The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical mixing time. In this article, we deal with analog quantum algorithms for mixing. First, we provide an analog quantum algorithm that, given a Markov chain, allows us to sample from its stationary distribution in a time that scales as the sum of the square root of the classical mixing time and the square root of the classical hitting time. Our algorithm makes use of the framework of interpolated quantum walks and relies on Hamiltonian evolution in conjunction with von Neumann measurements. There also exists a different notion for quantum mixing: the problem of sampling from the limiting distribution of quantum walks, defined in a time-averaged sense. In this scenario, the quantum mixing time is defined as the time required to sample from a distribution that is close to this limiting distribution. Recently, we provided an upper bound on the quantum mixing time for Erdős-Rényi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we also extend and expand upon our findings therein. Namely, we provide an intuitive understanding of the state-of-the-art random matrix theory tools used to derive our results. In particular, for our analysis we require information about macroscopic, mesoscopic, and microscopic statistics of eigenvalues of random matrices which we highlight here. Furthermore, we provide numerical simulations that corroborate our analytical findings and extend this notion of mixing from simple graphs to any ergodic, reversible, Markov chain.

We experimentally demonstrate a parametric iswap gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the two-qubit iswap gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomography measurements and numerical simulations as varying static $ZZ$ coupling strength. We quantitatively calculate the dynamic $ZZ$ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic $ZZ$ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic $ZZ$ coupling and high-order oscillation error degrades the parametric gate performance. This approach, which has not yet been previously explored, provides a guiding principle to improve gate fidelity of a parametric iswap gate by suppression of the unwanted qubit interactions. This controllable interaction, together with the parametric modulation technique, is desirable for crosstalk-free multiqubit quantum circuits and quantum simulation applications.

Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting in a click. How much information can a photon carry? We study a bipartite asymmetric “two-way signaling” protocol as an extension of that proposed by Del Santo and Dakić. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local $n$-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We show that, after the travel of a photon through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice and Bob whose detector clicks can access the other's full information of the $n$-bit string, while the other can gain one bit of information. That is, the wave-particle duality makes two-way signaling possible, and a single photon can carry an arbitrarily large (but finite) amount of information.

Measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD) protocol calibrates the phase reference frames by transmitting local oscillator pulses between two legitimate parties. The above implementation leaves massive loopholes; in particular, an eavesdropper can attack the system by manipulating the power of the local oscillator pulses. In this paper, a Bayesian phase-noise estimation model is proposed to estimate the phase drift and its uncertainty in the MDI-CVQKD protocol. The model employs the Bayesian estimation of the very weak quantum signal pulses and eliminates the necessity of transmitting local oscillator pulses between two legitimate parties. Moreover, the Bayesian inference algorithm has the characteristic of high robustness to noise and can achieve a well-motivated confidence interval of the estimated eigenphase. Comparing with its Gaussian counterpart, we adopt the discrete modulation in the MDI-CVQKD protocol, which allows a much better reconciliation efficiency at low signal-to-noise ratio. With simpler implementation, the proposed Bayesian phase-noise estimation model precisely avoids the security bottleneck due to the transmitted local oscillator pulses.

We report an investigation of the self-energy screening effects for the $g$ factor of the ground state of Li-like ions. The leading screening contribution of the relative order $1/Z$ is calculated to all orders in the binding nuclear strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). We also extend the known results for the $Z\alpha$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order ${\alpha }^{5}ln\alpha$ and obtaining approximate results for the ${\alpha }^5$ and ${\alpha }^6$ contributions. The comparison of the two approaches yields a stringent check of consistency of the two calculations and allows us to obtain improved estimations of the higher-order screening effects.

We study the dynamics of up to two Rydberg excitations and the correlation growth in a chain of atoms coupled to a photonic crystal waveguide. In this setup, an excitation can hop from one atom to another via exponentially decaying exchange interactions mediated by the waveguide. An initially localized excitation undergoes a continuous-time quantum walk for short-range hopping, and for long-range hopping, it experiences quasilocalization. In addition, the inverse participation ratio reveals a superballistic diffusion of the excitation in short times, whereas, at a long time, it becomes ballistic. For two initially localized excitations, intriguing and complex dynamical scenarios emerge for different initial separations due to the competition between the Rydberg-Rydberg and exchange interactions. In particular, the two-point correlation reveals a light-cone behavior even for sufficiently long-range exchange interactions. Additionally, we characterize the growth of bipartite entanglement entropy, which exhibits a global bound if only one excitation is present in the dynamics. Finally, we analyze the effect of imperfections due to spontaneous emission from the Rydberg state into photons outside the waveguide and show that all of the physical phenomena we predict are well within experimental reach.

