vacuum area, and this difference increases with increasing the charge velocity. If the charge velocity is larger than the speed of light in the second medium, then, along with the appearance of Cherenkov radiation, the properties of the spherical wave change radically. In particular, the main maximum of the angular distribution of the radiation energy increases essentially. If the distance from the charge entry point to the region of the bunch decay is sufficiently large, then a complicated interference pattern with many extremes arises due to the summation of different spherical waves.

We construct a full sawtooth lattice model with simulated magnetic and electric fields using orbital angular momentum (OAM) modes in a degenerate optical cavity. In our system, not only can we simulate a large lattice with a theoretically unbound OAM degree of freedom, but it is possible to adjust critical parameters such as the hopping strengths and simulated fields at will by taking advantage of optical interference implemented with simple optical circuit designs based on basic optical elements. Such versatility allows us to prepare appropriate wave packets in the OAM system and investigate their behavior dictated by fundamental physics in the sawtooth model, including Bloch oscillations induced by a driving electric field and Landau-Zener tunneling that arises due to the intricate band structure modulated by the simulated fields. As a first full implementation of the sawtooth model, our results extend photonic OAM quantum simulation significantly by enabling a sophisticated model involving both electric and magnetic fields.

In this paper we consider a spin chain locally coupled to dissipative environments with unbalanced gain and loss and explore the relation between the emergence of synchronization and exceptional points. For our model in the Liouvillian formalism the matrix of the Liouvillian superoperator is block diagonal and the different blocks correspond to the dynamics of different observables. We find that for ${\widehat{\sigma }}^z$ corresponding to the block having a single Liouvillian exceptional point (LEP), when the coupling strength between the nearest spins is beyond the LEP, the synchronization or antisynchronization will occur. For ${\widehat{\sigma }}^x$ and ${\widehat{\sigma }}^y$ corresponding to the block having two LEPs, when the coupling strength between the nearest spins is beyond both LEPs, the synchronization or antisynchronization will appear, and as time evolves the dynamical transition between synchronization and antisynchronization can occur. Moreover, we also find that the initial state of the system does not affect the emergence of synchronization or antisynchronization, but it determines whether the system is synchronized or antisynchronized and affects the time at which the dynamical transition between synchronization and antisynchronization occurs. Furthermore, by postselecting the quantum trajectories without quantum jump, the system can exhibit Hamiltonian exceptional points, and we find that quantum jumps play an important role in the synchronization of the system.

We present a study of the coherent interaction of a qubit with a pulse-shaped external field of a constant carrier frequency. We explore, theoretically and experimentally, the transition line profile (the dependence of the transition probability on the detuning) for five different pulse shapes: Rectangular, Gaussian, hyperbolic-secant, squared hyperbolic-secant, and exponential. The theoretical description for all cases but ${\mathrm{sech}}^2$ is based on the analytical solutions to the Schrödinger equation or accurate approximations available in the literature. For the ${\mathrm{sech}}^2$ pulse we derive an analytical expression for the transition probability using the Rosen-Zener conjecture, which proves very accurate. In addition, the same conjecture turns out to provide very accurate approximations for the Gaussian and exponential pulses. The experimental results are obtained with one of IBMQ's quantum processors. An excellent agreement between theory and experiment is observed, demonstrating some pulse-shape-dependent fine features of the transition probability profile. The mean absolute error (a measure of the accuracy of the fit) features an improvement by a factor of 4 to 7 for the analytic models compared to the commonly used Lorentzian fits. Moreover, the uncertainty of the qubit's resonance frequency is reduced by a factor of 4 for the analytic models compared to the Lorentzian fits. These results demonstrate both the accuracy of the analytic modeling of quantum dynamics and the excellent coherent properties of IBMQ's qubit.

A method for calculating the self-energy part of the Lamb shift is revisited. When the electron propagator in an external field is represented as an expansion in partial waves, the original method converges relatively slowly, requiring the calculation of dozens of partial waves. Here we show an improved method in which accurate results can be obtained using a much smaller number of partial waves. The method is illustrated for the ground states of hydrogenlike and lithiumlike boron and the possibility of high accuracy calculations on lower $Z$ hydrogenic ions is discussed.

We investigate the effect of a quench from a one-dimensional gas with strong and repulsive local interactions to a strongly attractive one, known as the super-Tonks-Girardeau effect. By incorporating both an optical lattice and nonlocal interactions (specifically nearest neighbor), we discover a previously unexplored phenomenon: the disruption of the state during the quench, but within a specific range of interactions. Our study employs the extended Bose-Hubbard model across various system sizes, starting with analytical results for two atoms and progressing to few-body systems using exact diagonalization, density matrix renormalization group and time-dependent variational principle methods. Finally, we use a numerical implementation of the local density approximation for a macroscopic number of atoms. Consistently, our findings unveil a region where the initially self-bounded structure expands due to the super-Tonks-Girardeau quench. The fast evaporation provides a tool to characterize the phase diagram in state-of-art experiments exploring the physics of the extended Bose-Hubbard model.

Confining the propagating wave packets of an atom interferometer inside a waveguide can substantially reduce the size of the device while preserving high sensitivity. We have realized a two-dimensional Sagnac atom interferometer in which Bose-condensed ${}^{87}\mathrm{Rb}$ atoms propagate within a tight waveguide formed by a collimated laser beam, a matter wave analog of the fiber optic gyro. The condensate is split, reflected, and recombined with a series of Bragg pulses while the waveguide moves transversely so that the wave-packet trajectories enclose an area. Delta-kick cooling is used to prepare low-density atomic wave packets with a temperature of $3\mathrm{n}\mathrm{K}$. The low density reduces the impact of interatomic interactions, while the low temperature limits the expansion of the wave packet during the interferometer cycle. The effective enclosed area is $0.8\mathrm{m}{\mathrm{m}}^2$ with an average fringe contrast of 20% and underlying contrast up to 60%. The main source of the reduced average contrast is phase noise caused by mechanical vibrations of the optical components. We present a measurement of Allan deviation for such an atom rotation sensor, showing that the interferometer phase noise falls with averaging time $\tau$ as ${\tau }^{-1/2}$ for $\tau$ up to 10 000 seconds. The statistical noise falls below the Earth rotation rate after 30 minutes of averaging.