Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that the Gram-Schmidt process is a widely used method to solve these two problems. However, existing methods, including the Gram-Schmidt process, have problems of high complexity, scaling $O\left(N^3\right)$ in the system dimension $N$, which leads to difficulties when calculating large-scale or ill-conditioned problems. With the development of quantum information processing, a series of quantum algorithms have been proposed, providing advantages and speedups over classical algorithms in many fields. In this paper we propose quantum algorithms to solve these two problems based on the idea of the Gram-Schmidt process and quantum phase estimation. The complexity of proposed quantum algorithms is theoretically and numerically analyzed. We find that our algorithms provide polynomial acceleration over the best-known quantum algorithms and a potential polynomial acceleration over the best-known classical algorithms on these two problems, scaling $O(N^2\mathrm{poly}(logN))$ in the dimension $N$ of the system when ignoring the complexity of state readout or $O(N^2\mathrm{poly}(logN))$ when considering the complexity of state readout.

We investigate the formation, stability, and dynamics of solitons in a one-dimensional binary Bose-Einstein condensate under the action of the spin-orbit-coupling and Lee-Huang-Yang (LHY) correction to the underlying system of the Gross-Pitaevskii equations. We identify the semi-dipole (SD) family of solitons and thoroughly analyze its properties. The numerical analysis reveals intricate bifurcations, including transitions from real to complex-valued stationary wave functions of the SD solitons and norm-dependent dynamical instabilities. Stability maps in the plane of the solitons' norm and interaction strength exhibit areas of monostability, oscillatory behavior, and soliton splitting. Solitons with complex stationary wave functions emerge as ground states in broad parameter areas due to the effects of the LHY terms. The other soliton species, in the form of mixed modes (MMs), do not feature the compexification bifurcation. In the LHY-dominated regime, the SD and MM solitons exhibit identical values of the energy for the same norm. The results deepen the understanding of nonlinear matter-wave states and reveal multistable ones in quantum gases.

We consider the dynamics of a supersolid state that is based on Leggett's idea of local phase flow around the atomic sites of the solid. This leads to a local microscopic superfluid velocity that is not Galilean and is defined only relative to the solid and a $T=0$ superfluid fraction ${\rho }_S/\rho <1$ (with $\rho$ being the macroscopic mass density). Landau's excitation-based argument for superfluids—that at temperature $T=0$ the normal fluid mass density ${\rho }_N$ is zero—should apply to supersolids. Together these two arguments imply that at low $T$ there is a missing mass density. We attribute this to a supersolid density ${\rho }_L$, with ${\rho }_L\equiv \rho -{\rho }_S-{\rho }_N$ and a momentum-bearing supersolid velocity $v_{Li}$. We derive the macroscopic dynamical equations for this system with three momentum-bearing macroscopic velocities $(v_{Li},v_{Ni},v_{Si})$ using Onsager's irreversible thermodynamics. For slow spatial variations, $v_{Si}$ accelerates along the negative gradient of the chemical potential or mass, like for an ordinary superfluid, and $v_{Ni}$ is subject to drag against $v_{Li}$ with a characteristic drag time $\tau$. There are three contributions to the acceleration of $v_{Li}$: drag against $v_{Ni}$, along the negative gradient of the chemical potential or mass, and due to the forces of lattice elasticity. For high-frequency motion relative to the drag time $\tau$, ${\rho }_L$ moves independently of ${\rho }_N$. The normal modes for such a system have a crossover frequency below which the normal fluid velocity $v_{Ni}$ is dragged into motion with $v_{Li}$ (so the theory reduces to the $v_{Si},v_{Ni}$ theory of Andreev and Lifshitz) and above which the normal fluid velocity $v_{Ni}$ is an independent variable. For an isotropic lattice we study the transverse and longitudinal responses. A frequency-dependent rotational inertia experiment is predicted to show, at frequencies that are low relative to $\tau$, that ${\rho }_L$ and ${\rho }_N$ move together but that at high frequencies ${\rho }_L$ moves much more than ${\rho }_N$.