Compared to single-component Bose-Einstein condensates, spinor Bose-Einstein condensates display much richer dynamics. In addition to density oscillations, spinor Bose-Einstein condensates exhibit intriguing spin dynamics that is associated with population transfer between different hyperfine components. This paper analyzes the validity of the widely employed single-mode approximation when describing the spin dynamics in response to a quench of the system Hamiltonian. The single-mode approximation assumes that the different hyperfine states all share the same time-independent spatial mode. This implies that the resulting spin Hamiltonian only depends on the spin interaction strength and not on the density interaction strength. Taking the spinor sodium Bose-Einstein condensate in the $f=1$ hyperfine manifold as an example and working within the mean-field theory framework, it is found numerically that the single-mode approximation misses, in some parameter regimes, intricate details of the spin and spatial dynamics. We develop a physical picture that explains the observed phenomenon. Moreover, using that the population oscillations described by the single-mode approximation enter into the effective potential felt by the mean-field spinor, we derive a semiquantitative condition for when dynamical mean-field induced corrections to the single-mode approximation are relevant. Our mean-field results have implications for a variety of published and planned experimental studies.

We study the properties of a homogeneous dilute Bose-Bose gas in a weak-disorder potential at zero temperature. By using the perturbation theory, we calculate the disorder corrections to the condensate density, the equation of state, the compressibility, and the superfluid density as a function of density, strength of disorder, and miscibility parameter. It is found that the disorder potential may lead to modifying the miscibility-immiscibility condition and a full miscible phase turns out to be impossible in the presence of the disorder. We show that the intriguing interplay of the disorder and intra- and interspecies interactions may strongly influence the localization of each component, the quantum fluctuations, and the compressibility, as well as the superfluidity of the system.

A flexible phase-matching method is introduced to manipulate the energy flow in nonlinear frequency conversion processes. With the use of photonic crystal as the reflective medium, the phase mismatching could be adjusted by the interface and the nonlinear crystal. We call this method the reflective phase matching. Here we present an experiment to demonstrate this idea in a single-domain MgO:CLN wafer with photonic crystal on the surface. A frequency-doubling signal enhanced 52 times is achieved. The result suggests the potential of the function to one more dimension phase matching without additional artificial structure inside the crystal. In addition, the proposed reflective phase-matching method could find broad application in the nonlinear optics and laser device miniaturization and integration.

We devise a protocol to build one-dimensional time-dependent quantum walks, maximizing the spatial spread throughout the procedure. We allow only one of the physical parameters of the coin-tossing operator to vary, i.e., the angle $\theta$, such that for $\theta =0$ we have the ${\widehat{\sigma }}_z$, while for $\theta =\pi /4$ we obtain the Hadamard gate. The optimal $\theta$ sequences present nontrivial patterns, with mostly $\theta \approx 0$ alternating with $\theta \approx \pi /4$ values after increasingly long periods. We provide an analysis of the entanglement properties, quasienergy spectrum, and survival probability, providing a full physical picture.

We present wave-particle-duality relations involving the relative entropy coherence measure, which plays a prominent role in the resource theory of coherence. The main input in these relations is an entropic bound for the which-way information, which we derive in this paper. We show that this latter crucially depends on the choice of the measurement strategy to obtain the path information. In particular, we present results for two strategies: zero-error identification of the path-detector states, which never produces an error but sometimes fails to return a conclusive answer, and a mixed strategy, where both errors and failure are allowed.

The no-masking theorem states that it is impossible to encode an arbitrary quantum state into the correlations between two subsystems so that no original information about the state is accessible in the marginal state of either subsystem. In this paper, we generalize this theorem to allow for failure of the protocol. We then bound the performance of a masking protocol when we are allowed a (probabilistic) approximate protocol.

We consider the problem of demonstrating non-Bell-local correlations by performing local measurements in randomly chosen triads, i.e., three mutually unbiased bases, on a multipartite Greenberger-Horne-Zeilinger state. Our main interest lies in investigating the feasibility of using these correlations to certify multipartite entanglement in a device-independent setting. In contrast with previous works, our numerical results up to the eight-partite scenario suggest that if each triad is randomly but uniformly chosen according to the Haar measure, one always (except possibly for a set of measure zero) finds Bell-inequality-violating correlations. In fact, a substantial fraction of these is even sufficient to reveal, in a device-independent manner, various higher-order entanglement. In particular, for the specific cases of three parties and four parties, our results—obtained from semidefinite programming—suggest that these randomly generated correlations always reveal, even in the presence of a non-negligible amount of white noise, the genuine multipartite entanglement possessed by these states. In other words, provided local calibration can be carried out to good precision, a device-independent certification of the genuine multipartite entanglement contained in these states can, in principle, also be carried out in an experimental situation without sharing a global reference frame.

