We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [Kerenidis and Prakash, Quantum recommendation system, in ITCS (2017)]. However, the SVE should be modified to solve the preconditioned linear system $C^{-1}Ax=C^{-1}b$. Moreover, different from the preconditioned linear system considered in [Phys. Rev. Lett. 110, 250504 (2013)], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1}A$, as well as the Frobenius norm ${\parallel A\parallel }_F$.

We study what is arguably the most experimentally appealing boson sampling architecture: Gaussian states sampled with threshold detectors. We show that, in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models. We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures. Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all boson sampling models that employ Gaussian states and threshold detectors.

Based on the novel idea of twin-field quantum key distribution [TF-QKD; Lucamarini et al., Nature (London) 557, 400 (2018)], we present a protocol named the “sending or not sending TF-QKD” protocol, which can tolerate large misalignment error. A revolutionary theoretical breakthrough in quantum communication, TF-QKD changes the channel-loss dependence of the key rate from linear to square root of channel transmittance. However, it demands the challenging technology of long-distance single-photon interference, and also, as stated in the original paper, the security proof was not finalized there due to the possible effects of the later announced phase information. Here we show by a concrete eavesdropping scheme that the later phase announcement does have important effects and the traditional formulas of the decoy-state method do not apply to the original protocol. We then present our “sending or not sending” protocol. Our protocol does not take postselection for the bits in $Z$-basis (signal pulses), and hence the traditional decoy-state method directly applies and automatically resolves the issue of security proof. Most importantly, our protocol presents a negligibly small error rate in $Z$-basis because it does not request any single-photon interference in this basis. Thus our protocol greatly improves the tolerable threshold of misalignment error in single-photon interference from the original a few percent to more than $45\%$. As shown numerically, our protocol exceeds a secure distance of 700, 600, 500, or 300 km even though the single-photon interference misalignment error rate is as large as $15\%, 25\%, 35\%$, or $45\%$.

Electron-positron pair production in low-energy collisions of heavy nuclei is considered beyond the monopole approximation. The calculation method is based on the numerical solving of the time-dependent Dirac equation with the full two-center potential. Bound-free and free-free pair-production probabilities as well as the energy spectra of the emitted positrons are calculated for the collisions of bare uranium nuclei. The calculations are performed for collision energy near the Coulomb barrier for different values of the impact parameter. The obtained results are compared with the corresponding values calculated in the monopole approximation.

Experimentally and theoretically, we explore the photoelectron momentum distributions of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ and their companion atoms Ar and Xe, which possess nearly equal electron binding energies to the corresponding molecules, subject to close-to-circularly polarized laser fields. Compared to Xe, significant deviations of the results for ${\mathrm{O}}_2$ have been observed experimentally. In the meantime, the measured photoelectron momentum distributions of ${\mathrm{N}}_2$ match those of Ar. With the theoretical analysis based on strong field approximation, the results that ${\mathrm{N}}_2$ behaves just like its companion atom Ar and ${\mathrm{O}}_2$ behaves significantly different from Xe have been attributed to the two-center interference effect of diatomic molecules, which is disparate for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ due to the parity difference of their molecular ground-state wave functions.

We theoretically investigate the wavelength dependence of high-order harmonic yields in solids driven by a mid-infrared laser field. By solving the three-dimensional two-band density matrix equations in the wavelength range of $2.0–7.5\mu \mathrm{m}$, it is shown that, in the limit of slow dephasing (dephasing time $T_2\to \infty$), the high-order harmonic yield from a crystal follows a scaling of ${\lambda }^{-4}$ for a fixed energy interval. The ${\lambda }^{-4}$ scaling is attributed to the wave-packet spreading (${\lambda }^{-3}$) for the overall yield and the energy distribution effect (${\lambda }^{-1}$) due to the increase of the cutoff. For the crystal with a finite dephasing time $T_2$, we find that the exponential factor $x$ of ${\lambda }^{-x}$ increases with a decay of $T_2$. An apparent and rapid fluctuation on a fine wavelength mesh is also observed in the harmonic yields. The fine-scale oscillation originates from the quantum interference effect, and the corresponding modulation period $\delta \lambda$ scales as ${\lambda }^{-1}$.

