Papers

We study time-evolving resonant states in an open double quantum-dot system, taking into account spin degrees of freedom as well as both on-dot and interdot Coulomb interactions. We exactly derived a non-Hermite effective Hamiltonian acting on the subspace of two quantum dots, where the non-Hermiticity arises from an effect of infinite external leads connected to the quantum dots. By diagonalizing the effective Hamiltonian, we identify four types of two-body resonant states. For the initial states of localized two electrons with opposite spins on the quantum dots, we exactly solve the time-dependent Schroedinger equation and obtain time-evolving two-body resonant states. The time-evolving resonant states are normalizable since their wave function grows exponentially only inside a finite space interval that expands in time with electron velocity. By using the exact solution, we analyze the survival and transition probabilities of localized two electrons on the quantum dots.

In Si/SiGe quantum dots, the decoherence behavior of spin qubits usually comes from the non-Markovian effect of the charge noise. To improve the performance of using the coherent noise models in the decoherence simulation and tomography analysis, here we propose a spin-phonon model derived from the electric dipole spin resonance to characterize the decoherence behavior of the spin qubit in a Si/SiGe quantum dot. Utilizing a 1/f spectrum to characterize quantum noise correlation, our stochastic model can yield a more precise prediction of decoherence compared to a random coherence model. We also use gate set tomography (GST) to address the error generator and analyze the model violation coming from the non-Markovian effect. Based on the results, we attribute certain error generators of this model to the incoherence error, which avoids the scenario of using too large a coherent noise strength in the previous study to account for the experimentally observed decoherence times, and thus underestimates the gate fidelity. We also perform a gate optimization and show that our optimized control pulse can substantially reduce the error contribution of the incoherent non-Markovian 1/f charge noise. We further demonstrate that the optimized pulse against incoherent noise is more robust against coherent noise than the regular Gaussian pulse through a filter function analysis in a CPMG protocol, demonstrating the significant effectiveness of the optimized pulse.

Spins in solid-state materials, molecules, and other chemical systems have the potential to impact the fields of quantum sensing, communication, simulation, and computing. In particular, color centers in diamond, such as negatively charged nitrogen vacancy (NV$^-$) and silicon vacancy centers (SiV$^-$), are emerging as quantum platforms poised for transition to commercial devices. A key enabler stems from the semiconductor-like platform that can be tailored at the time of growth. The large growth parameter space makes it challenging to use intuition to optimize growth conditions for quantum performance. In this paper, we use supervised machine learning to train regression models using different synthesis parameters in over 100 quantum diamond samples. We train models to optimize NV$^-$ defects in diamond for high sensitivity magnetometry. Importantly, we utilize a magnetic-field sensitivity figure of merit (FOM) for NV magnetometry and use Bayesian optimization to identify critical growth parameters that lead to a 300% improvement over an average sample and a 55% improvement over the previous champion sample. Furthermore, using Shapley importance rankings, we gain new physical insights into the most impactful growth and post-processing parameters, namely electron irradiation dose, diamond seed depth relative to the plasma, seed miscut angle, and reactor nitrogen concentration. As various quantum devices can have significantly different material requirements, advanced growth techniques such as plasma-enhanced chemical vapor deposition (PE-CVD) can provide the ability to tailor material development specifically for quantum applications.

This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schrödinger equation for a free particle, the work derives first-order symmetry generators, such as translations, rotations, and boosts, and examines their algebraic basis encompassing Lie and Jordan algebras. The analysis is then extended to higher-order operators, demonstrating how they can be constructed from the first-order ones through algebraic operations and Lie algebra simplification. This methodology is applied to the Klein-Gordon equation in Minkowski space-time, yielding relativistic symmetry operators. Furthermore, we defined an approximation to fractional symmetry operators of the Schrodinger equation, and a perturbative approach is employed for a case where the commutation is more general, illustrated with a one-dimensional harmonic oscillator and the fourth-order Klein-Gordon equation. The results include a general formula for the number of operators as a function of the order and the dimension of the algebraic basis, providing a reduced-form development of the differential higher-order centralizers' basis.

