Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data-processing inequalities are ubiquitous in this sense, assigning necessary conditions for all Markov processes. We address here the problem of the information-theoretic analysis of constraints on Markov processes in the quantum regime. We show the existence of a class of quantum data-processing inequalities called here quantum Markov monogamy inequalities. This class of necessary conditions on quantum Markov processes is inspired by its counterpart for classical Markov processes, thus providing a strong link between classical and quantum constraints on Markovianity. We go on to construct a family of multitime quantum Markov monogamy inequalities, based on the process tensor formalism and that exploits multitime correlations. We then show, by means of an explicit example, that the Markov monogamy inequalities can be stronger than the usual quantum data-processing inequalities.

Dynamical characterization of equilibrium topological phases has attracted considerable attention in recent years. In this paper, we make a thorough exploration of the nonadiabatic characterization of topological phases under slow quench protocol. We first propose an exactly solvable multistate Landau-Zener model that can be directly applied to the nonadiabatic slow quench dynamics of topological systems. Then we present two different schemes to characterize the bulk topology of the system based on the so-called spin inversion surface. The first one needs the least number of quenching processes, but requires measuring the gradients of time-averaged spin-polarization on the spin inversion surface. The second one only needs to measure the value of time-averaged spin-polarization on the spin inversion surface, thus making it possible to directly characterize the topological phases by introducing an extra quenching process. Moreover, high-order spin inversion surface or band inversion surface relying on the dimension reduction approach, is also generalized to the above two different characterization schemes. One can extract the topological invariant from pairs of points with opposite signs both on the zero-dimensional (0D) highest order band inversion surface and on the 0D highest order spin inversion surface, which greatly simplifies the measurement strategy and characterization process. In a word, superior to the sudden quench protocol, we demonstrate that the topological invariant can be captured not only by the topological information on band inversion surface, but also on the spin inversion surface. In particular, direct characterization of topological phases based on band inversion surface and spin inversion surface can be realized.

We use the variational quantum eigensolver (VQE) to simulate Kitaev spin models with and without integrability-breaking perturbations, focusing in particular on the honeycomb and square-octagon lattices. These models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a variational ansatz that takes advantage of this fermionic representation and is capable of expressing the exact ground state in the solvable limit. We also demonstrate that this ansatz can be extended beyond this limit to provide excellent accuracy when compared to other VQE approaches. In certain cases, this fermionic representation is advantageous because it reduces by a factor of two the number of qubits required to perform the simulation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite (and currently small) number of qubits, however, poses the risk of finding only the optimum within the restricted space supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence of improved problem Hamiltonians converges to the desired solution.

Generalized measurements may allow the control of its back-action on the quantum system by interpolating from a very weak to strong projective action. Such a measurement can fuel a quantum heat engine or extract work depending on the system-meter interaction. Here, we performed a proof-of-concept experiment using nuclear magnetic resonance techniques to investigate a spin quantum heat engine driven by nonselective generalized (weak) measurements without feedback control. Our prototype of a quantum thermal device operates with a measurement protocol and a single heat bath. The protocol is composed of two nonselective measurement channels with variable measurement strengths; one dedicated to fueling the device (analogous to a hot heat source) and the other committed to work extraction. The experimental results highlight that this kind of quantum thermal device can reach unit efficiency with maximum extracted power by fine-tuning of the measurement strengths.

We design a measurement-based quantum refrigerator with an arbitrary number of qubits situated in a one-dimensional array that interact through variable-range $XY$ interactions. The method proposed is based on repeated evolution followed by a measurement on the single accessible qubit, which has the potential to reduce the temperature in the rest of the subsystems, thereby demonstrating cooling in the device. The performance of the refrigerator is quantified by the fidelity of each local subsystem with the ground state of the local Hamiltonian and the corresponding probability of success. We identify system parameters, which include the interaction strength, range of interactions, initial temperature of each qubit, and the position of the measured qubit, so that the fidelities of all the unmeasured qubits approach unity with a nonvanishing probability. We observe that although strong interactions during evolution are required to achieve cooling, the long-range interactions typically deteriorate the performance of the refrigerator, which indicates that interactions are not ubiquitous. We report the scalability and the saturation property of the success probability with respect to the system size, which turns out to be independent of the involved system parameters and the number of repeated measurements. Furthermore, we show that the number of subsystems which can be cooled changes depending on the odd or even number of sites in the refrigerator. We argue that the distribution of entanglement between unmeasured qubits can give a possible explanation of the dependence of cooling process on the measured and unmeasured sites.

Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state to prepare has a certain structure that allows for faster preparation. In this paper, we consider quantum states that can be efficiently represented by (reduced) decision diagrams, a versatile data structure for the representation and analysis of Boolean functions. We design an algorithm that utilizes the structure of decision diagrams to prepare their associated quantum states. Our algorithm has a circuit complexity that is linear in the number of paths in the decision diagram. Numerical experiments show that our algorithm reduces the circuit complexity by up to 31.85% compared to the state-of-the-art algorithm, when preparing generic $n$-qubit states with $n^3$ nonzero amplitudes. Additionally, for states with sparse decision diagrams, including the initial state of the quantum Byzantine agreement protocol, our algorithm reduces the number of controlled-nots by 86.61–99.9%.

We design a quantum battery made up of bosons or fermions in an ultracold-atom setup, described by Fermi-Hubbard and Bose-Hubbard models, respectively. We compare the performance of bosons and fermions to determine which can function as a quantum battery more effectively given a particular on-site interaction and initial state temperature. The performance of a quantum battery is quantified by the maximum energy stored per unit time over the evolution under an on-site charging Hamiltonian. We report that when the initial battery state is in the ground state, fermions outperform bosons in a certain configuration over a large range of on-site interactions which are shown analytically for a smaller number of lattice sites and numerically for a considerable number of sites. Bosons take the lead when the temperature is comparatively high in the initial state for a longer range of on-site interaction. We study a number of up and down fermions as well as the number of bosons per site to find the optimal filling factor for maximizing the average power of the battery. We also introduce disorder in both on-site and hopping parameters and demonstrate that the maximum average power is robust against impurities. Moreover, we identify a range of tuning parameters in the fermionic and bosonic systems where the disorder-enhanced power is observed.

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m{\alpha }^{7}ln\left(\alpha \right)$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $m{\alpha }^6$-order relativistic correction, for the case of ${\mathrm{H}}_2^{+}$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.

We theoretically investigate the formation of highly charged ions in a germanium (Ge) solid driven by intense, ultrashort x-ray pulses and its effect on the cross sections for nonsequential two-photon absorption from the $K$ shell. Our investigation is related to an experiment conducted at the Linac Coherent Light Source, in which $K\alpha$ fluorescence was measured to identify nonsequential two-photon ionization. When a solid Ge target is irradiated by an intense x-ray free-electron-laser (XFEL) pulse, it undergoes severe ionization and turns into a plasma state. We employ a Monte Carlo molecular-dynamics approach to simulate the time evolution of Ge plasma formation, and the time-dependent configuration-interaction-singles method for cross-section calculations, taking into account various experimental x-ray beam parameters and Ge charge states created during the plasma formation dynamics. We find that under the given experimental condition at a photon energy of 7200 eV, charged ions are formed quickly (the average charge is $\approx +6$ at the peak of the pulse and $\approx +10$ at the end of the pulse). The cross sections of Ge for nonsequential two-photon absorption, however, turn out to be insensitive to different charge states, and the average value over all computed data is $(2.61\pm 0.05)\times {10}^{-59}{\mathrm{cm}}^4\mathrm{s}$. Our paper proposes a theoretical framework of photoabsorption cross-section calculations under the influence of plasma formation, when a solid target is employed in XFEL experiments.

We study a “helical” superfluid, a nonzero-momentum condensate in a frustrated bosonic model. At mean-field Bogoliubov level, such a novel state exhibits “smectic” fluctuation that are qualitatively stronger than that of a conventional superfluid. We develop a phase diagram and compute a variety of its physical properties, including the spectrum, structure factor, condensate depletion, momentum distribution, all of which are qualitatively distinct from that of a conventional superfluid. Interplay of fluctuations, interaction and lattice effects gives rise to the phenomenon of order by disorder, leading to a crossover from the smectic superfluid regime to the anisotropic $XY$ superfluid phase. We complement the microscopic lattice analysis with a field theoretic description for such a helical superfluid, which we derive from microscopics and justify on general symmetry grounds, reassuringly finding full consistency. Possible experimental realizations are discussed.

In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Ataman, Phys. Rev. A 105, 012604 (2022)], the second beam-splitter transmission coefficient is detection-scheme dependent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide detailed examples including both Gaussian and non-Gaussian input states, showing when an unbalanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.

We describe a simple quantum error correcting code built out of a time-dependent transverse-field Ising model. The code is similar to a repetition code, but has two advantages: an $N$-qubit code can be implemented with a finite-depth spatially local unitary circuit, and it can subsequently protect against both $X$ and $Z$ errors if $N\ge 10$ is even. We propose an implementation of this code with ten ultracold Rydberg atoms in optical tweezers, along with further generalizations of the code.

Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in continuous-variable (CV) teleportation, i.e., the fidelity deviation as the figure of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non-Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios: One is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again leads to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one, which leads to a “constructive effect,” and identify the noise models which are responsible for decreasing average fidelity and the increment in fidelity deviation.

Quantum key distribution (QKD), guaranteed by the principle of quantum physics, is a promising solution for future secure information and communication technology. However, device imperfections compromise the security of real-life QKD systems, restricting the wide deployment of QKD. This study reports a decoy-state Bennett-Brassard 1984 (BB84) QKD experiment that considers both source and detection imperfections. In particular, we achieve a rigorous finite-key security bound over fiber links of up to 75 km by applying a systematic performance analysis. Furthermore, our study considers more device imperfections than most previous experiments, and the proposed theory can be extended to other discrete-variable QKD systems. These features constitute a crucial step toward securing QKD with imperfect practical devices.

Simulations and analytical calculations that aim to describe flux-tunable transmons are usually based on effective models of the corresponding lumped-element model. However, when a control pulse is applied, in most cases it is not known how much the predictions made with the effective models deviate from the predictions made with the original lumped-element model. In this work we compare the numerical solutions of the time-dependent Schrödinger equation for both the effective and the lumped-element models, for microwave and unimodal control pulses (external fluxes). These control pulses are used to model single-qubit (X) and two-qubit gate (iswap and cz) transitions. First, we derive a nonadiabatic effective Hamiltonian for a single flux-tunable transmon and compare the pulse response of this model to the one of the corresponding circuit Hamiltonian. Here we find that both models predict similar outcomes for similar control pulses. Then, we study how different approximations affect single-qubit (X) and two-qubit gate (iswap and cz) transitions in two different two-qubit systems. For this purpose we consider three different systems in total: a single flux-tunable transmon and two two-qubit systems. In summary, we find that a series of commonly applied approximations (individually and/or in combination) can change the response of a system substantially, when a control pulse is applied.

We study the tunneling dynamics of a system with two bound states. We find that the system can be effectively described by a two-level leakage cavity model, with which we can reproduce the dynamics of tunneling ionization. It shows that tunneling via the excited-state resonance dominates over the ground-state tunneling within the field strength considered, where the electron prefers jumping to the excited-state resonance channel first and then tunneling out. Moreover, several key parameters of the system naturally emerge in our two-level model. Especially, one of the parameters is the physical correspondence of the tunneling time obtained from the ground-state tunneling.

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\alpha$ is presented for the ground and $n=2$ excited states of heliumlike ions. After subtracting the first terms of the $Z\alpha$ expansion from the all-order results, we identify the higher-order QED effects of order $m{\alpha }^7$ and higher. Combining the higher-order remainder with the results complete through order $m{\alpha }^6$ from Yerokhin and Pachucki [Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and nonmixing $n=2$ states of heliumlike ions with $Z=5\text{–}30$. For the mixing $2{}^{1}P_1$ and $2{}^{3}P_1$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z>10$.

Measuring the ionization and recombination times in high-order harmonic generation driven by strong laser fields is of fundamental importance in attosecond science and vital for assessing the temporal accuracy of trajectory-resolved high-harmonic spectroscopy. We investigate the effect of the electron-core interaction on the ionization and recombination times of the long trajectory in high-order harmonic generation. Using a classical model and the analytical $R$-matrix theory for helium, it is found that the attractive interaction leads to a 30-as shift of the ionization times for the long trajectory. By numerically solving the time-dependent Schrödinger equation for a helium atom model, we demonstrate that this small time shift can be probed by using orthogonally polarized two-color fields with high probe frequencies.

We study the nonequilibrium dynamics of two tunnel-coupled one-dimensional quasicondensates following a quench of the coupling strength from zero to a fixed finite value. More specifically, starting from two independent quasicondensates in thermal equilibrium, with initial temperature and chemical potential imbalance, we suddenly switch on the tunnel-coupling and analyze the postquench equilibration in terms of particle number and energy imbalances. We find that, in certain parameter regimes, the net energy can flow from the colder quasicondensate to the hotter one and is governed by the surplus of low-energy particles flowing from the cold to the hot system relative to the high-energy particles flowing in the reverse direction. In all cases, the approach to the new thermal equilibrium occurs through transient, damped oscillations. We also find that, for a balanced initial state, the coupled quasicondensates can relax into a final thermal equilibrium state in which they display a thermal phase coherence length that is larger than their initial phase coherence length, even though the new equilibrium temperature is higher. The increase in the phase coherence length occurs due to phase locking which manifests itself via an increased degree of correlation between the local relative phases of the quasicondensates at two arbitrary points.