Waveguiding structures made of anisotropic media support bound states in the continuum (BICs) that arise when the radiation channel of otherwise semileaky modes is suppressed. Hitherto, only structures with optical axes aligned in symmetric orientations inside the waveguide plane, where BICs appear as lines in the momentum-frequency dispersion diagram, have been considered. Here we address settings where such symmetry is broken and unveil a number of fundamental different features. Weak and strong symmetry-breaking regimes are identified, corresponding to azimuthal and polar optical axes orientation asymmetries, respectively. The azimuthal symmetry breaking is found to still preserve the existence loci of BICs in the momentum-frequency dispersion diagram as lines. However, all possible BICs become interferometric, while the polarization separable states that occur in symmetric settings cease to exist. The polar symmetry breaking has stronger effects and transforms the BICs' existence loci from lines to points, which correspond to full-vector states that exist at discrete values of the optical axis orientation for a given wavelength. Such transformation results in fundamental changes in the topological properties of the radiated field around the BICs.

We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in the CHSH game, which implies that Tsirelson's bound also holds in our setting. More generally, we show that the optimal success probability depends on the reversible or irreversible character of the gates, the quantum or classical nature of the system, and the system dimension. We analyze the bounds obtained in light of Landauer's principle, showing the entropic costs of the erasure associated with the game. This demonstrates a connection between the reversibility in fundamental operations embodied by Landauer's principle and Tsirelson's bound that arises from the restricted physics of a unitarily evolving single-qubit system.

Security analyses of quantum cryptographic protocols typically rely on certain conditions; one such condition is that the sender (Alice) and receiver (Bob) have isolated devices inaccessible to third parties. If an eavesdropper (Eve) has a side channel in one of the devices, then the key rate may be sensibly reduced. In this paper we consider an attack on a coherent-state protocol, where Eve not only taps the main communication channel but also hacks Alice's device. This is done by introducing a Trojan horse mode with low mean number of photons $\overline{n}$, which is then modulated in a similar way to the signal state. First we show that this strategy can be reduced to an attack without side channels but with higher loss and noise in the main channel. Then we show how the key rate rapidly deteriorates for increasing photons $\overline{n}$, being halved at long distances each time $\overline{n}+1$ doubles. Our work suggests that Alice's device should also be equipped with sensing systems that are able to detect and estimate the total number of incoming and outgoing photons.

In recent years, exploration of the possible use of separable states as a resource to achieve quantum information processing (QIP) tasks has been gaining increasing significance. In this context, a particularly important demonstration has been that nonvanishing discord is the necessary condition for separable states to be used as a resource for remotely preparing any arbitrary pure target state [Nat. Phys. 8, 666 (2012)]. The present work stems from our observation that not only can resource states with the same discord imply different efficiencies (in terms of average fidelity) of the remote state preparation (RSP) protocol, but also states with higher discord can imply lower RSP efficiency. Therefore, this necessitates identification of the relevant feature of quantum correlations that can appropriately quantify the effectiveness of the resource state for the RSP protocol. To this end, for the two-qubit Bell-diagonal states, we show that an appropriate measure of simultaneous correlations in three mutually unbiased bases can serve to quantify the usefulness of the resource for the RSP task using entangled as well as separable states, including nondiscordant states as a resource. In particular, it is revealed that zero-discord states with such a nonvanishing measure can be useful for remotely preparing a subset of pure target states. Thus, this work shows that, using separable states, an effective resource for QIP tasks such as RSP can be provided by simultaneous correlations in mutually unbiased bases.

We present a theoretical consideration of the radiative two-photon finite-nuclear-size contributions to the Lamb shift in a light muonic atom. They are of the order of $\alpha {\left(Z\alpha \right)}^{5}m$ and may depend differently on $m{R}_N$. The contributions are due to the electronic and muonic vacuum polarization and the muon self-energy. The consideration is done within the external field approximation. We also found the leading logarithmic finite-nuclear-size contributions in the next order. One of them is of the order $\alpha {\left(Z\alpha \right)}^6{ln}^2\left(Z\alpha \right){\left(m{R}_N\right)}^{2}m$ and the other is of the order ${\alpha }^2{\left(Z\alpha \right)}^5{ln}^2\left(m_e{R}_N\right){\left(m{R}_N\right)}^{3}m$. Special attention is paid to higher-order effects in muonic hydrogen and the related applications of various parametrizations of the proton electric form factors. We also consider the general expressions in coordinate space for the finite-size radiative contributions to the Lamb shift in two-body muonic atoms. The numerical results are present for the atoms with $Z\le 10$.

Nuclear structure corrections of orders $Z\alpha E_F$ and ${\left(Z\alpha \right)}^2{E}_F$ are calculated for the hyperfine splitting of the muonic deuterium. The obtained results disagree with previous calculations and lead to a $5\sigma$ disagreement with the current experimental value of the $2S$ hyperfine splitting in muonic deuterium.