In the present article, we assume that the first approximation of the scattering operator is given and that it has the logarithmic divergence. This first approximation allows us to construct the so called deviation factor. Using the deviation factor, we regularize all terms of the scattering operator's approximations. The infrared and ultraviolet cases as well as concrete examples are considered. Thus, for a wide range of cases, we provide a positive answer to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED: “Can the procedure be freed of the expansion in $\varepsilon$ and carried out rigorously?"

A variety of past research on superconducting qubits shows that these devices exhibit considerable variation and thus cannot be accurately depicted by a uniform noise model. To combat this often unrealistic picture of homogeneous noise in quantum processors during runtime, our work aims to define the boundaries of acceptable defectiveness (BADs), or the upper boundary of a qubit's physical error, past which this defective qubit entirely degrades the logical computation and should be considered faulty and removed from the surface code mapping. Here, we present a simulation framework based on the stabilizer simulation package STIM, that allows for rapid experimentation of quantum error correction (QEC) performance under any arbitrary and unique noise model. Using this tool, QEC circuits using rotated surface codes were generated, sampled, and analyzed from distances 3 to 17, with various defective error rates and outlier defect locations. The results suggest that there are, in fact, boundaries of acceptable defectiveness in which a defective qubit, with a physical error rate $\leq 0.75$, can be left in the lattice with negligible impact on logical error rate given sufficient code distances and proper placement in the lattice. Additionally, when modeling noise as a uniform distribution, the logical error rate shows minimal impact with increasing deviation, with $\sigma \leq \mu$. As a result, we propose that defectiveness of both individual qubits and the overall uniformity of lattice fidelity should not be viewed as all or nothing, but instead as a spectrum. Our research demonstrates how heterogeneity relates to the logical error rate and, through the framework provided, facilitates the development of preliminary goals and metrics for hardware designers to meet to achieve target logical performance with imperfect or nonuniform qubit qualities.

The identification of platforms with independently tunable nonlinearity and non-Hermiticity promises a quantitative route to far-from-equilibrium universality across many-body systems. Here we show that a conventional ferromagnetic multilayer realizes this paradigm: balancing a dc drive against Gilbert damping stabilizes a self-organized, current-carrying nonequilibrium condensate that spontaneously breaks spacetime-translation symmetry. The chirality of this spin superfluid limit cycle state generates an inherently nonreciprocal flow: long-wavelength magnons of opposite chirality acquire asymmetric dispersions and propagate direction-selectively, realizing a spin superfluid diode. This asymmetry is flow-borne - it reflects broken Galilean invariance and requires neither structural asymmetry nor finely tuned gain-loss balance. Linearized dynamics in the comoving superfluid frame are intrinsically pseudo-Hermitian and, in the long-wavelength sector, can be mapped to a (1+1)D wave equation on curved spacetime. Spatial modulation of the drive enables the generation of sonic horizons that parametrically amplify magnon pairs and produce Hawking-like particle-hole emission. Our results establish a tabletop route from nonlinear dissipative-driven magnetization dynamics to nonreciprocal transport, nonequilibrium phase transitions, and analogue-gravity kinematics.

Solutions of the time-dependent Schrödinger equation are mapped to other solutions for a (possibly) different potential by so-called form-preserving transformations. These time-dependent transformations of the space and time coordinates can produce remarkable solutions with surprising properties. A classic example is the force-free accelerating Airy beam found by Berry and Balazs. We review the 1-dimensional form-preserving transformations and show that they also yield Senitzky coherent excited states and the free dispersion of any harmonic-oscillator stationary state. Form preservation of the $D$- and 3-dimensional Schrödinger equation with both a scalar and a vector potential is then considered. Time-dependent rotations may be included when a vector potential is present; we find a general transformation formula for this case. Quantum form-preserving maps are also considered in phase space. First, the wave-function transformation is shown to produce a simple result for Wigner functions: they transform as a true phase-space probability would. The explicit transformation formula explains and generalizes the rigid evolution of curves in phase space that characterize the Airy beam and the coherent excited states. Then we recover the known form-preserving transformations from the Moyal equation obeyed by Wigner functions.

