Papers

On the space of density matrices $D(H)$, Kadison's theorem establishes that all invertible convex transformations $K:D(H)\to D(H)$ are unitarity or antiunitary. For a finite Hilbert space, we propose a similar theorem which replaces the invertibility requirement with that of entropy conservation. Thus, we argue, the supposition of reversibility in quantum mechanics may be replaced with a principle of entropy conservation.

Spinor structure is usually introduced as part of relativistic quantum theory. We show that its underlying algebra can instead emerge without quantisation from a covariant statistical description of a massive relativistic particle subject to an explicit finite-dimensional linear factorisation of the complete massive mass-shell constraint motivated by requiring the theory retain both sheets of the massive mass shell. A finite-dimensional factorisation of the complete mass-shell constraint, linear in all four momentum components, forces a Clifford algebra. In (3+1) dimensions its minimal complex representation is four-dimensional, while each on-shell factor selects a rank-two sector; in this representation statistical completeness requires an arbitrary $2\times2$ matrix distribution within that sector before quantisation. Projecting the Weyl-ordered matrix Liouvillian gives relativistic transport while preserving all internal populations and coherences. For universal deformations on flat canonical phase space satisfying the stated covariance, matrix-neutrality, homogeneity and associativity assumptions, the resulting product is the matrix Weyl–Moyal product. Its parameter has dimensions of action and, when identified with $\hbar$, supplies the scale of physical spin-$\tfrac12$. Requiring all-order constraint preservation gives a vanishing star commutator, while preservation of the selected star-spectral sector yields the two-sided Dirac–Wigner equations. Our central conclusion is therefore that relativistic mass-shell factorisation supplies spinor structure, while completion of the constraint-preservation hierarchy within the stated deformation class leads to the Weyl–Moyal phase-space formulation of quantum mechanics.

A parametrized quantum circuit reports its state geometry through a quantum Fisher information matrix (QFIM), often singular. A small Fisher value can reflect exact state-preserving redundancy, compression by the circuit chart, or weak intrinsic distinguishability, and these mechanisms call for different numerical treatments. We show that the circuit metric factors as $F=B^{*}MB$, where $B$ is the state-level circuit-to-orbit differential and $M$ is the intrinsic Fisher operator on the reachable orbit. The factorization identifies the exact kernel as $\ker B$, separates coordinate transfer from intrinsic geometry, and yields the condition for a circuit to realize an orbit-level quantum natural-gradient (QNG) direction. When the prescribed redundancy exhausts the Fisher kernel, the Moore–Penrose update is the minimum-norm horizontal lift of the quotient Riemannian gradient. At critical points with a locally diffeomorphic quotient-to-orbit map, chart singular values cancel from the linearized QNG operator while intrinsic anisotropy remains; in the trace-orthonormal full-control generator frame, excitation-gap anisotropy gives $\kappa_{\mathrm{QNG}}=\kappa_{\mathrm{Eucl}}$. Representation theory makes $M$ explicit on highest-weight, Slater, and fermionic-Gaussian orbits, and cominuscule fidelity flow becomes integrable, with conserved principal-defect ratios, cubic Lie-retracted convergence at $\eta=2$, and stability boundary $\eta=4$. Finite data impose a second boundary: an estimated QFIM and its confidence radius alone cannot distinguish an exact zero from a small physical mode, so the estimated spectrum alone cannot license hard projection. Under depolarization, inverse-Fisher scaling amplifies mean updates and fluctuations together and cannot restore update signal-to-noise. A redundant Slater/Givens circuit confirms exact transfer identities and illustrates finite-shot tradeoffs.

We determine the computational complexity of deciding whether a supersymmetric quantum system on a one-dimensional chain has a zero-energy ground state. We prove $\mathrm{QMA}_1$-completeness for two input models, formulated in terms of Hermitian and nilpotent supercharges, respectively. In the Hermitian model, both the supercharge terms and the Hamiltonian have bounded range on the chain; in the nilpotent model, this geometric restriction applies only to the Hamiltonian. The hardness reduction from quantum satisfiability on a chain preserves exact zero energy and gives an inverse-polynomial ground-energy lower bound for negative instances. A common verification method establishes membership in $\mathrm{QMA}_1$ while allowing cancellations between supercharge terms.

