We experimentally reconstruct Wigner's current of quantum phase-space dynamics. We reveal the “push-and-pull” associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only “pulls” the system toward the origin of phase space, we also observe an outward “push” because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeezing dynamics and its central stagnation point with a topological charge of “$-1$”. This work demonstrates high resolving power and establishes an experimental paradigm for measuring the quantumness and nonclassicality of the dynamics of open quantum systems.

The aim of this article is to generate the superposition state of nonorthogonal wavelike and particlelike states without ancillary qubits. Although it has been demonstrated that wavelike and particlelike states can be nonorthogonal, it remains unclear whether a superposition state of the two states can be achieved without the use of orthogonal ancillary qubits. To address this question, we employ a designed double-layer Mach-Zehnder interferometer that could continuously morph the single-photon state from particlelike to wavelike. Through both a theoretical analysis and experimental demonstration, we show that the nonorthogonality of wavelike and particlelike states can be maintained without ancillary qubits. The results showed that the two states are naturally nonorthogonal and can be directly utilized. As a variant of the delayed-choice experiment, our research will contribute to a deeper understanding of the nature of quantum objects, and also provide a different framework for discussions on wave-particle duality.

Causal influences are at the core of any empirical science, the reason why its quantification is of paramount relevance for the mathematical theory of causality and applications. Quantum correlations, however, challenge our notion of cause and effect, implying that tools and concepts developed over the years having in mind a classical world have to be reevaluated in the presence of quantum effects. Here, we propose the quantum version of the most common causality quantifier, the average causal effect, measuring how much a target quantum system is changed by interventions on its presumed cause. Not only does it offer an innate manner to quantify causation in two-qubit gates but also in alternative quantum computation models such as the measurement-based version, suggesting that causality can be used as a proxy for optimizing quantum algorithms. Considering quantum teleportation, we show that any pure entangled state offers an advantage in terms of causal effects as compared to separable states. This broadness of different uses showcases that, just as in the classical case, the quantification of causal influence has foundational and applied consequences and can lead to a yet totally unexplored tool for quantum information science.

Quantum entanglement lies at the heart of quantum information-processing tasks. Although many criteria have been proposed, efficient and scalable methods to detect the entanglement of generally given quantum states are still not available yet, particularly for high-dimensional and multipartite quantum systems. Based on FixMatch and Pseudo-Label methods, we propose a deep semisupervised learning model with a small portion of labeled data and a large portion of unlabeled data. The data-augmentation strategies are applied in this model by using the convexity of separable states and performing local unitary operations on the training data. We verify that our model has good generalization ability and gives rise to better accuracies than traditional supervised learning models with detailed examples.

Gottesman-Kitaev-Preskill (GKP) codes encode a qubit in displaced phase-space combs of a continuous-variable (CV) quantum system and are useful for correcting a variety of high-weight photonic errors. Here we propose atomic ensemble analogs of the single-mode CV GKP code by using the quantum central limit theorem to pull back the phase-space structure of a CV system to the compact phase space of a quantum spin system. We study the optimal recovery performance of these codes under error channels described by stochastic relaxation and isotropic ballistic dephasing processes using the diversity combining approach for calculating channel fidelity. We find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes. Our spin GKP codes based on the two-axis countertwisting interaction and superpositions of SU(2) coherent states are direct spin analogs of the finite-energy CV GKP codes, whereas our codes based on one-axis twisting do not yet have well-studied CV analogs. A state preparation scheme for the spin GKP codes is proposed which uses the linear-combination-of-unitaries method, applicable to both the CV and spin GKP settings. Finally, we discuss a fault-tolerant approximate gate set for quantum computing with spin-GKP-encoded qubits, obtained by translating gates from the CV GKP setting using the quantum central limit theorem.

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning, and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the key problems to handle GEPs is that the memory usage and computational complexity explode as the size of the system of interest grows. This paper aims at extending sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms that iteratively solve the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the GEP as the minimization or maximization problem of the fractional form of the expectations of two Hermitians. We then show that the fractional objective function can be analytically minimized or maximized with respect to a single-qubit gate by solving a GEP of a $4\times 4$ matrix. Second, we show that a system of linear equations characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to important engineering problems formulated with the finite-element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.