This paper presents a novel formalism for the out of equilibrium dynamics of the density matrix, capable of describing highly entangled many-body interactions. The evolution of quantum states is evaluated via eigenvalue dynamics of a general Hamiltonian system, perturbed by a parametrically evolving variable $\lambda(t)$ that carries the time-dependence. This is achieved using the Pechukas-Yukawa mapping of the evolution of the energy levels governed by their initial conditions on a generalised Calogero-Sutherland model of a 1D classical gas. As such, quantum systems can be described exactly in their entirety from eigenvalue dynamics. Under this description, we provide an improved understanding of the relationship between nonequilibrium quantum phase transitions and decoherence which has significant impacts to a wide range of applications.

Controlling topological phases is a central goal in quantum materials and related fields, enabling applications such as robust transport and programmable edge states. Here we uncover a mechanism in which local on-site impurities act as knobs to decompose global topological properties in discrete steps. In non-Hermitian lattices with spectral winding topology, we show that each impurity sequentially reduces the winding number by one, which is directly manifested as a stepwise decomposition of quantized plateaus in the steady-state response. Based on this principle, we further develop a scheme that sequentially induces topological edge states under impurity control, in a class of Hermitian topological systems constructed by doubling the non-Hermitian ones. Our findings reveal a general scheme to tune global topological properties with local perturbations, establishing a universal framework for impurity-controlled topological phases and offering a foundation for future exploration of reconfigurable topological phenomena across diverse physical platforms.

The influence matrix (IM) provides a powerful framework for characterizing nonequilibrium quantum many-body dynamics by encoding multitime correlations into tensor-network states. Understanding how its computational complexity relates to underlying dynamics is crucial for both theoretical insight and practical utility, yet remains largely unexplored despite a few case studies. Here, we address this question for a family of brickwork quantum circuits ranging from integrable to chaotic regimes. Using tools from geometric group theory, we identify three qualitatively distinct scalings of temporal entanglement entropy, establishing a hierarchy of computational resources required for accurate tensor-network representations of the IM for these models. We further analyze the memory structure of the IM and distinguish between classical and quantum temporal correlations. In particular, for certain examples, we identify effectively classical IMs that admit an efficient Monte Carlo algorithm for computing multitime correlations. In more generic settings without an explicit classical description of the IM, we introduce an operational measure of quantum memory with an experimental protocol, and discuss examples exhibiting long-time genuinely quantum correlations. Our results establish a new connection between quantum many-body dynamics and group theory, providing fresh insights into the complexity of the IM and its intricate connection to the physical characteristics of the dynamics.

The Cable Routing Optimization Problem (CROP) is a Multi-Commodity Flow Problem (MCFP) central to industrial layouts and smart manufacturing. Historically, quantum optimization has modeled MCFPs as Quadratic Unconstrained Binary Optimization problems (QUBOs). Recent studies suggest that mapping routing problems to Polynomial Unconstrained Binary Optimization problems (PUBOs) can improve efficiency. However, solving full-scale MCFPs with quantum optimization remains computationally challenging. To bridge this gap, we introduce a Decomposed Variational Quantum Pipeline that exploits the block-diagonal structure of CROP, breaking the multi-cable routing task into modular, single-commodity subproblems. We explicitly derive both the QUBO and PUBO representations for CROP and demonstrate that our pipeline can evaluate both formulations within the same pipeline. Our empirical study highlights a trade-off: PUBO eliminates auxiliary qubits at the cost of circuit depth. In our experiments, the decomposed pipeline accelerates time-to-solution, reliably generating feasible cable layouts while trading strict optimality for computational scalability. PUBO formulations achieved full routing feasibility across all tested seeds, while global QUBO formulations showed substantially lower robustness.

Here we address the fundamental question of whether an idealized system of $N$ atoms will show collective behavior and superradiance when it emits fermions instead of photons. We show that for single-fermion emission processes, the maximum emission is $\propto N$ and not $\propto N^2$, which proves the absence of superradiance and shows that the recent proposal to realize a superradiant neutrino laser is impossible. This can be understood as either destructive interference of fermionic transition amplitudes, or Pauli blockade by collective excitations with fermionic nature. We derive the exact solution of the fermionic Dicke problem and analyze the decay dynamics in various regimes. We extend the proof to arbitrary Hamiltonians and show that the jump rate operator for neutrino emission has a maximum eigenvalue of $N$ times the single-particle rate $\Gamma_0$. States with low excitation can show collective behavior and emit at a rate of $N \Gamma_0$.