Delayed dissociation of doubly ionized ethylene, produced by collisions of highly charged ions, was studied at low and medium collision energies. Position-sensitive time-of-flight measurements of all the recoil fragments, triggered by detection of a charge-selected scattered ion, or emitted electrons, allowed us to identify ionic dissociation processes accompanied by delayed processes. We found that the delayed dissociation processes are well described by the power-law decay, rather than the exponential decay.

Canonical semiclassical methods can be used to develop an intuitive definition of tunneling time through potential barriers. An application to atomic ionization is given here, considering both static and time-dependent electric fields. The results allow one to analyze different theoretical constructions proposed recently to evaluate ionization experiments based on attoclocks. They also suggest new proposals of determining tunneling times, for instance through the behavior of fluctuations.

We propose and analyze continuous measurements of atom number and atomic currents using dispersive probing in an optical cavity. For an atom-number measurement in a closed system, we relate both the detection noise and the heating rate due to measurement backaction to Tan's contact and identify an emergent universal quantum nondemolition (QND) regime in the good-cavity limit. We then show that such a continuous QND measurement of atom number serves as a quantum-limited current transducer in a two-terminal setup. We derive a universal bound on the precision of the current measurement, which results from a trade-off between detection noise and backaction of the atomic current measurement. Our results apply regardless of the strength of interaction or the state of matter and set fundamental bounds on future precision measurements of transport properties in cold-atom quantum simulators.

We characterize the properties of a vortex line in an elongated dipolar Bose–Einstein condensate. Increasing the strength of the dipole-dipole interactions (DDIs) relative to the short-ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.

We investigate the transverse mode structure of the down-converted beams generated by a type-II optical parametric oscillator (OPO) driven by a structured pump. Our analysis focuses on the selection rules imposed by the spatial overlap between the transverse modes of the three fields involved in the nonlinear interaction. These rules imply a hierarchy of oscillation thresholds that determine the possible transverse modes generated by the OPO, as remarkably confirmed with experimental results.

We introduce an efficient iterative method to prepare a target state in Hilbert spaces with high dimensionality using a combination of unitary evolution, measurements, and quantum Zeno dynamics. The latter confines the evolution within Zeno subspaces of decreasing size. This gives an exponential speedup relative to the case of states evolving in the full Hilbert space between projective measurements. We demonstrate our approach on the control problem of rapidly transferring a superfluid into the Mott insulator in the Bose-Hubbard model. We discuss the general applicability of the method by preparing arbitrary superpositions with random Hamiltonians.

We present a scheme for a universal device which can be programed by quantum states to approximate a chosen projective measurement to a given precision. Our scheme can be viewed as an extension of the swap test to the instance where one state is supplied many times. As such, it has many potential applications given the variety of quantum information tasks which make use of the swap test. In particular, we show that our scheme is optimal for state discrimination under the one-sided error requirement, and optimally approximates any projective measurement. Furthermore, we propose a practical implementation of our scheme with passive linear optics, which involves a simple interferometer composed only of balanced beam splitters.

Calculation of the electron correlation energy $E_c$ of ground and excited states through the partitioning and evaluation of the dynamic $E_c^d$ and nondynamic $E_c^{nd}$ components requires one to account for the interplay of these correlation modes as well as for the excitation effect. In this paper it is demonstrated that both local suppression of dynamic correlation (SDC) by nondynamic correlation and enhancement of dynamic correlation (EDC) due to excitation to a state of the ionic nature can be quantified with the ratio $x\left(\mathit{r}\right)$ between the correlated and uncorrelated on-top pair densities $\mathrm{\Pi }\left(\mathit{r}\right)$. A $\mathrm{CAS}\mathrm{\Pi }\mathrm{DFT}$ scheme is proposed, in which $E_c^{nd}$ is calculated with the complete active space approach in a small basis, while $E_c^d$ is calculated in the same basis with a functional of density functional theory corrected for SDC and EDC with an original correction function of $x\left(\mathit{r}\right)$. Correlation energies calculated with $\mathrm{CAS}\mathrm{\Pi }\mathrm{DFT}$ along the bond-dissociation coordinate for the paradigmatic ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ molecules as well as for the ${\mathrm{C}}_2$ molecule with strong nondynamic correlation at the equilibrium agree well with the reference data, thus providing a proof of concept for $\mathrm{CAS}\mathrm{\Pi }\mathrm{DFT}$.