We investigate the quench dynamics of a two-dimensional Rashba spin-orbit-coupled Bose-Einstein condensate. Our study focuses on quenching the system from a zero-momentum phase to a stripe phase. During this quench, topological defects emerge in the form of vortices. These vortices and antivortices exhibit a random spatial distribution with equal numbers. In a uniform system, we observe an exponential scaling of both the vortex production time and the vortex number with the quench rate, consistent with the conventional Kibble-Zurek mechanism, the decay of which adheres to a logarithmic law, aligning with experimental observations.

We consider a scheme of a thin film deposited on periodically modulated amplifying materials. We demonstrate that the reflection from such a metainterface can undergo amplification due to Fano resonances in the film. The amplification increases when the film waveguiding modes approach the edge of the continuum and degenerate into the leaky surface modes, guided by a thin film. Such modes possess a strong evanescent tail that extends into the active substrate and are therefore amplified. The study is performed by simplified analytical models, as well as by rigorous coupled wave analysis.

Recently [T. A. Freitas et al., Phys. Rev. A 108, L051501 (2023)], it was shown that, in a centrosymmetric cubic system, two photons from a broadband intense laser field can be converted into a pair of Stokes and anti-Stokes (SaS) entangled photons. While the previous work was based on symmetry arguments, here we present a fully quantum theory for the SaS scattering that properly explains, quantitatively describes, and provides a means to predict its spectral and polarization properties (for diamond). We also explore the possibilities offered by such a system, designing an entanglement map based on changes in the light-matter system. In particular, we show how the broadband polarization entanglement that emerges from the interference between electronic and phononic degrees of freedom in the SaS scattering depends on parameters such as the Stokes–anti-Stokes Raman shift, scattering geometry, and laser bandwidth, opening the avenue of exploration of such phenomenon in information processing.

Information engines, sometimes referred to as Maxwell Demon engines, utilize information obtained through measurement to control the conversion of energy into useful work. Discussions around such devices often assume the measurement step to be instantaneous, assessing its cost by Landauer's information erasure within the measurement device. While this simplified perspective is sufficient for classical feedback-controlled engines, for nanoengines that often operate in the quantum realm, the overall performance may be significantly affected by the measurement duration (which may be comparable to the engine's cycle time) and cost (energy needed to create the system-meter correlation). In this study, we employ a generalized von Neumann measurement model to highlight that obtaining a finite amount of information requires a finite measurement time and incurs an energetic cost. We investigate the crucial role of these factors in determining the engine's performance, particularly in terms of efficiency and power output. Furthermore, for the information engine model under consideration, we establish a precise relationship between the acquired information in the measurement process and the maximum energy extractable through the measurement. We also discuss ways to extend our considerations using these concepts, such as in measurement-enhanced photochemical reactions.

A quantum system subject to an external perturbation can experience leakage between uncoupled regions of its energy spectrum separated by a gap. To quantify this phenomenon, we present two complementary results. First, we establish time-independent bounds on the distances between the true dynamics and the dynamics generated by block-diagonal effective evolutions constructed via the Schrieffer-Wolff and Bloch methods. Second, we prove that, under the right conditions, this leakage remains small eternally. That is, we derive a time-independent bound on the leakage itself, expressed in terms of the spectral gap of the unperturbed Hamiltonian and the norm of the perturbation, ensuring its validity for arbitrarily large times. Our approach only requires a finite spectral gap, thus accommodating continuous and unbounded spectra. Finally, we apply our bounds to specific systems of practical interest.

Discrete-time quantum walks (DTQWs) have broad applications in quantum computation and simulation, particularly in universal quantum computing. Prior research in circuit quantum electrodynamics (QED) has focused on implementing DTQWs in one-dimensional chains. However, to achieve practical quantum tasks, it is crucial to extend DTQWs to multidimensional networks with diverse structures. Here, we propose a protocol for realizing DTQWs in multidimensional networks, which accommodate nodes with different numbers of neighbors. Using this protocol, we numerically simulate a Grover walk search algorithm in a cubic network with circuit QED. Our simulations, which consider decoherence, align well with theoretical predictions. Our universal protocol can be adapted for various quantum systems and paves the way for DTQWs in multidimensional networks, which has potential applications in quantum computing and simulation.