This paper lays out the principles of how Bose-Einstein condensates can modify radioactive decay. We highlight the challenges of many modes and short coherence times due to the $\approx$ MeV energies of the emitted radiation. Recent proposals for gamma ray and neutrino lasers claim that using a Bose-Einstein condensate as a source would solve these issues. We show that this is not the case, and the proposed experiments would have a gain of only $10^{-16}$ or smaller. We also analyze proposals for gamma ray lasers based on stimulated annihilation of positronium Bose-Einstein condensates.

In the quantum world, the process of energy storage can be enhanced thanks to various nonclassical phenomena. This inspiring fact suggests quantum batteries as plausible sources of power for future quantum devices, at least in principle. However, thermodynamically not all of the energy stored in a quantum battery is useful for doing work. By considering a class of models based upon quantum continuous variables, here we show how the maximum extractable energy from a bosonic quantum battery can be intimately related to Heisenberg's uncertainty principle. We found that realizing minimum uncertainty essentially guarantees that all of the energy stored in a Gaussian quantum battery can be withdrawn and used to do work. For a standard system where the charger and battery are coupled linearly, this criterion is satisfied rather trivially. However, our theoretical results demonstrate that - for a quantum battery with nonlinear coupling - a state of minimum uncertainty can also be achieved nontrivially via the generation of quantum squeezing. We characterize the charging performance of our proposed continuous variable quantum batteries in detail, and we hope that our theory may be useful in the design of a new generation of efficient quantum batteries harnessing bosonic excitations, such as those built with photonic architectures.

The time-dependence of multi-point observable correlation functions are essential quantities in analysis and simulation of quantum dynamics. Open quantum systems approaches utilize two-point correlations to describe the influence of an environment on a system of interest, and in studies of chaotic quantum system, the out-of-time-ordered correlator (OTOC) is used to probe chaoticity of dynamics. In this work we analytically derive the time dependence of multi-point observable correlation functions in quantum systems from a random matrix theoretic approach, with the highest order function of interest being the OTOC. We find in each case that dynamical contributions are related to a simple function, related to the Fourier transform of coarse-grained wave-functions. We compare the predicted dynamics to exact numerical experiments in a spin chain for various physical observables. We comment on implications towards the emergence of Markovianity and quantum regression in closed quantum systems, as well as relate our results to known bounds on chaotic dynamics.

An elementary particle such as a photon cannot be cut in two pieces. Still it must be possible to truncate a photon with an optical shutter. The result is neither another photon nor a mix of a photon and a vacuum. Instead it is a superposition and mix of photon numbers up to infinity. This state is rather complicated, but nevertheless locally equivalent to a single photon or vacuum to the left and right, respectively, of a narrow transition region.

Rydberg atomic radio-frequency (rf) sensors are an emerging technology platform that relies on vaporous atoms, interrogated with laser beams and nearly ionized, to receive rf signals. Rydberg rf sensors have a number of interesting fundamental distinctions from traditional receiver technologies, such as those based on metallic antennas, since they are governed by the quantum physics of atom-light interactions. As Rydberg sensors quickly advance from laboratory experiments into fieldable devices, there is a need for a general software modeling tool that fully encompasses the internal physics of the sensor. The Rydberg Interactive Quantum Module (RydIQule) is a Python package designed to fill this need. The initial public release of RydIQule in late 2023 built the core functionality described above. Here we outline RydIQule's version 2 release which expands on its capabilities to more accurately model real-world atoms.