Intrinsic spin–orbit interaction in germanium provides electrically active flopping-mode qubits without requiring magnetic-field gradients to generate spin–charge hybridization. We study double quantum dots (DQDs) with a multiband Luttinger–Kohn framework that retains heavy-hole (HH) and light-hole (LH) states on equal footing. Modeling vertical confinement with a finite confinement potential along the growth direction brings selected subbands into a regime of appreciable HH–LH mixing. This admixture activates electric-dipole spin-coupling through LH–LH and LH–HH transitions, complementing the conventional HH–HH pseudospin-flip resonance. For the parameter sets considered, these additional channels can produce larger spin–photon figures of merit than the HH–HH transition. HH–LH mixing thus supplies a tunable ingredient for qubit–cavity coupling in germanium hole-spin qubits and extends the operating regimes available to circuit-QED architectures.

Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.

Superconducting high-kinetic inductance materials like granular aluminum (grAl) are a versatile part of the circuit quantum electrodynamics (cQED) toolbox, provided their losses at microwave frequencies are low enough. To further advance the use of grAl in quantum devices, it is indispensable to identify the dominant loss mechanisms. The standard approach pairs electromagnetic simulations of resonator geometry with measured temperature and power dependence of resonance frequency and loss rate. Most materials follow the phenomenological theory of two-level systems (TLSs) at low temperatures, resulting in an initial decrease of the resonance frequency with increasing temperature. In our work, we observe an opposite behavior at the lowest temperatures: The resonance frequency initially increases with both temperature and readout power, contradicting the standard TLS model predictions. We are able to explain a part of the data by an alternative mechanism associated with the effect of superconducting quasiparticles in a granular system with spatially-nonuniform gap. Yet, the observed change in the resonance frequency with temperature is not matched by a proportional change in the loss rate. We also observe anomalous positive frequency responses following high-energy events, characterized by several time scales. While anomalous behavior has been reported previously in grAl, the disagreement with standard models is particularly visible in our devices thanks to their exceptionally low loss rates.

Quantum key distribution (QKD) guarantees information-theoretic security by the laws of physics, but deployment at scale requires compact, manufacturable photonic terminals. Continuous-variable QKD (CV-QKD) is well suited for this transition through telecom-compatible, room-temperature coherent detection. However, unifying full on-chip core terminal integration, room-temperature operation, high loss tolerance, and composable end-to-end security in long-distance QKD remains a key bottleneck. Here we report a fully integrated CV-QKD platform in which two hybrid III–V/Si$_3$N$_4$ integrated lasers, a silicon transmitter, and a silicon coherent receiver implement the core terminal functions, operating with a local local oscillator (LLO) over fibre links of 25–150 km. A Bayesian machine-learning algorithm maintains robust phase lock throughout the long records required for composable security, consistently outperforming the conventional unscented Kalman filter, while rate-matched multidimensional reconciliation approaches the Shannon limit. The system certifies a composable finite-size secret-key rate of 29.3 kbps at 100 km from a 140-billion-symbol block, with 12.9 kbps at 125 km under finite-size analysis and 9.17 kbps at 150 km under asymptotic analysis. By establishing the longest finite-size and asymptotic reaches and the highest secret-key rate per symbol reported for integrated CV-QKD, this work advances the development of practical chip-based quantum networks.

We investigate the dynamics of a quadratically coupled system under the influence of an external drive applied to the second oscillator, where the coupling facilitates a high-order synchronization with phase-locking emerging in the form of 2:1 between the oscillators. Our analysis reveals a synchronization blockade in the first oscillator, characterized by the complete suppression of conventional 1:1 phase-locking with the drive. In contrast, we observe that the directly driven second oscillator synchronizes with the drive, showing 1:1 phase-locking but notably at second harmonic frequency. A classical mean-field analysis of the corresponding equations of motion reproduces this asymmetric phase-locking geometry which demonstrates that the phase-locking structure itself can be understood from the nonlinear classical dynamics. The quantum analysis, however, reveals the microscopic origin of the synchronization blockade. Furthermore, we show that the system exhibits mutual synchronization when both the oscillators satisfies the resonance condition, enabling coherent energy exchange facilitated by nonlinear quadratic coupling. The mutual synchronization shows synchronized regimes and also subtle suppression of synchronized regimes near resonance occurring due to spectral splitting of the energy states. Using perturbation analysis of the master equation within the low excitation subspace, we analyze steady-state phase distribution and synchronization measures, supported by population statistics and spectral responses. We also propose possible experimental realizations in trapped-ions and optomechanical setups. These findings highlight the crucial role of quadratic coupling in enabling nonclassical synchronization phenomena, offering deeper insights for quantum control strategies and the development of quantum information platforms.

