Quantum circuits with local particle-number conservation restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and nonvalid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggests the possibility of more resource-efficient error-mitigation techniques for circuits preserving symmetries that are not possible for general circuits. Here, we analyze the probability of staying in such symmetry-preserved subspaces under noise, providing an exact formula for local depolarizing noise. We apply our findings to benchmark, under depolarizing noise, the symmetry robustness of the XY quantum alternating operator Ansatz, which has local particle-number conserving symmetries and is a special case of the quantum alternating operator Ansatz. We also analyze the influence of the choice of encoding the problem on the symmetry robustness of the algorithm and discuss a simple adaption of the bit-flip code to correct for symmetry-breaking errors with reduced resources.

We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased noise where the bit-flip error rate is exponentially suppressed with the mean number of photons. In a recent work we suggested that the remaining phase-flip error channel could be suppressed using a one-dimensional repetition code. Indeed, using only bias-preserving gates on the cat qubits, it is possible to build a universal set of fault-tolerant logical gates at the level of the repetition cat qubit. In this paper we perform Monte Carlo simulations of all the circuits implementing the protected logical gates, using a circuit-level error model. Furthermore, we analyze two different approaches to implement a fault-tolerant Toffoli gate on repetition cat qubits. These numerical simulations indicate that very low logical error rates could be achieved with a reasonable resource overhead, and with parameters that are within the reach of near-term circuit QED experiments.

Single-photon avalanche diode (SPAD) arrays are essential tools in biophotonics, optical ranging and sensing, and quantum optics. However, their small number of pixels, low quantum efficiency, and small fill factor have so far hindered their use for practical imaging applications. Here, we demonstrate full-field entangled photon-pair correlation imaging using a 100-kpixel SPAD camera. By measuring photon coincidences between more than 500 million pairs of positions, we retrieve the full point spread function of the imaging system and subsequently high-resolution images of target objects illuminated by spatially entangled photon pairs. We show that our imaging approach is robust against stray light, enabling quantum imaging technologies to move beyond laboratory experiments towards real-world applications such as quantum light detection and ranging.

We present a theoretical method for calculating multiphoton ionization amplitudes and cross sections of few-electron atoms. The present approach is based on an extraction of partial-wave amplitudes from a scattering wave function, which is calculated by solving a system of driven Schrödinger equations. The extraction relies on a description of partial waves in terms of a small number of Coulomb waves with fixed wave numbers. The method can be used for photon energies below and above the ionization threshold and to treat resonance-enhanced multiphoton ionization. We use it to calculate two-, three-, and four-photon ionization cross sections of hydrogen and helium atoms for a wide range of photon energies and to determine the asymmetry parameters of photoelectron angular distributions for two-, three-, and four-photon ionization of the helium atom.

We propose a variational approach to the dynamics of the Bose-Hubbard model beyond the mean-field approximation. To develop a numerical scheme, we use a discrete overcomplete set of Glauber coherent states and its connection to the generalized coherent states studied in depth by Perelomov [Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986)]. The variational equations of motion of the generalized coherent state parameters as well as of the coefficients in an expansion of the wave function in terms of those states are derived and solved for many-particle problems with large particle numbers $S$ and increasing mode number $M$. For $M=6$, it is revealed that the number of complex-valued parameters that have to be propagated is more than one order of magnitude less than in an expansion in terms of Fock states.

Quantum mechanics allows operations to be in indefinite causal order, leading to advantages in computational and communication tasks. However, basic notions such as communication capacity have not yet been formalized. In light of this, through the process matrix formalism, we formulate different classical capacities for a bipartite quantum process. For one-way communication, we find that general quantum processes satisfy a generalization of the Holevo bound, i.e., we can send, at most, one bit per qubit. The result also holds for processes with indefinite causal order and with shared entanglement between the sender and the receiver. We further extend known bounds to classical channel capacities, showing that general processes cannot outperform causally separable ones. Next, we study bidirectional communication through a causally separable process. Our result shows that a bidirectional protocol cannot exceed the limit of a one-way communication protocol. Finally, we generalize this result to a multiparty broadcast communication protocol through a definite ordered process.