We introduce a prototype FPGA decoder implementing the recently discovered Relay-BP algorithm and targeting memory experiments on the $[[144,12,12]]$ bivariate bicycle quantum low-density parity check code. The decoder is both fast and accurate, achieving a belief propagation iteration time of 24ns. It matches the logical error performance of a floating-point implementation despite using reduced precision arithmetic. This speed is sufficient for an average per cycle decoding time under $1\,\mathrm{\mu s}$ assuming circuit model error probabilities are less than $3 \times 10^{-3}$. This prototype decoder offers useful insights on the path toward decoding solutions for scalable fault-tolerant quantum computers.

Although Shapley additive explanations (SHAP) can be computed in polynomial time for simple models like decision trees, they unfortunately become NP-hard to compute for more expressive black-box models like neural networks - where generating explanations is often most critical. In this work, we analyze the problem of computing SHAP explanations for *Tensor Networks (TNs)*, a broader and more expressive class of models than those for which current exact SHAP algorithms are known to hold, and which is widely used for neural network abstraction and compression. First, we introduce a general framework for computing provably exact SHAP explanations for general TNs with arbitrary structures. Interestingly, we show that, when TNs are restricted to a *Tensor Train (TT)* structure, SHAP computation can be performed in *poly-logarithmic* time using *parallel* computation. Thanks to the expressiveness power of TTs, this complexity result can be generalized to many other popular ML models such as decision trees, tree ensembles, linear models, and linear RNNs, therefore tightening previously reported complexity results for these families of models. Finally, by leveraging reductions of binarized neural networks to Tensor Network representations, we demonstrate that SHAP computation can become *efficiently tractable* when the network's *width* is fixed, while it remains computationally hard even with constant *depth*. This highlights an important insight: for this class of models, width - rather than depth - emerges as the primary computational bottleneck in SHAP computation.

We investigate precise structural relations between the standard Schrödinger equation and its Carrollian analogue-the Carroll-Schrödinger equation-in 1+1 dimensions, with emphasis on dualities, potential maps, and solution behavior. Our contributions proceed in the order of the paper: (i) we encode both dynamics with operators $H$ and $F$ under external potentials and explore conditions for obtaining the same type of solutions within both formalisms; (ii) we construct a potential-dependent reparametrization $x = \delta(t)$ mapping the space-independent Carroll equation to the time-independent Schrödinger equation, and derive a Schwarzian relation that specifies the map $\delta$ for any static $V_{sch}$ (with harmonic, Coulomb-like, and free examples); (iii) we relate conserved densities and currents by removing $V_{car}$ through a gauge transform followed by a coordinate inversion, establishing equivalence of the continuity equations; (iv) we obtain a Carrollian dispersion relation from an ultra-boost of the energy-momentum two-vector and also derive the classical limit of the Carroll wave equation via the Hamilton-Jacobi formalism; (v) we place Carroll dynamics on an equal-$x$ Hilbert space $L^2(R_t)$, prove unitary $x$-evolution, and illustrate dynamics with an exactly solvable Gaussian packet and finite-time quantization for time-localized perturbations; and (vi) for general $V(x; t)$ we perform a gauge reduction to an interaction momentum and set up a controlled Dyson expansion about solvable time profiles.

Non-Hermitian Hamiltonians with complex eigenenergies are useful tools for describing the dynamics of open quantum systems. In particular, parity and time (PT) symmetric Hamiltonians have generated interest due to the emergence of exceptional-point degeneracies, where both eigenenergies and eigenvectors coalesce as the energy spectrum transitions from real- to complex-valued. Because of the abrupt spectral response near exceptional points, such systems have been proposed as candidates for precision quantum sensing. In this work, we emulate a passive PT dimer using a two-mode, non-Hermitian system of superconducting qubits comprising one high-coherence qubit coupled to an intentionally lossy qubit via a tunable coupler. The loss is introduced by strongly coupling the qubit to a continuum of photonic modes in an open waveguide environment. Using both pulsed and continuous-wave measurements, we characterize the system dynamics near the exceptional point. We observe a behavior broadly consistent with an ideal passive PT dimer with some corrections due to the tunable coupler element. We extract the complex eigenenergies associated with the two modes and calculate the sensitivity as a function of the coupling strength. Confirming theoretical predictions, we observe no sensitivity enhancement near the quantum exceptional point. This work elucidates the limitations of exceptional-point systems as candidates for quantum-enhanced sensing. We establish waveguide quantum electrodynamics as a versatile platform for exploring non-Hermitian quantum dynamics in superconducting circuits.