Superpositions of macroscopically distinct coherent states, or cat states, are a key resource for quantum technologies. In particular, two-mode binomial cat states can give rise to exact quantum error correction in continuous-variable quantum computing. However, their preparation typically requires non-Gaussian initial states, such as Fock or NOON states, which are challenging to realize experimentally. Here, we propose a protocol to generate two-mode binomial cat states where the only requirements are Gaussian initial states in combination with heralded heterodyne measurements. Our approach utilizes cross-Kerr interactions between bosonic modes commonly realizable in superconducting circuit architectures. We show that by adjusting the input state parameters, our protocol remains robust to dissipation under realistic experimental conditions. Our work provides a practical route to realizing multinomial cat states in current experimental platforms without requiring non-Gaussian initial resources, overcoming a key limitation of existing preparation schemes.

We investigate the redistribution of continuous-variable Gaussian quantum discord under the Unruh effect for both one and two uniformly accelerated observers. The discord shared between the inertial mode and the accessible accelerated mode, as well as that between the two accessible accelerated modes, decays monotonically with acceleration and vanishes in the limit $a\to\infty$, while the Unruh effect generates discord in all causally disconnected Rindler mode pairs. The initial quantum correlation is therefore redistributed across Rindler partitions rather than destroyed. We further characterize how the squeezing parameter $s$ and field frequency $\omega$ control the discord in different mode-pair classes. For causally connected pairs, $s$ and $\omega$ exert comparable, interchangeable effects; for cross-region pairs, the squeezing parameter dominates; and for intra-observer cross-region pairs, the field frequency is more influential. In the two-observer case, the $A_{II}$-$B_{II}$ pair exhibits non-monotonic behavior with a peak whose position shifts to larger $a$ as $\omega$ increases, and both parameters contribute only weakly except near an optimal $\frac{\omega}{s}$ ratio.

For a bipartite state $\rho$, information about the spectrum of its partial transpose $\rho^{\Gamma_B}$ can be inferred from measurements on multiple copies of $\rho$, without full state tomography. This raises a natural question: which eigenvalue lists can arise as $\operatorname{spec}(\rho^{\Gamma_B})$ for a density operator $\rho$? We completely solve this inverse eigenvalue problem for two qubits. Every nonnegative trace-one spectrum is realized as $\operatorname{spec}(\rho^{\Gamma_B})$ by some PPT state $\rho$, whereas an ordered candidate eigenvalue list $(x,y,z,-q)$, with $x\ge y\ge z\ge0$, $q>0$, and $x+y+z-q=1$, is realized by an NPT state iff $q\le y$ and $qy\le xz$. Sufficiency in the latter case is established by an explicit $X$ state whose quantum steering ellipsoid has center $c=(y-q)/(1-z)$ and normalized volume $V/V_{\max}(c)=qy/(xz)$, providing a geometric interpretation of the inequalities $q\le y$ and $qy\le xz$ as the allowed ellipsoid-center region and the fixed-center volume bound. Beyond this geometric picture, the two-qubit inverse theorem also yields exact negativity bounds from the two lowest nontrivial PT moments. Given fixed values of $p_2=Tr[(\rho^{\Gamma_B})^2]$ and $p_3=Tr[(\rho^{\Gamma_B})^3]$, we determine the exact minimum and maximum negativity over all two-qubit states subject to these moment constraints. When no PPT state is consistent with the pair $(p_2,p_3)$, the minimum is attained either at $x=y$ or $qy=xz$, while the maximum is attained either at $y=z$ or $q=y$. Finally, we show how the two-qubit inequalities persist as necessary constraints for the inverse eigenvalue problem in qubit–qudit systems.

