Papers

We study spectral moments of the Bures-Hall random matrices ensemble. The main result establishes a recurrence relation for the $k$-th spectral moment valid for a real-valued $k$, in contrast to prevailing results in the literature of different ensembles of assuming an integer $k$. The key to establish the recurrence relation is the obtained Christoffel-Darboux formulas of correlation kernels of the ensemble that avoid tedious summations. As an application of our spectral moment results, we re-derive the formulas of average von Neumann entropy and quantum purity of Bures-Hall ensemble conjectured by Ayana Sarkar and Santosh Kumar. This work is dedicated to the memory of Santosh Kumar.

Superconducting qubits are a leading candidate for utility-scale quantum computing due to their fast gate speeds and steadily decreasing error rates. The requirement for millikelvin operating temperatures, however, creates a significant scaling bottleneck. Modular architectures using optical fiber links could bridge separate cryogenic nodes, but superconducting circuits do not have coherent optical transitions and microwave-to-optical conversion has not been shown for any non-classical photon state. In this work, we demonstrate the on-demand generation and tomographic reconstruction of itinerant single microwave photons at 8.9 GHz from a superconducting qubit. We upconvert this non-Gaussian state with a transducer added noise below 0.012 quanta and count the converted telecom photons at 193.4 THz with a signal-to-noise ratio of up to 5.1$\pm$1.1. We characterize the trade-offs between throughput and noise, and establish a viable path toward heralded entanglement distribution and gate teleportation. Looking ahead, these results empower existing superconducting devices to take a key role in distributed quantum technologies and heterogeneous quantum systems.

One-sided device-independent quantum key distribution (1SDI-QKD) offers a practical middle ground between fully device-independent protocols and standard QKD, achieving security with detection efficiencies as low as 50.1% on the untrusted side. However, prior analyses assumed idealized channels. This work extends the 1SDI-QKD framework to amplitude damping, dephasing, and depolarizing noise. Results reveal a clear noise hierarchy: dephasing tolerates the most noise before security is lost ($p_{\text{crit}} \approx 0.50$ versus 0.449 and 0.220 respectively), while depolarizing noise imposes the most stringent detection efficiency requirements, exceeding 97% at 20% noise where amplitude damping requires 76%. Security is lost while substantial entanglement remains ($C \approx 0.67$–$0.74$), demonstrating that steering violation, not merely entanglement, determines 1SDI-QKD security. Integrating the BBPSSW purification protocol shows that it functions primarily as a range-extension mechanism: five rounds extend dephasing-limited operation from 10~km to 36~km at 90% detection efficiency. Accounting for both the $2^n$ pair cost and the cumulative success probability, the effective rate peaks at $ 10^{-3}$ bits per initial pair for dephasing but only $ 10^{-6}$ for amplitude damping and depolarizing noise, identifying phase noise limited links as the regime where purification is worthwhile.

Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.

Quantum dynamics retains a permanent and universal memory of its initial conditions, even in systems whose spectra display fully chaotic, random-matrix behavior. This effect, known as the quantum birthmark, appears as an enhancement of the long-time return probability of any non-stationary state compared to the overlap with a typical ergodic state. In this work, we develop the full theoretical foundation for this universal contribution that depends only on the global symmetry class and accessible Hilbert-space dimension, not on the microscopic dynamics. Our findings reveal that quantum evolution preserves an unavoidable, symmetry-controlled imprint of its origin, a quantum effect calling into question classical expectations of ergodicity and the resulting thermalization scenarios.