We propose and theoretically analyze the use of coherent population trapping of a single diamond nitrogen-vacancy (NV) center for continuous real-time sensing. The formation of the dark state in coherent population trapping prevents optical emissions from the NV center. Fluctuating magnetic fields, however, can kick the NV center out of the dark state, leading to a sequence of single-photon emissions. A time series of the photon counts detected can be used for magnetic field estimations, even when the average photon count per update time interval is much smaller than 1. For a theoretical demonstration, the nuclear spin bath in a diamond lattice is used as a model fluctuating magnetic environment. For fluctuations with known statistical properties, such as an Ornstein-Uhlenbeck process, Bayesian inference-based estimators can lead to an estimation variance that approaches the classical Cramer-Rao lower bound and can update dynamical information in real time with the detection of just a single photon. Real-time sensing using coherent population trapping adds a powerful tool to the emerging technology of quantum sensing.

The Perdew-Zunger self-interaction correction (PZ-SIC) offers a route to remove self-interaction errors on an orbital-by-orbital basis. A recent formulation of PZ-SIC by Pederson, Ruzsinszky, and Perdew proposes restricting the unitary transformation to localized orbitals called Fermi-Löwdin orbitals. This formulation, called the FLOSIC method, simplifies PZ-SIC calculations and was implemented self-consistently using a Jacobi-like (FLOSIC-Jacobi) iteration scheme. In this work we implement the FLOSIC approach using the Krieger-Li-Iafrate (KLI) approximation to the optimized effective potential. We compare the results of the present FLOSIC-KLI approach with the FLOSIC-Jacobi scheme for atomic energies, atomization energies, ionization energies, barrier heights, polarizability of chains of hydrogen molecules, etc., to validate the FLOSIC-KLI approach. The FLOSIC-KLI approach, which is within the realm of Kohn-Sham theory, predicts smaller energy gaps between frontier orbitals due to the lowering of eigenvalues of the unoccupied orbitals. Results show that atomic energies, atomization energies, ionization energy as an absolute of highest occupied orbital eigenvalue, and polarizability of chains of hydrogen molecules between the two methods agree within 2%. Finally the FLOSIC-KLI approach is used to determine the vertical ionization energies of water clusters.

Quantum memories are a crucial technology for enabling large-scale quantum networks through synchronization of probabilistic operations. Such networks impose strict requirements on quantum memory, such as storage time, retrieval efficiency, bandwidth, and scalability. On- and off-resonant ladder protocols on warm atomic vapor platforms are promising candidates, combining efficient high-bandwidth operation with low-noise on-demand retrieval. However, their storage time is severely limited by motion-induced dephasing caused by the broad velocity distribution of atoms composing the vapor. In this paper, we demonstrate velocity selective optical pumping to overcome this decoherence mechanism. This will increase the achievable memory storage time of vapor memories. This technique can also be used for preparing arbitrarily shaped absorption profiles, for instance, preparing an atomic frequency comb absorption feature.

We find, for two-electron closed-shell systems (${\mathrm{H}}_2$ molecule, $\mathrm{He}$ atom), symmetry-forbidden peaks in the high-order harmonic spectra obtained by the time-dependent Kohn-Sham equations, and clarify their origin. It turns out that fixation of the number of Kohn-Sham orbitals and their occupations gives rise to unphysical transition paths and, therefore, incorrect populations of the one-electron excited states, which leads to even-order harmonics in systems with inversion symmetry. We show that the time-dependent natural Kohn-Sham and time-dependent configuration interaction equations do not suffer from this shortcoming.