We investigate various properties of multipartite block-positive operators, decomposable EWs (DEWs), and non-decomposable EWs. We provide a necessary and sufficient condition to construct a special DEW using the multipartite GHZ state. For multipartite DEW, we explicitly characterize the supremum and infimum of maximum and minimum eigenvalues, as well as the trace of its square. We also derive other results concerning NDEW, eigenvalues of $2 \times n$ EWs and the corresponding physical implications. Furthermore, we investigate the tightness of inequalities of these eigenvalues with examples.

Standard universal quantum computing using exchange-only qubits typically requires three physical spins per logical qubit, leading to significant hardware overhead. Conversely, two-spin units offer higher density but rely on local magnetic field gradients for control, increasing integration complexity. In this paper, we propose a resource-efficient quantum machine learning (QML) architecture that achieves high expressibility using minimal two-spin units and Heisenberg exchange interactions alone, without any magnetic gradients. We shift the paradigm from universal gate-based control to utilizing the intrinsic, time-domain dynamics of a spin chain as a learning resource. Numerical simulations on MNIST digit classification demonstrate that the symmetry-protected constraints of isolated spin pairs are bypassed by leveraging inter-pair exchange coupling. This interference-mediated state mixing significantly enhances the expressibility of the Hilbert space. The model reaches a test-set accuracy of 90.9% +/- 0.2% over five independent seeds on the full 10,000-image MNIST test set. Under an identical linear readout, the trained quantum feature map (88.1%) clearly outperforms a classical linear baseline on the same PCA inputs (83.2%) as well as an untrained (reservoir-style) version of the same dynamics (53.0%), demonstrating that the learned, input-dependent exchange pulses implement a genuinely non-linear and trainable feature map. The protocol is also robust to experimentally relevant imperfections: accuracy remains at 89.9% under 10% quasi-static pulse-area noise and at 89.8% when every observable is estimated from 10^3 measurement shots. These findings suggest that competitive QML can be executed on the simplest possible semiconductor spin-chain hardware, bypassing the need for leakage-prone encodings or complex micro-magnet integration.

Recent studies have shown that Bargmann invariants provide effective detectors of set imaginarity. In this paper, we investigate set imaginarity as a quantum resource in qubit systems. By exploiting the structure of Bargmann invariants, we show that the free operations for qubit set imaginarity consist precisely of common unital operations and common planarized operations. Based on this characterization, we introduce an axiomatic framework for set-imaginarity measures (SIMs). In particular, we propose two refined notions, namely unified SIMs and complete SIMs, which allow a more fine-grained quantification of set imaginarity. To make these notions concrete, we construct two qubit SIMs from the Bargmann invariants of three-state subsets. We prove that one of them is a unified SIM, while the other satisfies the stronger requirements of a complete SIM. Furthermore, we revisit the robustness of set imaginarity previously introduced in the literature. We show that, although this robustness is a valid SIM for qubit systems, it is neither a unified SIM nor a complete SIM. To overcome this limitation, we propose an improved robustness-type measure and rigorously prove that it defines a complete qubit SIM.

Universal recovery – the existence of a single recovery map that corrects an entire family of error channels – is a central feature of quantum error correction (QEC). In exact QEC, linearity guarantees that a code correcting a given error set also corrects every channel whose Kraus operators lie in its linear span, and that a single recovery map suffices for all such channels. Approximate quantum error correction (AQEC), which relaxes perfect recovery to recovery with controlled error, has traditionally lacked this structure. In a recent paper (arXiv:2607.22995), we developed a theory of approximate quantum error correction showing that a restricted form of linearity persists in the approximate setting, yielding uniform AQEC guarantees for the family of channels controlled by a given error set. In this work, we complete the picture by establishing the second half of universal recovery in the approximate setting: a single recovery map can simultaneously correct every channel controlled by a given error set. The error-set theory we proposed quantifies approximate correctability through two parameters: the environment-leakage distance, governing worst-case performance, and the Knill–Laflamme Hellinger distance, governing average-case performance. We show here that both quantities also control universal decoding. We further study the Petz map naturally associated with an error set as an explicit universal recovery, and obtain uniform average- and worst-case guarantees across the entire family of channels.