Starting from a coarse-grained map of a quantum many-body system, we construct the inverse map that assigns a microscopic state to a coarse-grained state based on the maximum entropy principle. Assuming unitary evolution in the microscopic system, we examine the resulting dynamics in the coarse-grained system using the assignment map. We investigate both a two-qubit system, with swap and controlled-not gates, and $n$-qubit systems, configured either in an Ising spin chain or with all-to-all interactions. We demonstrate that these dynamics exhibit atypical quantum behavior, such as nonlinearity and non-Markovianity. Furthermore, we find that these dynamics depend on the initial coarse-grained state and establish conditions for general microscopic dynamics under which linearity is preserved. As the effective dynamics induced by our coarse-grained description of many-body quantum systems diverge from conventional quantum behavior, we anticipate that this approach could aid in describing the quantum-to-classical transition and provide deeper insights into the effects of coarse graining on quantum systems.

Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to the standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non-$n$-locality in two distinct network topologies (linear and star). We have studied the extremal violations of $n$-local inequalities (compatible with linear and star network) for any fixed amount of entanglement (in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non-$n$-locality in a linear network. However, the same is not true for star $n$-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-$n$-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the $n$-local inequalities is also provided. Interestingly, detection of non-$n$-locality is ensured in the network if product of concurrence of all the sources involved exceeds $\frac{1}{2}.$

The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such a process involves the coupling of a single system of interest, called signal, with a single probe system, so that the relevant information in the signal system is indirectly measured by observing the probe system. Here we extend the concept of quantum nondemolition interaction to the cases in which the signal and the probe systems are each one multipartite continuous-variable system. Specifically, we propose a general scheme that performs the multipartite QND interactions, relying on beam-splitter couplings between the signal and probe modes with only two ancillary modes prepared offline in squeezed states. The scheme is also composed of homodyne detection and feedforward modulation. The ancillary modes are detected in the process, providing photocurrents for postmodulation of the output systems, as well as sufficient information to calculate genuine multipartite entanglement conditions of the input systems and to monitor similar conditions of the output systems.

Geometric phases depend only on the evolution path determined by the closed circuit in the projective Hilbert space but not on evolution details of the quantum system, leading to geometric quantum computation possessing some intrinsic robustness against control errors. Coordinated with dynamical decoupling, geometric quantum computation admits additional resilience to the environment-induced decoherence. However, the previous schemes of geometric quantum computation protected by dynamical decoupling require multiple physical qubits to encode a logical qubit, which undoubtedly increases the consumption of physical-qubit resources and the difficulty in the implementation of the logical-qubit manipulation based on physical-qubit driving. In this work, we put forward a scheme of decoherence-mitigated geometric quantum computation based only on physical qubits rather than logical qubits, hence avoiding the additional overhead of physical-qubit resources for logical-qubit encoding as well as the difficulty in the manipulation of logical qubits. Moreover, our scheme focuses on the most general interaction between an individual qubit and its environment so that it mitigates not just dephasing noise but rather regular decoherence. Our proposal thus represents a more realistic and effective approach towards the realization of geometric control with decoherence mitigation.

Self-testing, a correlation-based protocol, enables certification of both the quantum state and measurements without requiring knowledge of the internal workings of the device. While well studied in bipartite Bell scenarios, its extension to the multipartite regime remains limited due to the complex structure of multipartite correlations. In this work, we derive the optimal quantum bound of the $m$-partite Svetlichny inequality by finding suitable sum-of-squares decomposition, without assuming any fixed Hilbert space dimension. This enables us to self-test both the $m$-partite Greenberger-Horne-Zeilinger state and the local anticommuting observables (up to local unitaries and complex conjugation). Applying the self-testing relations obtained from the sum-of-squares decompositions in a swap circuit framework, we can assess the closeness of the reference states and measurements to their ideal counterparts in the presence of noise and imperfections, thereby demonstrating the robustness of our protocol. Our analysis additionally enables certified randomness generation from correlations achieving the optimal Svetlichny violation.