Given the query, key and value matrices $Q, K, V\in \mathbb{R}^{n\times d}$, the attention module is defined as $\mathrm{Att}(Q, K, V)=D^{-1}AV$ where $A=\exp(QK^\top/\sqrt{d})$ with $\exp(\cdot)$ applied entrywise, $D=\mathrm{diag}(A{\bf 1}_n)$. The attention module is the backbone of modern transformers and large language models, but explicitly forming the softmax matrix $D^{-1}A$ incurs $\Omega(n^2)$ time, motivating numerous approximation schemes that reduce runtime to $\widetilde O(nd)$ via sparsity or low-rank factorization. We propose a quantum data structure that approximates any row of $\mathrm{Att}(Q, K, V)$ using only row queries to $Q, K, V$. Our algorithm preprocesses these matrices in $\widetilde{O}\left( \epsilon^{-1} n^{0.5} \left( s_\lambda^{2.5} + s_\lambda^{1.5} d + \alpha^{0.5} d \right) \right)$ time, where $\epsilon$ is the target accuracy, $s_\lambda$ is the $\lambda$-statistical dimension of the exponential kernel defined by $Q$ and $K$, and $\alpha$ measures the row distortion of $V$ that is at most $d/{\rm srank}(V)$, the stable rank of $V$. Each row query can be answered in $\widetilde{O}(s_\lambda^2 + s_\lambda d)$ time. To our knowledge, this is the first quantum data structure that approximates rows of the attention matrix in sublinear time with respect to $n$. Our approach relies on a quantum Nyström approximation of the exponential kernel, quantum multivariate mean estimation for computing $D$, and quantum leverage score sampling for the multiplication with $V$.

Bidirectional devices are devices for which the roles of the input and output ports can be exchanged. Mathematically, these devices are described by bistochastic quantum channels, namely completely positive linear maps that are both trace-preserving and identity-preserving. Recently, it has been shown that bidirectional quantum devices can, in principle, be used in ways that are incompatible with a definite input-output direction, giving rise to a new phenomenon called input-output indefiniteness. Here we characterize the most general forms of input-output indefiniteness, associated with a hierarchy of higher-order transformations built from transformations of bistochastic quantum channels. Some levels of the hierarchy correspond to transformations that combine bistochastic channels in a definite causal order, while generally using each channel in an indefinite input-output direction. For other levels of the hierarchy, the indefiniteness can involve both the local input-output direction of each process and the global causal order among the processes. On the foundational side, the hierarchy of higher-order transformations characterized here can be regarded as the largest set of physical processes compatible with a time-symmetric variant of quantum theory, where the possible state transformations are restricted to bistochastic channels.

Barren plateaus in variational quantum algorithms are typically described by gradient concentration at random initialization. In contrast, rigorous results for the Hessian, even at the level of entry-wise variance, remain limited. In this work, we analyze the scaling of Hessian-entry variances at initialization. Using exact second-order parameter-shift identities, we write $H_{jk}$ as a constant-size linear combination of shifted cost evaluations, which reduces ${\rm Var}_\rho(H_{jk})$ to a finite-dimensional covariance–quadratic form. For global objectives, under an exponential concentration condition on the cost at initialization, ${\rm Var}_\rho(H_{jk})$ decays exponentially with the number of qubits $n$. For local averaged objectives in bounded-depth circuits, ${\rm Var}_\rho(H_{jk})$ admits polynomial bounds controlled by the growth of the backward lightcone on the interaction graph. As a consequence, the number of measurement shots required to estimate $H_{jk}$ to fixed accuracy inherits the same exponential (global) or polynomial (local) scaling. Extensive numerical experiments over system size, circuit depth, and interaction graphs validate the predicted variance scaling. Overall, the paper quantifies when Hessian entries can be resolved at initialization under finite sampling, providing a mathematically grounded basis for second-order information in variational optimization.