The Schrodinger equation in one spatial dimension admits a small set of exactly solvable potentials that serve as natural proving grounds for any new eigenvalue solver. We formulate Physics-Informed Neural Networks (PINNs) and Physics-Informed Quantum Neural Networks (PIQNNs) for the time-independent Schrodinger equation and apply them to three of these benchmarks: the harmonic oscillator, the infinite square well, and the finite square well. In each case a composite loss encodes the differential-equation residual, the normalization condition, the boundary behavior, and the orthogonality between eigenstates, so that the trial wave function is driven toward a genuine eigenfunction without supervised data. The eigenvalues and wave functions returned by both methods are compared against the exact spectra and against three classical references: the matrix Numerov method, the finite difference method, and the shooting method. For the smooth oscillator the two neural solvers reproduce the lowest four eigenvalues to parts per million, while for the square wells they recover the analytic levels with comparable fidelity even where the potential is discontinuous. The quantum circuit, built as a layered angle-embedding ansatz with strongly entangling blocks, converges more reliably than its classical counterpart on the higher excited states, where the loss landscape of the classical network becomes harder to navigate.

In high energy physics experiments $^3$He$^{2+}$ nucleons are suitable to test the internal structure of neutrons, which makes them the perfect substitute. Moreover, it is one of the atomic species for which high polarization values are achievable through the use of optical pumping methods. Therefore, nuclear polarized sources for $^3$He$^{2+}$ ions are currently under development. Consequently, detector systems validating their nuclear polarization value need to be established. Such a detector system, based on the Lamb-shift polarimeter, is introduced in this work. Its advantage is that it can operate at low energies in the range of 10 to 100 keV, which makes pre-acceleration unnecessary. In addition, a fast evaluation of the nuclear polarization within seconds leads to shorter disruptions for beam times. Another option of this Lamb-shift polarimeter might be that it can serve as a valuable tool for further investigation of the bound tritium decay into $^3$He atoms, similar to the hydrogen spin filter for the bound beta decay of the free neutron.

Environmental modification of dipole interactions has long been explored in energy transport. Here we consider the effects of a tunable graphene monolayer upon nearly H-type or J-type molecular aggregates, concentrating on the inversion of one type of coupling to the other. Modelling the graphene as being deposited on a metallic substrate, we find that as the surface conductivity of the graphene is varied, there is a corresponding change in the parameter region over which coupling inversion is predicted. This provides a route towards observing the predicted coupling inversion in a real system by dynamically changing the surface conductivity during a single run of an experiment.

The pseudo-density matrix (PDM) formalism naturally extends the notion of density operator to the spatiotemporal domain. While PDMs are Hermitian and of unit trace, they admit negative eigenvalues when encoding temporal correlations unattainable for spacelike separated systems. Consequently, there have been various approaches to extending the von~Neumann entropy—which is only defined for positive operators—to PDMs. Here, we prove that there exists a unique extension of the von~Neumann entropy functional to Hermitian matrices of unit trace satisfying two simple assumptions: unitary invariance and strong additivity with respect to affine combinations within the interval $[-1,1]$, which we prove contains the eigenvalues of a PDM. We also prove that this unique extension of von~Neumann entropy to PDMs is subadditive for single qubit dynamics, and we analyze its behavior in a number of examples.