The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate or wire cutting, are a powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently executing relatively easy-to-implement (or noisy) quantum channels. However, such virtual simulation necessitates an exponentially large number of decompositions, thereby significantly limiting their practical applicability. This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states, namely, unitaries with pre- and postselection. Specifically, we explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. Furthermore, we elucidate the structure of the resulting decomposed unitary. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method.

The vibronic coupling effect in nitrogen $1s$ x-ray photoelectron spectra was systematically studied for a family of 17 bicyclic indole molecules by combining Franck-Condon simulations (including the Duschinsky rotation effect) and density-functional theory. The simulated vibrationally resolved spectra of four molecules agree well with available experiments. Reliable predictions for this family further allows us to summarize rules for spectral evolution in response to three types of common structural changes (side chain substitution, $\mathrm{CH}\leftrightarrow \mathrm{N}$ replacement, and isomerization). Interestingly, vibronic properties of amine and imine nitrogen are clearly separated. They show negative and positive zero-point vibration energies of the core-ionized state with respect to the ground state, respectively, indicating flatter and steeper potential energy surfaces induced by the N $1s$ ionization; amine N atoms show stronger mode mixing effects than imine N atoms; and the $1s$ ionizations on two types of nitrogen led to distinct changes in local bond lengths and angles. The rules are useful for a basic understanding of vibronic coupling in this family, and the precise spectra are useful for future reference and data mining studies.

We present a simple and general coherence model for multiorbital tunnel ionization of molecules, which we incorporate into our previously developed density-matrix approach for sequential double ionization [C. H. Yuen and C. D. Lin, Phys. Rev. A 106, 023120 (2022)]. The influence of this coherence is investigated through simulations of single ionization and sequential double ionization of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ using few-cycle near-infrared laser pulses. In the case of single ionization, our results reveal the crucial role played by this coherence in generating population inversion in $\mathrm{N}{{}_2}^{+}$, suggesting a potential mechanism for air lasing. Regarding sequential double ionization, we observe only minor changes in the kinetic energy release spectra when the coherence is included, while noticeable differences in the angle-dependent dication yield for both ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ are found. Based on these findings, we recommend the inclusion of multiorbital tunnel ionization coherence in models for single ionization of general molecules, while suggesting that it can be safely neglected in the case of sequential double ionization.

We study the topological properties of interacting and noninteracting bosons loaded in the orbital angular momentum states $l=1$ in a lattice of rings with alternating distances. At the single-particle level, the two circulation states within each site lead to two decoupled Su-Schrieffer-Heeger lattices with correlated topological phases. We characterize the topological configuration of these lattices in terms of the alternating distances, as well as their single-particle spectrum and topologically protected edge states. Second, we add on-site interactions for the two-boson case, which lead to the appearance of multiple bound states and edge bound states. We investigate the doublon bands in terms of a strong-link model and we analyze the resulting subspaces using perturbation theory in the limit of strong interactions. All analytical results are benchmarked against exact diagonalization simulations.

We propose a system for passive magnetic levitation and three-dimensional harmonic trapping of soft ferromagnets. Our protocol utilizes the magnetic-field gradient for vertical trapping, and the finite-size effect of the Meissner effect for horizontal trapping. We provide numerical and analytical estimations of possible mechanical dissipations to show that our system allows high mechanical $Q$ factors above $Q>{10}^8$, and quantum control of the levitated object is within reach of current technologies. The utilization of the soft ferromagnet's internal collective spin excitation may allow quantum mechanical phenomena with particles as large as the submillimeter scale.