Energy Absorption Interferometry (EAI) is a technique for measuring the responsivities and complex-valued spatial polarimetric forms of the individual degrees of freedom through which a many-body system can absorb energy. It was originally formulated using the language of quantum correlation functions, making it applicable to different kinds of excitation (electromagnetic, elastic and acoustic fields). EAI has been applied in a variety of theoretical and experimental ways. It is particularly effective at characterising the multimode behaviour of ultra-low-noise far-infrared and optical devices, imaging arrays, and complete instruments, where it can be used to ensure that a system is maximally responsive to those partially coherent fields that carry signal whilst avoiding those that only carry noise. Despite its utility there is no comprehensive overview of electromagnetic EAI. In this paper we describe the theoretical foundations of the method, and present a range of new techniques in areas relating to sampling, phase referencing, mode reconstruction and noise. We present, for the first time, an analysis of how noise propagates through an experiment resulting in errors and artefacts on spectral and modal plots. A noise model is essential, because it determines the signal to noise ratio needed to ensure a given level of experimental fidelity.

We describe a spin interferometer using ultracold YbF molecules and develop the complete set of techniques needed to measure the electron's electric dipole moment, $d_e$, with this apparatus. The molecules are cooled in an optical molasses and prepared in a single internal quantum state. A Raman transition prepares a spin superposition which evolves in parallel magnetic and electric fields before a second Raman transition maps the phase onto the populations of two hyperfine states. These populations are read out using detectors that have spatial and temporal resolution and approach unit efficiency. We characterize the efficiencies and fidelities of all these steps and evaluate the sensitivity of this approach to measuring $d_e$.

This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory, Kubo formulas and semiclassical Boltzmann transport theory to the nonlinear response regime, we discuss several predictions of novel transport effects and physical insights that emerge from these developments.

Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach–Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér–Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.

Nitrogen-vacancy (NV) centers in diamond enable quantitative magnetic imaging, yet practical implementations must balance spatial resolution against acquisition time (and thus per-pixel sensitivity). Single-NV scanning magnetometry achieves genuine nanoscale resolution, nonetheless requires typically a slow pixel-by-pixel acquisition. Meanwhile, wide-field NV-ensemble microscopy provides parallel readout over a large field of view, however is jointly limited by the optical diffraction limit and the sensor-sample standoff. Here, we present a sparse-sampling strategy for reconstructing high-resolution wide-field images from only a small number of measurements. Using simulated NV-ensemble detection of ac magnetic fields, we show that a mean-adjusted Bayesian estimation (MABE) framework can reconstruct 10000-pixel images from only 25 sampling points, achieving SSIM values exceeding 0.999 for representative smooth field distributions, while optimized dynamical-decoupling pulse sequences yield an approximately twofold improvement in magnetic-field sensitivity. The method further clarifies how sampling patterns and sampling density affect reconstruction accuracy and suggests a route toward faster and more scalable magnetic-imaging architectures that may extend to point-scanning NV sensors and other magnetometry platforms, such as SQUIDs, Hall probes, and magnetic tunnel junctions.

Dirac exceptional points (EPs) represent a novel class of non-Hermitian singularities that, unlike conventional EPs, reside entirely within the parity-time unbroken phase and exhibit linear energy dispersion. Here, we theoretically investigate the quantum geometry of Dirac EPs realized in nitrogen-vacancy centers in diamond, utilizing fidelity susceptibility as a probe. We demonstrate that despite the absence of a symmetry-breaking phase transition, the Dirac EP induces a pronounced geometric singularity, confirming the validity of the fidelity in characterizing non-Hermitian EPs. Specifically, the real part of the fidelity susceptibility diverges to negative infinity, which serves as a signature of non-Hermitian criticality. Crucially, however, we reveal that this divergence exhibits a distinct anisotropy, diverging along the non-reciprocal coupling direction while remaining finite along the detuning axis. Furthermore, we establish that this anisotropy, characterized by at least one exact dark direction coexisting with divergent directions, is a generic consequence of the Dirac EP structure whenever the parameter derivatives collectively span the off-diagonal operator space at the Dirac EP. This behavior stands in stark contrast to the omnidirectional divergence observed in conventional EPs. Our findings provide a comprehensive picture of the fidelity probe near the Dirac EP, highlighting the critical role of parameter directionality in exploiting Dirac EPs for quantum control and sensing applications.