Planar $k$-uniform states have maximally mixed reductions on every $k$-site interval of a ring. We introduce planar $k$-purity—the mean purity of those intervals—as a faithful cost function for this simultaneous constraint. For a Haar-random pure state of $n$ parties with local dimension $p$, the joint purity of two intervals depends only on their overlap. An exhaustive four-replica calculation therefore yields the complete cyclic covariance kernel and a closed variance for every $1\le k\le\lfloor n/2\rfloor$. In the balanced qubit case, $k=\lfloor n/2\rfloor$ and $N=2^n$, the variance is asymptotic to $20/(3nN^2)$ for even $n$ and $6/(nN^2)$ for odd $n$. A site-factorized permutation representation gives all raw moments and permits exact finite-sum evaluation of the skewness. Fixed-seed simulations validate nonbalanced qubit and qutrit cases, while balanced-qubit simulations through $n=10$ validate the parity formulas and finite-size skewness. Balanced planar and absolute balanced purity have the same Haar mean but different fluctuations; the planar variance is approximately $2.83$ times larger at $n=10$. Thus subsystem incidence, although invisible to every one-cut marginal distribution, controls the collective fluctuations of geometrically related cuts. Together with universal attainability and a linear number of interval constraints at balance, this provides a geometry-aware benchmark for multipartite entanglement beyond AME existence regimes.

It is natural to expect that the electromagnetic spin-spin interaction has roots in a more fundamental theory: quantum electrodynamics in this case. To show this, we take the non-relativistic limit of the Dirac-Maxwell Lagrangian, using the Foldy-Wouthuysen transformation and derive the Breit interaction by an alternative approach. By adding the Pauli term (i.e., a higher-order interaction between spin and the electromagnetic field), we calculate the correction terms to electromagnetic spin-spin interactions in the non-relativistic limit. Finally, we study some of the physical effects of these terms regarding spin-spin interactions and spin-spin entanglements. Accordingly, we provide theoretical estimates that are not yet accessible with current experiments.

The existence of quantum gravity is the most important question in theoretical physics. Besides the theoretical development in this direction, looking for its low-energy consequences can provide clues. However, besides availability, it is crucial to ensure that what is observed uniquely comes from quantum gravity and not from other forces in the environment. What is the unique feature of gravity? The spin-$2$ nature of its propagator. In this Letter, we calculate what the unique feature of the spin-$2$ graviton is in the interaction of two spin-$\frac{1}{2}$ particles. This unique feature shows itself in intertwining the spin and momentum of two particles simultaneously as a dipole-dipole interaction. This cannot happen for any spin-$0$ or spin-$1$ propagator, at least at leading order, which scales as $\frac{1}{r^3}$ in real space. We re-calculate the results using an independent approach, i.e., the Foldy-Wouthuysen transformation, and reach the same results. Due to simultaneous coupling of both particles' spins and momenta, a four-partite entanglement framework is suggested to observe this effect.

Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every $\alpha\in[0,1)$, we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for $\alpha\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $\alpha\in[1,2)$, including the von Neumann case $\alpha=1$, remains open, and we conjecture additivity there throughout the same family.

Tensor networks (TNs), originally developed for simulating many-body quantum systems, provide a systematic framework for approximating high-dimensional fields. This is achieved by factorizing the field into interconnected tensors with small bond dimensions, thereby restricting the correlations captured across field bipartitions. Belonging to the family of TNs, the matrix product state (MPS) ansatz is utilized here as a reduced-order modeling framework to construct truncated representations of isotropic turbulent flow data. Two direct numerical simulation (DNS) datasets are considered: the hydrodynamic field of an incompressible three-dimensional flow, and a conserved Fickian scalar in a similar flow. Each field is encoded as an MPS through a sequence of singular value decompositions (SVDs) in which small singular values are discarded. The truncated representation is contracted back to the full grid, and the resulting reconstructed field is compared against DNS. An interleaved ordering of the spatial tensor indices of the transport variables is applied prior to decomposition in order to localize the dominant inter-tensor correlations. Velocity reconstructions achieve $99.8\%$ fidelity using only $5\%$ of the original DNS memory, while the scalar field reaches the same fidelity at $15\%$ memory usage. A wide range of lower- and higher-order statistics, including velocity gradients, dissipation, and structure functions, are systematically examined. At these compression levels, the total kinetic energy and the scalar energy are both recovered within $0.2\%$ relative error, while the mean dissipation and mean scalar dissipation remain within approximately $10\%$ of the DNS generated values. These findings support the suitability of MPS for scalable reduced-order analysis of complex turbulent datasets and motivate further exploration of TN-based methods in computational turbulence.