We report on the fragmentation of multiply charged ${\mathrm{CH}}_3\mathrm{I}$ ions through dissociative ionization and Coulomb explosion induced by moderately intense (${10}^{12}–{10}^{13} \mathrm{W}/{\mathrm{cm}}^2$) ultrashort laser fields. Velocity map imaging of the fragment ions as a function of pulse duration, ranging from 25 fs to 1.5 ps, leads to kinetic energies, angular distributions, and the relative ion yield in different channels of these fragments. We propose possible pathways for the fragmentation channels based on the kinetic energies and theoretical potential energy curves. For the energetic fragments, we observe an enhanced yield with increasing pulse duration. A simple one-dimensional classical model of wave-packet propagation over the proposed intermediate state potential energy curve is used to estimate the ionization probability as a function of pulse duration. Our results suggest that a delayed enhanced ionization is a consequence of rearrangement of the energies of the molecular orbitals following bond stretching. The resultant energy upshift of the inner orbitals at larger internuclear separation gives rise to resonant multiorbital coupling at a critical distance, which enables enhanced ionization for longer pulses.

We study the low-temperature thermodynamics of weakly interacting uniform liquids in one-dimensional attractive Bose-Bose mixtures. The Bogoliubov approach is used to simultaneously describe quantum and thermal fluctuations. First, we investigate in detail two different thermal mechanisms driving the liquid-to-gas transition, the dynamical instability, and the evaporation, and we draw the phase diagram. Then, we compute the main thermodynamic quantities of the liquid, such as the chemical potential, the Tan's contact, the adiabatic sound velocity, and the specific heat at constant volume. The strong dependence of the thermodynamic quantities on the temperature may be used as a precise temperature probe for experiments on quantum liquids.

Advances in creating stable dipolar Bose systems and ingenious box traps have generated great interest in the field of cold bosons. Theory study of dipolar bosons at finite temperature $T$ has been limited. We study two-dimensional dipolar bosons at arbitrary tilt angle $\theta$ using finite-$T$ random phase approximation. We show that a comprehensive understanding of phases and instabilities at nonzero $T$ can be obtained by concurrently considering dipole strength, density, temperature, and $\theta$. We find the system to be in a homogeneous noncondensed phase that undergoes a collapse transition at large $\theta$, and a finite momentum instability, signaling a striped phase, at large dipolar strength; there are important differences from the $T=0$ case. As $T\to 0$, a Bose-condensed phase appears at critical dipolar strength, and at critical density. Our predictions for a polar molecule system, ${}^{41}\mathrm{K}{}^{87}\mathrm{Rb}$, and ${}^{166}\mathrm{Er}$ may provide tests of our results.

We investigate the Kerr and magneto-optical effects for a probe laser field with two orthogonally polarized components, propagating in a cold Rydberg atomic gas with an inverted-$\mathsf{Y}$-type level configuration via double electromagnetically induced transparency (EIT). Through an approach beyond both mean-field and ground-state approximations, we make detailed calculations on third-order nonlinear optical susceptibilities and show that the system possesses giant nonlocal self- and cross-Kerr nonlinearities contributed by Rydberg-Rydberg interaction. The theoretical result of the cross-Kerr nonlinearity obtained for ${}^{85}\mathrm{Rb}$ atomic gas is very close to the experimental one reported recently. Moreover, we demonstrate that the probe laser field can acquire a very large magneto-optical rotation via the double EIT, which may be used to design atomic magnetometers with high precision. The results presented here are promising not only for the development of nonlocal nonlinear magneto-optics but also for applications in precision measurement and optical information processing and transmission based on Rydberg atomic gases.