We present a quantum circuit architecture for the one-to-two cloning of $N$-qubit registers. It implements the broad class of Pauli cloners by extending the Niu–Griffiths architecture to multi-qubit systems. In the single-qubit case, we provide explicit constructions for asymmetric universal, phase covariant and biased cloners. We explore the fundamental relationship between Pauli errors, mutually unbiased bases and Pauli cloning. Furthermore, we demonstrate how Pauli cloners can be tailored to specific noise models in the context of quantum communication, especially quantum key distribution.

As quantum computing transitions from theoretical physics to engineering applications, there is a growing need for accessible simulation tools that bridge the gap between abstract linear algebra and practical implementation. While text-based frameworks (like Qiskit or Cirq) are standard, they often present a steep learning curve for students and engineers accustomed to graphical system design. This paper introduces QuVI (Quantum Virtual Instrument), an open-source quantum circuit toolkit developed natively within the NI LabVIEW environment. Moving beyond initial proof-of-concept models, QuVI establishes a robust framework that leverages LabVIEW's "dataflow" paradigm, in which wires represent data and nodes represent operations, to provide an intuitive, visual analog to standard quantum circuit notation while enabling the seamless integration of classical control structures like loops and conditionals. The toolkit's capabilities are demonstrated by constructing and visualizing fundamental quantum algorithms and verifying results against theoretical predictions. By translating "Block Diagrams" directly into quantum state evolutions ("Bloch Spheres"), QuVI offers educators and researchers a powerful platform for prototyping quantum logic without leaving the graphical engineering workspace.

We study mirror descent in which the objective gradient is replaced by a general vector field. Since such a field does not automatically relate the mirror update to the objective gap, we introduce a trajectory-wise generalized relative-smoothness condition and a generalized star-convexity interface. Together they yield a finite-horizon, a posteriori last-iterate certificate with an accumulated-stepsize term and an exceptional-region-dependent error term. We also give a pointwise sufficient condition for positive admissible stepsizes, displaying the effects of objective smoothness, mirror-map conditioning, and vector-field mismatch. We then construct a deterministic zeroth-order instance from coordinate central differences. The function values place the unknown gradient in an explicit uncertainty box, and verification of the interface reduces to robust conic dominance. We derive an explicit scaling of the central-difference vector that guarantees the required dominance over the gradient uncertainty set. Under uniform Hessian bounds, the resulting vector field satisfies the interface outside an explicit resolution-dependent neighborhood. The final guarantee combines a rate term governed by accumulated accepted stepsizes with a finite-resolution error floor.

Thermal light sources exhibiting photon bunching have been suggested for sensing applications that exploit timing correlations of stationary light, including range finding, clock synchronization, and non-line-of-sight imaging. However, these proposals have remained unrealized in practice because available sources of photon bunching either possess coherence times too short to be timing resolved by photodetectors, or produce brightness levels too low to tolerate realistic return losses. In this work, we demonstrate a low-loss method for generating photon bunching with a conversion efficiency nearly 9 orders of magnitude higher than that achieved by many other bunching processes.

We advance “Latent entropy" (L-entropy) as a novel measure to characterize genuine multipartite entanglement in pure states, applicable to quantum systems with both finite and infinite degrees of freedom. This measure, derived from an upper bound on reflected entropy, attains its maximum for three-party GHZ states and $n=4,5$-party $2$-uniform states. We establish that it satisfies all essential properties of a genuine multipartite entanglement measure, including being a pure-state entanglement monotone. We further obtain an analogue of the Page curve by analyzing the behavior of L-entropy in multiboundary wormholes, emphasizing their connection to multipartite entanglement in random states. Specifically, for $n = 5$, we show that random states approximate $2$-uniform states, exhibiting maximal multipartite entanglement. Extending these ideas to finite temperatures, we introduce the Multipartite Thermal Pure Quantum (MTPQ) state, a generalization of the thermal pure quantum state to multipartite systems, and demonstrate that the entanglement structure in states of the multicopy SYK model exhibits finite-temperature $2$-uniform behavior.

