Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating nonunitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics, such as Markovian processes described by the Lindblad master equation. In this paper, we analyze the convergence criteria and speed of a Markovian, purely dissipative quantum random walk on an unstructured classical search space. Notably, we show that certain jump operators make the quantum process replicate a classical one, while others yield differences between open quantum (OQRW) and classical random walks. We also clarify a previously observed quadratic speedup, demonstrating that OQRWs are no more efficient than classical search. Finally, we analyze a dissipative discrete-time ground-state preparation algorithm with a lower implementation cost. This allows us to interpolate between the dissipative and the unitary domain and thereby illustrate the important role of coherence for the quadratic speedup.

Quantum Monte Carlo integration (QMCI) is a quantum algorithm to estimate expectations of random variables, with applications in various industrial fields such as financial derivative pricing. When QMCI is applied to expectations concerning a stochastic process $X\left(t\right)$, e.g., an underlying asset price in derivative pricing, the quantum circuit $U_{X\left(t\right)}$ to generate the quantum state encoding the probability density of $X\left(t\right)$ can have a large depth. With time discretized into $N$ points, using state-preparation oracles for the transition probabilities of $X\left(t\right)$, the state preparation for $X\left(t\right)$ results in a depth of $O\left(N\right)$, which may be problematic for large $N$. Moreover, if we estimate expectations concerning $X\left(t\right)$ at $N$ time points, the total query complexity scales on $N$ as $O\left(N^2\right)$, which is worse than the $O\left(N\right)$ complexity in the classical Monte Carlo method. In this paper, to improve this, we propose a method to divide $U_{X\left(t\right)}$ based on orthogonal-series-density estimation. This approach involves approximating the densities of $X\left(t\right)$ at $N$ time points with orthogonal series, where the coefficients are estimated as expectations of the orthogonal functions by QMCI. By using these approximated densities, we can estimate expectations concerning $X\left(t\right)$ by QMCI without requiring deep circuits. Our error and complexity analysis shows that to obtain the approximated densities at $N$ time points, our method achieves the circuit depth and total query complexity scaling as $O\left(\sqrt{N}\right)$ and $O\left(N^{3/2}\right)$, respectively.

Quantum error mitigation (EM) is a collection of strategies to reduce errors on noisy intermediate scale quantum (NISQ) devices on which proper quantum error correction is not feasible. One of such strategies entails implementing the inverse of a known noise map of an environment by using a set of completely positive maps weighted by a quasiprobability distribution, i.e., a probability distribution with positive and negative values. This distribution is realized using classical postprocessing after final measurements of desired observables have been made. Here we make a connection with quasiprobability EM and recent results from quantum trajectory theory for open quantum systems. We show that the inverse of noise maps can be realized by performing classical postprocessing with a quasiprobability measure called the influence martingale on the quantum trajectories generated by an additional engineered reservoir coupled to the system. We demonstrate our result on a model relevant for current NISQ devices. Finally, we show the required quantum trajectories themselves can be simulated by coupling an ancillary qubit to the system. In this way, we can avoid the introduction of the engineered reservoir.

Parameterized quantum circuits are the core of new technologies such as variational quantum algorithms and quantum machine learning, which makes studying its properties a valuable task. We implement parameterized circuits with definite and indefinite causal order and compare their performance under particular descriptors. One of these is the expressibility, which measures how uniformly a given quantum circuit can reach the whole Hilbert space. Another property that we focus on this work is the entanglement capability, more specifically the concurrence and the entangling power. We also find the causal relation between the qubits of our system with the quantum average causal effect measure. We have found that indefinite circuits offer expressibility advantages over definite ones while maintaining the level of entanglement generation. Our results also point to the existence of a correlation between the quantum average causal effect and the entangling power.

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications to Hamiltonian downfolding in quantum computing and Heisenberg dynamics. This work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

In this study, we apply a thermodynamical approach to elucidate the primary constraints on the energy scaling of dissipative solitons (DS). We rely on the adiabatic theory of strongly chirped DS and define the DS energy scaling in terms of dissipative soliton resonance (DSR). Three main experimentally verifiable signatures identify a transition to DSR: (i) growth of a Lorentzian spike at the centrum of the DS spectrum, which resembles a spectral condensation in Bose-Einstein condensate, (ii) saturation of the spectrum broadening, and (iii) asymptotic DS stretching. We connect the DSR breakup with three critical factors: (i) decoupling of two correlation scales inherent in strongly chirped DS, (ii) resulting rise of the DS entropy with energy, which provokes its disintegration, and (iii) transition to a nonequilibrium phase, which is characterized by negative temperature. The breakup results in multiple stable DS generation. Theoretical results are in good qualitative agreement with the experimental data from a Kerr-lens mode-locked ${\mathrm{Cr}}^{2+}$:ZnS chirped-pulse oscillator (CPO) that paves the way for optimizing high-energy femtosecond pulse generation in solid-state CPO and all-normal-dispersion fiber lasers.