We present a communication system based on quantum degenerate four-wave mixing for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings (cross-talking) among $2N$ optical modes (spatial and polarization modes), represented by arbitrary $\mathrm{SU}\left(2N\right)$ transformations and due to mechanical and thermal perturbations, imperfections, and so on, are autocompensated after a single round trip between Alice and Bob. Bob uses a source of single photons or, alternatively, attenuated coherent states and thus autocompensated 1-qudit states are received by Bob for using them with high-dimensional quantum key distribution (QKD) protocols that provide larger secret key rates for large $N$. A security study is also presented for this autocompensating quantum cryptography system, where it is found that the secure key rate increases with respect to nonautocompensated links for decoy-state QKD in the case of collective attacks. This plug-and-play system can be used in both optical fiber and free-space communication systems.

A method involving intensity correlation measurements is described, which allows for the complete removal of Doppler broadening in the emission of electromagnetic radiation from faraway sources that are inaccessible to conventional Doppler-free measurements. The technique, relying on a correction to $g^{\left(2\right)}$ of order $N^{-1}$, probes the separation between neighboring spectral lines and is also applicable to the elimination of broadening due to collisions ($N$ is the number of emitting particles and $g^{\left(2\right)}$ is the second-order field correlation function). Possible applications include a determination of cosmological parameters from redshifts of gravitationally lensed quasars.

Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\epsilon n$, where $\epsilon$ is the maximum error rate and $n$ is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\le 12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.

We study numerically the evolution of the velocity distribution of atoms under the action of the bichromatic force. The comparison of the time dependencies of the distribution width and the average acceleration of atoms reveals the correlation of these quantities. We show that the estimation of the momentum diffusion coefficient on the basis of the analogy between the interaction of atoms with the counterpropagating bichromatic waves and the interaction of atoms with the counterpropagating sequences of the $\pi$ pulses roughly corresponds to the results of numerical calculations. To separate the influence of the momentum diffusion on the evolution of atomic momentum distribution from the influence of the time-dependent Doppler shift, we study the motion of a “heavy” atom, for which the velocity change during the interaction of an atom with the field can be neglected. Provided that the parameters of the atom-field interaction are optimal, we show that the momentum diffusion coefficient is proportional to the intensity of the laser radiation. We used the Monte Carlo wave-function method for the numerical simulation of the atomic motion.

The quantum kicked rotor is well known to display dynamical localization in the noninteracting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate remains debated beyond mean field. Here we study the kicked Lieb-Liniger model in the few-body limit. We show that for any interaction strength, two kicked interacting bosons always dynamically localize, in the sense that the energy of the system saturates at long times. However, contrary to the noninteracting limit, the momentum distribution $\mathrm{\Pi }\left(k\right)$ of the bosons is not exponentially localized, but decays as $\mathcal{C}/k^4$, as expected for interacting quantum particles, with Tan's contact $\mathcal{C}$ which remains finite at long times. We discuss how our results will impact the experimental study of kicked interacting bosons.

We theoretically explore the tunneling dynamics for the tight-binding model of a single spin-orbit-coupled atom trapped in an optical lattice subjected to lattice shaking and to time-periodic Zeeman field. By means of analytical and numerical methods, we demonstrate that the spin-orbit (SO) coupling adds some results to the tunneling dynamics in both multiphoton resonance and far-off-resonance parameter regimes. When the driving frequency is resonant with the static Zeeman field (multiphoton resonances), we obtain an unexpected dynamical localization (DL) phenomenon where the single SO-coupled atom is restricted to making perfect two-site Rabi oscillation accompanied by spin flipping. By using the unconventional DL phenomenon, we are able to generate a ratchetlike effect which enables directed atomic motion towards different directions and accompanies periodic spin flipping under the action of SO coupling. For the far-off-resonance case, we show that by suppressing the usual intersite tunneling alone, it is possible to realize a type of spin-conserving second-order tunneling between next-nearest-neighboring sites, which is not accessible in the conventional lattice system without SO coupling. We also show that simultaneous controls of the usual intersite tunneling and the SO-coupling-related second-order tunneling are necessary for quasienergies flatness (collapse) and completely frozen dynamics to exist. These results may be relevant to potential applications such as spin-based quantum information processing and design of spintronics devices.