We study the generation of quantum entanglement between two giant atoms coupled to a one-dimensional waveguide. Since each giant atom interacts with the waveguide at two separate coupling points, there exist three different coupling configurations in the two-atom waveguide system: separated, braided, and nested couplings. Within the Wigner-Weisskopf framework for single coupling points, the quantum master equations governing the evolution of the two giant atoms are obtained. For each coupling configuration, the entanglement dynamics of the two giant atoms is studied, including the cases of two different atomic initial states: single- and double-excitation states. It is shown that the generated entanglement depends on the coupling configuration, phase shift, and atomic initial state. For the single-excitation initial state, there exists steady-state entanglement for these three couplings due to the appearance of the dark state. For the double-excitation initial state, an entanglement sudden birth is observed via adjusting the phase shift. In particular, the maximal entanglement for the nested coupling is about one order of magnitude larger than those of separate and braided couplings. In addition, the influence of the atomic frequency detuning on the entanglement generation is studied. This work can be utilized for the generation and control of atomic entanglement in quantum networks based on giant-atom waveguide-QED systems, which have wide potential applications in quantum information processing.

The cxceptional point (EP) denotes the non-Hermitian degeneracy, in which both eigenvalues and eigenstates become identical. By the conventional local Markovian master equation, the EP can be constructed by parity-time $\left(\mathcal{PT}\right)$ or anti-$\mathcal{PT}$ symmetry in a system composed of coupled subsystems. However, the coupling between two systems makes the conventional local Markovian master equation become inconsistent. By using the self-consistent Markovian master equation, we show that there is no EP in the system composed of two bosonic subsystems suffering from the incoherent gain and loss. We further prove that the conventional local Markovian master equation can be valid when the coupling strength is much smaller than the difference in resonance frequency between the two subsystems, rather than the resonance frequencies. In a system composed of three bosonic subsystems, the EP can be obtained by adiabatically eliminating one of the three subsystems.

We investigate whether pure entangled states can be associated to a measurement basis in which all vectors are local unitary transformations of the original state. We prove that for bipartite states with a local dimension that is either 2, 4, or 8, every state corresponds to a basis. Via numerics, we strongly evidence the same conclusion for two qutrits and three qubits also. However, for some states of four qubits, we are unable to find a basis, leading us to conjecture that not all quantum states admit a corresponding measurement. Furthermore, we investigate whether there can exist a set of local unitaries that transform any state into a basis. While we show that such a state-independent construction cannot exist for general quantum states, we prove that it does exist for real-valued $n$-qubit states if and only if $n=2,3$, and that such constructions are impossible for any multipartite system of an odd local dimension. Our results suggest a rich relationship between entangled states and iso-entangled measurements with a strong dependence on both particle numbers and dimension.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is: how might we use imperfect near-term quantum computers to solve problems of practical value? We propose a quantum algorithm to estimate the properties of molecules using near-term quantum devices. The method is a recursive variational series estimation method, where we expand an operator of interest in terms of Chebyshev polynomials and evaluate each term in the expansion using a variational quantum algorithm. We test our method by computing the one-particle Green's function in the energy domain and the autocorrelation function in the time domain.

We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyze their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to timekeeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single-qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$-qubit operations.

The physical symmetries of a system play a central role in quantum error correction. In this work we encode a qubit in a collection of systems with angular momentum symmetry (spins), extending the tools developed by Gross [J. A. Gross, Phys. Rev. Lett. 127, 010504 (2021)] for single large spins. By considering large spins present in atomic systems and focusing on their collective symmetric subspace, we develop codes with octahedral symmetry capable of correcting errors up to second order in angular momentum operators. These errors include the most physically relevant noise sources such as microwave control errors and optical pumping. We additionally explore qubit codes that exhibit distance scaling commensurate with the surface code while permitting transversal single-qubit Clifford operations.

This paper introduces photon-varied quantum states (PVQSs), which generalize the nonclassical states obtained via photon addition or subtraction operations. We provide a unified characterization of PVQSs in terms of characteristic function, quasiprobability distribution, Fock representation, and Mandel $Q$ parameter. In the special case of photon-varied Gaussian states (PVGSs), the characteristic functions and the quasiprobability distributions are found to be in a simple canonical product structure. Necessary and sufficient conditions for the negativity of the quasiprobability distributions are also obtained for PVGSs. The unified characterization enables the design and analysis of quantum systems that exploit the non-Gaussian properties of PVQSs.