Multi-period stock-keeping unit (SKU) allocation in supply chains is a combinatorial optimization problem that is both NP-hard and operationally critical, requiring simultaneous attention to profitability, feasibility, and diversity. Quadratic unconstrained binary optimization (QUBO) provides a principled framework for such tasks, yet prior studies often rely on simplified assumptions or omit real operational constraints. This work proposes a hybrid QUBO framework integrating three advances: (i) a quantum-derived similarity kernel, obtained from a variational RX embedding, to discourage redundant SKU selections; (ii) exact per-period capacity enforcement via slack-bit encoding to maintain feasibility; and (iii) execution on a time-multiplexed Coherent Ising Machine (CIM) benchmarked against simulated quantum annealing (SQA) and classical optimization algorithms. The resulting model, with over one million quadratic terms and about 4,100 variables, captures profit, risk, and capacity interactions within a unified formulation. On a dataset of 500 SKUs across eight planning periods, Quanfluence's CIM achieved an energy of minus 2.95 times 10 to the power of 16, producing robust solutions with 288 distinct SKUs (approximately 60 percent of the catalog), 226,813 allocated units, and 12.75 million dollars profit, all with zero capacity violations. These results demonstrate that hybrid quantum-classical QUBO methods can deliver feasible and profitable supply-chain allocations at an industrial scale.

From "surreal" trajectories to which-way measurements, Basil Hiley had a lesson: claims of falsifying the Bohmian model do not withstand scrutiny provided the model is applied correctly. In this work we compute de Broglie-Bohm trajectories for particles tunneling in coupled waveguides relevant to a recent experiment having claimed to challenge the Bohmian model. We show that the Bohmian model - correctly applied - gives results identical to the standard quantum approach, first by working out a simple one-dimensional model, and then by computing Bohmian trajectories for the full two-dimensional problem representing a quantum particle propagating inside coupled waveguides. We further recall the contextual nature of the Bohmian trajectories whereby the trajectories of a closed system differ from the ones observed when an interaction with a measurement apparatus takes places.

Hybrid quantum systems that combine discrete-variable (DV) and continuous-variable (CV) architectures represent a promising direction in quantum information science. However, transferring concepts, information, and states between these platforms poses practical and theoretical challenges, as their formalisms assign different properties and physical interpretations to many shared notions. We construct a bridge between DV spin systems and restricted CV bosonic systems within corresponding sectors using the tomographic probability representation of quantum states and the Jordan–Schwinger and Holstein–Primakoff maps. Although these maps are well known at the operator level, their action on tomograms and other probability representations has not been addressed in the literature. To the best of our knowledge, we provide the first explicit demonstration of their action on tomographic probability distributions and Wigner functions, establishing direct correspondences between the measurement statistics of DV systems and the corresponding restricted CV bosonic representations. Our tomographic mapping transfers measurement data between quantum architectures through an intrinsic data compression kernel that selects the Hilbert space sector relevant to the target representation. It yields the tomogram of a target sector directly from experimental data in another representation, without reconstructing the density matrix. This provides a unified framework for transferring and comparing quantum information across different hardware platforms within the corresponding restricted sectors, with applications to hybrid protocols, device benchmarking, and the validation of error correction schemes based on mappings between finite-dimensional systems and sector restricted bosonic representations.

Photonic quantum gases explore the physics of open driven-dissipative quantum systems under ambient conditions and thus open access to thermodynamics and transport phenomena in quantum gases in the weakly interacting regime. Here we introduce the technology of 3D micro-printing to create potential landscapes for photonic quantum gases in dye-filled micro cavities, which surpass the current state of the art in terms of potential size and definition, potential depth, coupling strength, and number of coupled potentials by at least an order of magnitude. We realize as demonstration of the capabilities box potentials with rectangular side walls, anisotropic harmonic potentials, double-well potentials with dimensions on the scale of the wavelength of light as well as potential lattices with topological non-trivial properties. This approach paves the way for experimentally studying the physics of open quantum systems on lattices and might find applications in solving complex ground-state problems like the XY-model.