Quantum reservoir computing (QRC) is a promising quantum machine learning framework for near-term quantum platforms, yet the performance of different QRC architectures under realistic constraints remains largely unexplored. Here, we provide a comparative numerical study of single-step-QRC (SS-QRC) and multi-step-QRC (MS-QRC) architectures implemented on a Rydberg atom array. We demonstrate that while MS-QRC performance is highly sensitive to the underlying dynamical phase of matter and decoherence, SS-QRC exhibits greater robustness. Using the randomized measurement toolbox to mitigate measurement overhead, we reveal that sampling noise undermines the convergence property required for MS-QRC. This leads to a significant reduction in the information processing capacity (IPC) of MS-QRC, deteriorating its performance on nonlinear time-series benchmarks. In contrast, SS-QRC maintains high IPC and accuracy across both temporal and non-temporal tasks. Our results suggest SS-QRC as a preferred candidate for near-term practical applications due to its resilience to system configurations and statistical noise.

Determining the fundamental limits of nonlinear functionals of quantum measurement statistics is a crucial yet generally intractable nonconvex optimization problem. We introduce a generic support-function-based outer-approximation framework for solving concave-minimization (or convex-maximization) problems over the quantum state space. By mapping the problem onto a reduced $\mathcal{Z}$ space, we characterize the exact quantum boundary through supporting half space derived from the largest eigenvalues of effective observables. This yields an effective method that produces tight bounds for general measurements in finite-dimensional quantum systems with preassigned numerical precision. As an initial application, we recover the exact variance-based uncertainty relations of [PRL 119, 170404 (2017)] and efficiently compute optimal entropic uncertainty relations (EURs). Our results reveal that standard analytical and majorization-based EUR bounds are fundamentally loose for generic measurements, and we show that the resulting exact bounds directly enhance quantum steering detection under asymmetric settings. We further apply the framework to determine the maximal athermality resource certifiable from a restricted measurement scenario. Our method thus provides a universal computational tool for exploring the boundaries of quantum state space and the limits of quantum resources.

We establish tight connections between entanglement entropy and the approximation error in Trotter-Suzuki product formulas for Hamiltonian simulation. Product formulas remain the workhorse of quantum simulation on near-term devices, yet standard error analyses yield worst-case bounds that can vastly overestimate the resources required for structured problems. For systems governed by geometrically local Hamiltonians with maximum entanglement entropy $S_\text{max}$ across all bipartitions, we prove that the first-order Trotter error scales as $\mathcal{O}(t^2 S_\text{max} \operatorname{polylog}(n)/r)$ rather than the worst-case $\mathcal{O}(t^2 n/r)$, where $n$ is the system size and $r$ is the number of Trotter steps. This yields improvements of $\tilde{\Omega}(n^2)$ for one-dimensional area-law systems and $\tilde{\Omega}(n^{3/2})$ for two-dimensional systems. We extend these bounds to higher-order Suzuki formulas, where the improvement factor involves $2^{pS^*/2}$ for the $p$-th order formula. We further establish a separation result demonstrating that volume-law entangled systems fundamentally require $\tilde{\Omega}(n)$ more Trotter steps than area-law systems to achieve the same precision. This separation is tight up to logarithmic factors. Our analysis combines Lieb-Robinson bounds for locality, tensor network representations for entanglement structure, and novel commutator-entropy inequalities that bound the expectation value of nested commutators by the Schmidt rank of the state. These results have immediate applications to quantum chemistry, condensed matter simulation, and resource estimation for fault-tolerant quantum computing.