We study the effect of quantum preconditioning on constrained combinatorial optimization problems, focusing on balanced graph bi-partitioning. The proposed approach uses two-point correlations between decision variables derived from the Quantum Approximate Optimization Algorithm (QAOA) to construct a modified objective function that is subsequently provided to mixed-integer programming (MIP) solvers. The preconditioned MIP formulation retains the original hard constraint, and all incumbent solutions are evaluated under the original objective. Computational experiments on dense, weighted complete-graph instances show that the preconditioned problem instances reach near-optimal solutions faster, with most of the benefit already realized at the shallowest QAOA depth tested. Solver callback trajectories show this arises from earlier discovery of high-quality incumbents during the solution search. These results support a hybrid optimization framework in which quantum algorithms provide problem-specific information to guide classical exact MIP solvers.

Representation learning begins when training changes the features that define similarity between data. A frozen-kernel model only reweights a fixed geometry. We establish quantum signal processing (QSP) as a solvable quantum model of the representation-learning regime. At arbitrary depth, we compute the exact mean and variance of its quantum neural tangent kernel, revealing an input-dependent angular geometry whose diagonal remains non-self-averaging even when the underlying unitary approaches Haar randomness. We also prove a sparse-data guarantee for the full nonlinear gradient flow without freezing or ensemble-averaging the kernel: the realized dynamics converges to an integrable scalar flow with a time-dependent kernel closure and explicit convergence times. A finite-depth speed limit holds for every data set and trajectory. At higher data density, numerical results show coupled evolution beyond both the scalar and frozen-kernel descriptions. These results give a controlled theory of learned quantum data geometry with provable training dynamics beyond the frozen limit.

Mechanical resonators ultrastrongly coupled to quantum two-level systems provide a promising route towards mechanical qubits by introducing significant anharmonicity to the mechanical modes, particularly in the slow-oscillator regime. Although the resulting hybrid system is well described by the quantum Rabi model, a consistent treatment of dissipation remains challenging across the broad parameter space routinely probed in current nanotube electromechanical devices. Here, we investigate dissipation in the open quantum Rabi model using a Born-Markov framework based on the slowly varying bath spectrum approximation, yielding a Lindblad master equation applicable far beyond conventional descriptions while recovering them in their respective limits. Using this framework, we analyze experimentally accessible observables across this parameter space. As the secular approximation breaks down, phonon blockade progressively washes out. Our approach remains valid in this regime, enabling a quantitative description of the continuous evolution of phonon blockade with coupling strength and dissipation. At finite temperature, we find a suppression of the temperature-induced increase of coherence decay rate for weak anharmonicity. Under driving, our approach remains applicable to substantially stronger perturbations than conventional dressed-state master equations and shows that an apparently classical observable can coexist with Wigner negativity. We further capture the weakly anharmonic regime arising from finite detuning in the double-quantum dot. These results establish a unified description of dissipation from weakly anharmonic operating regimes to the strongly anharmonic mechanical-qubit regime and provide experimentally relevant predictions for ultrastrong electromechanical systems.

Variational quantum algorithms (VQAs) suffer from unstable optimization due to temporal noise drift and static qubit mappings that distort gradient signals across iterations. We present BAHAMAS, an online control framework that stabilizes noise exposure by adaptively selecting physical mappings via consensus-based fidelity estimation, without requiring simulators, offline training, or prior executions. Across real quantum devices, BAHAMAS improves optimization reliability and supports inference-time retargeting under drift through robust, per-iteration control.

We experimentally investigate quantum synchronization for one of the simplest possible quantum systems, namely an externally driven few-level system with equally spaced energy levels effectively acting as a spin-1 system. Coupling to excited auxiliary states, we realize additive effective Lindblad operators that are associated with non-conventional dissipative pathways, which are shown to enhance, in certain parameter regimes, quantum synchronization. The experimental set-up, which utilizes cold $^{87}$Rb atoms in a MOT, and associated synchronization extraction protocol are benchmarked carefully through dedicated simulations. Convincing agreement is found between experiment and simulations. The dissipation engineering approach established in our work can be readily extended to systems with more energy levels, such as effective spin-$3/2$ or spin-$2$ systems, and has implications for quantum synchronization studies in higher-spin systems as well as for a wide range of quantum science studies and technology applications.