Coherent control of quantum emitters is essential for scalable quantum photonic technologies. The recently proposed swing-up of quantum emitter (SUPER) scheme allows efficient and coherent preparation of single photons via off-resonant, red-detuned laser pulses, simplifying laser suppression and enhancing photon collection. We present a systematic study of SUPER excitation applied to a single GaAs quantum dot in a low-Q micropillar cavity. We perform a comparison of the key figures of merit against the well-established two-photon excitation (TPE). Despite requiring higher excitation powers, SUPER achieves near-unity population inversion of the exciton state ($\sim$95%) and high single-photon purity ($g^{(2)}=0.03$) comparable to that under TPE, while also exhibiting a shortened decay time ($\sim$200 ps) reducing the time jitter in the exciton population. A polarization-resolved analysis reveals that when both excitation and collection are aligned with one of the exciton dipoles, SUPER results in polarized single-photon emission, exceeding the resonant TPE saturation by a factor of 1.45. Under optimized excitation conditions, we also observe biexciton preparation via a distinct SUPER resonance, confirmed by the appearance of the biexciton emission line, constituting the first experimental demonstration of biexciton preparation using SUPER. These findings are in good agreement with a proposed four-level theoretical model that incorporates the biexciton state. We also report that a slight misalignment of laser polarization induces an additional SUPER resonance that selectively populates the orthogonal exciton dipole, without altering the nominal excitation polarization. This unexpected behavior reveals a new degree of freedom for coherent state preparation. Our findings establish the SUPER scheme as a versatile tool for state-selective exciton and biexciton control.

We examine excitation suppression in the transverse-field Ising model (TFIM), where finite-time drive across a quantum critical point is assisted by the presence of a time-dependent coupling parameter. While conventional counterdiabatic protocols are designed to eliminate excitations, they often require complex many-body terms that are difficult to realize experimentally. In contrast, our approach employs a local, time-dependent modulation of an existing coupling term in the Hamiltonian. Within the framework of quantum optimal control, we find that under a linear ramp of the transverse field, the optimal evolution of the second parameter follows a non-monotonic trajectory. For the TFIM, this protocol yields higher fidelity and improved robustness against noise compared to several orders of approximate counterdiabatic driving. Furthermore, we provide an analytical demonstration of anti-Kibble-Zurek scaling in the presence of noise acting on either the transverse field or the longitudinal coupling. These results highlight the potential of this approach for developing simple, noise-resilient protocols for finite-time quantum state preparation.

Unnormalized probability distributions are central to modeling complex physical systems across various scientific domains. Traditional sampling methods, such as Markov Chain Monte Carlo (MCMC), often suffer from slow convergence, critical slowing down, poor mode mixing, and high autocorrelation. In contrast, likelihood-based and adversarial machine learning models, though effective, are heavily data-driven, requiring large datasets and often encountering mode covering and mode collapse. In this work, we propose ScoreNF, a score-based learning framework built on the Normalizing Flow (NF) architecture, integrated with an Independent Metropolis-Hastings (IMH) module, enabling efficient and unbiased sampling from unnormalized target distributions. We show that ScoreNF maintains high performance even with small training ensembles, thereby reducing reliance on computationally expensive MCMC-generated training data. We also present a method for assessing mode-covering and mode-collapse behaviours. We validate our method on synthetic 2D distributions (MOG-4 and MOG-8) and the high-dimensional $\phi^4$ lattice field theory distribution, demonstrating its effectiveness for sampling tasks.

Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian exponents, in order to improve the accuracy of the fitting approach. Second, an indirect fitting method is proposed, allowing for the oscillatory behaviour of continuum functions to be conserved up to infinity as a factorized asymptotic function, while the Gaussian representation is applied to some appropriately defined distortion factor with limited spatial extension. As an illustration, the method is applied to radial Coulomb functions with realistic energy parameters. We also show that the indirect fitting approach keeps the advantageous analytical structure of typical one-electron transition integrals occurring in molecular ionization applications.