We present a physics-informed classical-quantum machine learning framework for discriminating pristine CaF$_2$ from Er-doped CaF$_2$ using first-principles optical descriptors. Finite Ca$_8$F$_{16}$ and Ca$_7$ErF$_{16}$ clusters were constructed from the fluorite structure (a=5.46~$\AA$) and treated using density functional theory (DFT) and linear-response time-dependent DFT (LR-TDDFT) within the GPAW code. Geometry optimization was performed in LCAO mode with a DZP basis and PBE exchange-correlation functional, followed by real-space finite-difference ground-state calculations with grid spacing h=0.30~$\AA$ and N$_{bands}$=N$_{occ}$+20. Optical excitations up to 10~eV were obtained via the Casida formalism and converted into continuous absorption spectra using Gaussian broadening ($\sigma$=0.1-0.2~eV). From 1,589 energy-resolved points per system, physically interpretable descriptors including transition energy $E$, extinction coefficient $\kappa$, and absorption coefficient $\alpha$ were extracted. A classical RBF-kernel support vector machine (SVM) achieves a test accuracy (ACC) of 0.983 and ROC-AUC of 0.999. Quantum support vector machines (QSVMs) evaluated on statevector and noisy simulators reach accuracies of 0.851 and 0.817, respectively, while execution on IBM quantum hardware yields a test-slice accuracy of 0.733 under finite-shot and decoherence constraints. A hybrid quantum neural network (QNN) with a 3-qubit feature map and depth-4 ansatz achieves a test accuracy of 0.93 and AUC of 0.96. Results here demonstrate that dopant-induced optical fingerprints form a robust, physically grounded feature space for benchmarking near-term quantum learning models against strong classical baselines.

The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under these conditions, the stationary continuity constraint induces a nonlinear amplitude equation of Ermakov Pinney type in each degree of freedom, revealing a hidden invariant structure that is independent of whether the evolution parameter is time or space. By reformulating the separated stationary equations in Sturm Liouville form and applying Liouville normalization, we demonstrate that the quantum potential is encoded as a curvature contribution of the self adjoint operator rather than appearing as an additional dynamical term. This correspondence preserves the standard probabilistic predictions of quantum mechanics while yielding exact stationary Bohmian amplitudes and their associated invariants. The resulting invariant-based formulation provides stationary guiding fields and clarifies the ontological status of Bohmian amplitudes as geometrically encoded structures rather than auxiliary dynamical additions. The results further show that stationary constrained Bohm Madelung systems naturally admit variational formulations whose extremals preserve the Ermakov Lewis invariant.

Quantum phase transitions in many-body systems are fundamentally characterized by complex correlation structures, which pose computational challenges for conventional methods in large systems. To address this, we propose a hybrid quantum-classical attention model. This model uses an attention mechanism, realized through swap tests and a parameterized quantum circuit, to extract correlations within quantum states and perform ground-state classification. Benchmarked on the cluster-Ising model with system sizes of 9 and 15 qubits, the model achieves high classification accuracy with less than 100 training data and demonstrates robustness against variations in the training set. Further analysis reveals that the model successfully captures phase-sensitive features and characteristic physical length scales, offering a scalable and data-efficient approach for quantum phase recognition in complex many-body systems.

In open quantum systems, reduced dynamics is commonly described by a master equation, whose Liouvillian gap closing (LGC) typically signals the emergence of decoherence-free subspace. By contrast, the dynamics of the full system-environment compound is governed by the underlying Hamiltonian spectrum, where bound states in the continuum (BICs) can protect long-lived quantum resources. Despite these parallel perspectives, the relation between LGC and BIC formation has remained largely unexplored. Here we bridge this gap in a paradigmatic giant-atom waveguide platform and show that the occurrence of LGC necessarily benchmarks the presence of a BIC in the full Hamiltonian description. By engineering the giant-atom geometry, we further demonstrate rich dynamical regimes-including Rabi oscillations, fractional decay, and complete exponential relaxation-depending on the number of supported BICs, which can be tuned from three to zero. Remarkably, when two BICs become frequency-degenerate, the long-time dynamics approaches a steady state rather than exhibiting persistent oscillations. Our results establish a direct spectral-dynamical connection between effective Markovian and underlying non-Markovian descriptions, and provide a route toward flexible control of open-system dynamics.