In quantum resource theory, one is often interested in identifying which states serve as the best resources for particular quantum tasks. If a relative comparison between quantum states can be made, this gives rise to a partial order, where states are ordered according to their suitability to act as a resource. In the literature, various different partial orders for a variety of quantum resources have been proposed. In discrete variable systems, vector majorization of Wigner functions in discrete phase space provides a natural partial order between quantum states. In the continuous variable case, a natural counterpart would be continuous majorization of Wigner functions in quantum phase space. Indeed, this concept was recently proposed and explored (mostly restricting to the single-mode case) by Van Herstraeten et al. [Quantum 7, 1021 (2023)]. In this work, we develop the theory of continuous majorization in the general $N$-mode case. In addition, we propose extensions to include states with finite Wigner negativity. For the special case of the convex hull of $N$-mode Gaussian states, we prove a conjecture made by Van Herstraeten, Jabbour, and Cerf. We also prove a phase space counterpart of Uhlmann's theorem of majorization.

Characterizing quantum processes is indispensable for the implementation of any task in quantum information processing. In this paper, we develop an efficient method to fully characterize arbitrary Gaussian processes in continuous-variable quantum systems. This is done by directly obtaining all elements of the symplectic matrix that describes the process. Only Gaussian resources such as coherent probes and quadrature measurements are needed for this task. The method is efficient, involving only $O\left(N^2\right)$ steps to characterize an $N$-mode system. Further, the method is resilient to uniform loss. We simulate this procedure using the Python package Strawberry Fields. We observe that heterodyne measurements outperform homodyne measurements for reconstructing Gaussian processes.

In quantum networks, a set of entangled states distributed over multiple, alternative, distinct paths between a pair of source-destination nodes can be purified to obtain a higher fidelity entangled state between the nodes. This multipath entanglement purification (MP-EP) strategy can exploit the network's complex structure to strengthen the entanglement connection between node pairs separated by appropriate graph distances. We investigate the network scenarios in which MP-EP outperforms entanglement distribution over single network paths utilizing a statistical model of a quantum network and find that MP-EP can be an effective entanglement distribution strategy over a range of node separations determined by the average edge fidelities and probabilities of the network. We find that MP-EP can boost the entanglement connection between suitably separated node pairs to reach fidelities sufficient for a given quantum task thereby increasing the functionality of a quantum network. Further, we provide statistical criteria for the feasibility of MP-EP in terms of network parameters that can determine the regions of the network where MP-EP can be a useful entanglement distribution strategy.

We introduce a spin-based receiver to sensitively detect the electric fields of millimeter waves by using a quantum interferometric approach. The proposed quantum sensor consists of many surface-state electrons trapped individually on liquid helium by an electrode network at the bottom of the liquid helium film. A dc current in this chip is biased to generate strong spin-orbit coupling of each of the trapped electrons. The millimeter wave signals are conducted to nondissipatedly drive the orbital motions of the trapped electrons and result in Stark shifts of the spin-orbit dressed states of the electrons. As a consequence, the electric fields of the conducted millimeter waves could be detected sensitively by using Hahn echo interferometry with the long-lived spin states of the electrons trapped on liquid helium.

Blind quantum computation (BQC) provides a secure framework for clients to delegate quantum computations to servers without revealing their private information. Among BQC protocols, those built on iterated gate teleportation (IGTBQC) have demonstrated promising potential in overcoming the constraints imposed by the no-programming theorem and significantly reducing communication overhead. However, existing IGTBQC protocols lack mechanisms for clients to verify the correctness of computation results and deal with only one type of clients capable of preparing qubits. To address these limitations, we first extend the current IGTBQC protocol to be a verifiable one and then propose another verifiable IGTBQC protocol tailored for a different type of clients with the capability of measuring single-qubit states. Furthermore, both protocols are shown to satisfy blindness and verification simultaneously in a relatively formal way. Our results not only broaden the applicability to a wider range of clients but also enhance the practicality of delegated quantum computation.