Although the superradiant phase transition (SRPT) is prohibited in the paradigmatic quantum Rabi model due to the no-go theorem caused by the ${\mathbf{A}}^2$ term, we demonstrate two distinct types of SRPTs emerging from the normal phase in the anisotropic quantum Rabi model. A discontinuous phase transition between the two types of superradiant phases also emerges in the presence of a strong ${\mathbf{A}}^2$ term. Additionally, a rich phase diagram featuring a triple point, which connects first- and second-order phase transitions, is derived analytically and confirmed through numerical diagonalization at large effective system sizes. Finally, distinct critical behavior at the triple point is revealed and contrasted with that of a single continuous SRPT. This work may open a new avenue for observing SRPTs in their intrinsic form without altering the ${\mathbf{A}}^2$ term, while also offering a practical platform for exploring rich quantum phenomena.

We explore the wireless charging of a quantum battery (QB) via $n$ charging units, whose coupling is mediated by a common bosonic reservoir. We consider the general scenarios in which the charger energy is not maximal and the QB has residual ergotropy initially. It is found that the charging performance improves with the increase of the coupling strength. In the strong coupling regime, the charging time is insensitive to the charger energy, the number of charging units, and the residual ergotropy in the QB, while the ergotropy charged on the QB strongly depends on the charger energy and ergotropy, and the residual ergotropy in the QB does not help to enhance its performance. Moreover, the multiple charging units help to enhance the charging performance in the weak and moderate coupling regimes, while they are less efficient in the strong coupling regime.

Quantum networks (QNs) promise to enhance the performance of various quantum technologies in the near future by distributing entangled states over long distances. The first step towards this is to develop novel entanglement measures that are both informative and computationally tractable at large scales. While numerous such entanglement measures exist for discrete-variable (DV) systems, a comprehensive exploration for experimentally preferred continuous-variable (CV) systems is lacking. Here, we introduce a class of CV entanglement measures, among which we identify a nonconvex entanglement monotone—the ratio negativity, which possesses a simple, scalable form that determines the exponential decay of optimal entanglement swapping on a chain of pure Gaussian states. This characterization opens avenues for leveraging statistical physics tools to analyze swapping-protocol-based CV QNs.

In previous work within Gross-Pitaevskii (GP) theory for ultracold gases, wetting phase transitions were predicted for a phase-segregated two-component Bose-Einstein condensate (BEC) adsorbed at an optical wall. The wetting phase diagram was found to depend on intrinsic atomic parameters, being the masses and the scattering lengths, and on the extrinsic wall boundary condition. Here we study wetting transitions in GP theory without an optical wall in a setting with three phase-segregated BEC components instead of two. The boundary condition is removed by replacing the wall with the third component and treating the three phases on an equal footing. This leads to an unequivocal wetting phase diagram that depends only on intrinsic atomic parameters. It features first-order and critical wetting transitions, and prewetting phenomena. The phase boundaries are computed by numerical solution of the GP equations. In addition, useful analytic results are obtained by extending the established double-parabola approximation to three components.

We report the explosive events of unidirectional and bidirectional soliton rains (SRs) in a Tm-doped fiber laser mode locked by the nonlinear amplifying loop mirror technology. It is observed that the explosive evolution undergoes a disintegrating process from a multi-SR state to a normal SR, and to a soliton group followed by annihilation, and eventually to the explosion. Continuous observations reveal that each explosion exhibits a decay, a sudden drop, and an eruption of energy, thereby manifesting a quasiperiodic characteristic. A numerical experiment has effectively simulated the explosive processes and confirmed the $Q$-switching effect inside the collective soliton explosions. An analysis of the orbit diagrams derived from nonlinear mapping solidly substantiates the origin of the SR explosions: a gain-modulated mode-locking mechanism. These findings unveil an extreme collective soliton behavior in dissipative systems.