It has been asked by different authors whether the two classes of Schatten-$p$-norm-based functionals $C_p\left(\rho \right)={min}_{\sigma \in \mathcal{I}}{\parallel \rho -\sigma \parallel }_p$ and ${\tilde{C}}_p\left(\rho \right)={\parallel \rho -\mathrm{\Delta }\rho \parallel }_p$ with $p\ge 1$ are valid coherence measures under incoherent operations, strictly incoherent operations, and genuinely incoherent operations, respectively, where $\mathcal{I}$ is the set of incoherent states and $\mathrm{\Delta }\rho$ is the diagonal part of density operator $\rho$. Of these questions, all we know is that $C_p\left(\rho \right)$ is not a valid coherence measure under incoherent operations and strictly incoherent operations, but all other aspects remain open. In this paper, we prove that (1) ${\tilde{C}}_1\left(\rho \right)$ is a valid coherence measure under both strictly incoherent operations and genuinely incoherent operations but not a valid coherence measure under incoherent operations, (2) $C_1\left(\rho \right)$ is not a valid coherence measure even under genuinely incoherent operations, and (3) neither $C_{p>1}\left(\rho \right)$ nor ${\tilde{C}}_{p>1}\left(\rho \right)$ is a valid coherence measure under any of the three sets of operations. This paper not only provides a thorough examination on the validity of taking $C_p\left(\rho \right)$ and ${\tilde{C}}_p\left(\rho \right)$ as coherence measures, but also finds an example that fulfills the monotonicity under strictly incoherent operations but violates it under incoherent operations.

It is shown that divergences in the susceptibility of any geometric measure of nonclassicality are sufficient conditions to identify phase transitions at arbitrary temperature. This establishes that geometric measures of nonclassicality, in any quantum resource theory, are generic tools to investigate phase transitions in quantum systems. For the zero-temperature case, we show that geometric measures of quantum coherence are especially useful for identifying first-order quantum phase transitions and can be a particularly robust alternative to other approaches employing measures of quantum correlations.

The silicon-vacancy center in diamond has recently attracted significant attention as a candidate for quantum information processing as it overcomes many of the optical issues present in the nitrogen-vacancy center. Historically it has been hampered by short dephasing times; however the recent development of high-purity samples at low temperatures resolves this issue. Hence it is timely to explore whether silicon-vacancy centers are useful for quantum tasks beyond single-photon sources. Here we investigate the potential of the silicon-vacancy center to realize two important operations required for quantum information processing: high-efficiency projective measurement and efficient single-qubit rotations. Due to its similar nature, the germanium-vacancy center is discussed as a point of comparison.

We propose a protocol to realize atomic nonadiabatic holonomic quantum computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics of the system is analyzed in the regime of Rydberg blockade, and robust laser pulses are designed via reverse engineering, so that quantum gates can be easily realized with hig h fidelities. In addition, we also study the evolution suffering from dissipation with a master equation. The result indicates that decays of atoms can be heralded by measuring the state of the auxiliary atom, and nearly perfect unitary evolution can be obtained if the auxiliary atom remains in its Rydberg state. Therefore, the protocol may be helpful to realize NHQC in a dissipative environment.

The problem of quantum metrology in the context of a particular non-Markovian quantum evolution is explored. We study the dynamics of the quantum Fisher information (QFI) of a composite quantum probe coupled to a Lorentzian environment, for a full variety of different classes of parameters. We are able to find the best metrological state, which is not maximally entangled but is the one which evolves the most rapidly. This is shown by demonstrating a connection between QFI and different quantum speed limits. At the same time, by optimizing a control field acting on the probes, we show how the total information flow is actively manipulated by the control so as to enhance the parameter estimation at a given final evolution time. Finally, under this controlled scenario, a sharp interplay between the dynamics of QFI, non-Markovianity, and entanglement is revealed within different control schemes.

We consider ionization of an atom by the electromagnetic field in a Fock state $|N\rangle$: An eigenvector of the operator ${\widehat{N}}_{\mathit{k},\lambda }={\widehat{a}}_{\mathit{k},\lambda }^{†}{\widehat{a}}_{\mathit{k},\lambda }$ of the number of photons in the mode $\mathit{k},\lambda$. We treat the electromagnetic field in a quantized way, which allows us to obtain the photon picture of the strong field ionization. We obtain, in particular, probability distributions for the number of absorbed photons in the process of strong field ionization for atomic systems governed by short-range and Coulomb potentials.