Can superconducting order be engineered as a robust attractor of open-system dynamics in strongly correlated systems? We demonstrate this possibility by proposing a minimal dissipation-engineering protocol for the particle-hole symmetric Hubbard model. By applying a rotated quantum jump operator, specifically a locally transformed $\eta$-pair lowering operator, on a single lattice site only, we show that the Lindblad evolution autonomously pumps the system from the vacuum into a nonequilibrium steady state (NESS) exhibiting macroscopic $\eta$-pair off-diagonal long-range order (ODLRO). Crucially, this local-to-global synchronization stands in stark contrast to schemes reliant on spatially extensive reservoirs: here, a single local dissipative seed suffices to establish long-range coherence across the entire interacting lattice system. We elucidate the underlying mechanism via three core features: local dark-state selection, the controlled elimination of off-manifold excursions induced by hopping, and a Liouvillian invariant-subspace structure that yields an attractive fixed point with a finite dissipative gap. Furthermore, we systematically classify the stability of this NESS with respect to static disorder, and identify a wide regime in which the superconducting attractor remains robust against Hamiltonian perturbations that preserve the effective subspace structure. We also pinpoint specific perturbations that directly cause dephasing of the $% \eta$-pseudospin coherence and suppress ODLRO. These findings open up a disorder-tolerant pathway for stabilizing superconducting order as a non-thermal attractor through minimal local quantum-jump control.

Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems such as the many-body Schrödinger problem. So far, there has been no demonstration of extracting nuclear eigenstates using such method. Here, we tackle realistic nucleon-nucleon interaction in momentum space, including models with strong high-momentum correlations, and demonstrate highly accurate results for the deuteron. We further provide additional benchmarks in coordinate space. We introduce an expression for the variational energy that enters the loss function, which can be evaluated efficiently within the PINNs framework. Results are in excellent agreement with proven numerical methods, with a relative error between the value of the predicted binding energy by the PINN and the numerical benchmark of the order of $10^{-6}$. Our approach paves the way for the exploitation of PINNs to solve more complex atomic nuclei.

Quantum chaos in isolated quantum systems is intimately linked to thermalization and the rapid relaxation of observables. Although the spectral properties of the chaotic phase in the tilted Bose-Hubbard model have been well characterized, the corresponding dynamical signatures across the transition to regularity remain less explored . In this work, we investigate this transition by analyzing the time evolution of the survival probability, the single-site entanglement entropy, and the half-chain imbalance. Our results reveal a clear hierarchy in the sensitivity of these observables: the relaxation value of the entanglement entropy varies smoothly as a function of the Hamiltonian parameters across the chaos-regular transition, while the imbalance exhibits a more pronounced distinction. Most notably, the survival probability emerges as the most robust indicator of the transition between chaos and regularity. When appropriately scaled, all three observables converge onto a common behavior as a function of the Hamiltonian parameters for different numbers of sites and bosons,enabling a universal characterization of the transition between chaotic and regular dynamics.

This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the star-exponential with the quantum propagator for bosonic systems, this work develops the analogous extension for the fermionic case. A rigorous method, based on Grassmann variables and coherent states, is constructed to obtain a closed-form expression for the fermionic star-exponential from its associated propagator. As a primary application, a fermionic version of the Feynman-Kac formula is derived within this formalism, allowing for the calculation of the ground state energy directly in phase space. Finally, the method is validated by successfully applying it to the simple and driven harmonic oscillators, where it is demonstrated that a simplified ("naive") approach (with an ad-hoc "remediation") is a valid weak-coupling limit of the rigorous ("meticulous") formalism, thereby providing a new and powerful computational tool for the study of fermionic systems.