A cascade of two-level superconducting artificial atoms—a source and a probe—strongly coupled to a semi-infinite waveguide is a promising tool for observing nontrivial phenomena in quantum nonlinear optics. The probe atom can scatter an antibunched radiation emitted from the source, thereby generating a field with specific properties. We experimentally demonstrate wave mixing between nonclassical light from the coherently cw-pumped source and another coherent wave acting on the probe. We observe unique features in the wave mixing stationary spectrum which differs from the mixing spectrum of two classical waves on the probe. These features are well described by adapting the theory of Gardiner et al. [Phys. Rev. A 50, 1792 (1994)] for a strongly coupled cascaded system of two atoms. We further analyze the theory to predict nonclassical mixing spectra for various ratios of atoms' radiative constants. Both experimental and numerical results confirm the domination of the multiphoton scattering process with only a single photon from the source. We evaluate entanglement of atoms in the quasistationary state and illustrate the connection between the expected second-order correlation function of the source field and wave mixing side peaks corresponding to a certain number of scattered photons.

We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to quantum jumps between the pointer states associated with the nondemolition measurement. A surprising discovery in earlier work [A. Tilloy et al., Phys. Rev. A 92, 052111 (2015)] on quantum trajectories with Brownian noise was the phenomena of spikes observed in-between the quantum jumps. Here, we show that spikes are observed also for Poisson noise. We consider three cases where the nondemolition is broken by adding, to the basic strong measurement dynamics, either unitary evolution or thermal noise or additional measurements. We present a complete analysis of the spike and jump statistics for all three cases using the fact that the dynamics effectively corresponds to that of stochastic resetting. We provide numerical results to support our analytic results.

Quantum-state texture is a newly recognized quantum resource that has garnered attention with the advancement of quantum theory. In this work, we introduce several potential quantum-state texture measure schemes and check whether they satisfy the three fundamental conditions required for a valid quantum-state texture measure. Specifically, the measure induced by the $l_1$ norm serves as a vital tool for quantifying coherence, but we prove that it cannot be used to quantify quantum-state texture. Furthermore, we show that while relative entropy and robustness meet three fundamental conditions, they are not optimal for quantifying quantum-state texture. Fortunately, we still find that there are several measures that can be used as the measure standard of quantum-state texture. Among them, the trace distance measure and the geometric measure are two good measurement schemes. In addition, the two measures based on Uhlmann's fidelity are experimentally friendly and can serve as an ideal definition of quantum-state texture measures in nonequilibrium situations. All this research on quantum-state texture measure theory can enrich the resource theory framework of quantum-state texture.

The simulation of quantum lattice gauge theories faces the major challenge of maintaining gauge invariance because various errors in the simulation push the state of the system out of the physical subspace of the system's exponentially larger Hilbert space. This paper outlines a method, based off of previous work [Phys. Rev. A 110, 022417 (2024)], that uses gauge transformations in two ways. First, the method exploits the Zeno effect by conducting frequent projections to suppress gauge drift. These projections utilize local gauge transformations to destructively interfere unphysical amplitudes via coupling to an ancillary qubit while the physical amplitudes are left untouched, up to a less than unity normalization factor. Second, gauge transformations are conducted throughout the time evolution of the system to hamper the speed of gauge drift. This paper demonstrates this method on a pure one-dimensional SU(2) toy model.

Estimating the ground-state energy of Hamiltonians in quantum systems is an important task. In this work, we demonstrate that the ground-state energy can be accurately estimated without controlled time evolution by using adiabatic state preparation (ASP) and Ramsey-type measurement. By considering the symmetry of the Hamiltonian governing the time evolution during ASP, we can prepare a superposition of the ground state and reference state whose eigenvalue is known. This enables the estimation of the ground-state energy via a Ramsey-type measurement. Furthermore, our method is robust against nonadiabatic transitions, making it suitable for use with early fault-tolerant quantum computers and quantum annealing.

We present a comprehensive theoretical study of the ionization potentials of $M\mathrm{F}$ $(M=\mathrm{Sc},\mathrm{Y},\mathrm{La},\mathrm{Ac})$ molecules using a state-of-the-art relativistic coupled-cluster approach with single, double, and perturbative triple excitations. We further correct our results for higher-order excitations (up to full triples), the QED self-energy, and vacuum-polarization contributions. We extensively investigate the effect of the various computational parameters on the calculated ionization potentials, allowing us to assign realistic uncertainties to our predictions.