Papers

We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.

Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental decoherence can lead to improved semi-classical theories that are exact descriptions of the original quantum dynamics. In doing so, we show how consistent models of classical-quantum dynamics can arise as effective descriptions of open quantum systems.

The dark-state effect, caused by destructive interference, not only is an important fundamental research topic in atomic physics and quantum optics, but also has wide potential application in quantum physics and quantum information science. Using the arrowhead-matrix method, here we study the dark-state effect in a coupled cavity-Rydberg-atom system, in which $N$ Rydberg atoms with the dipole-dipole interactions are coupled to a single-mode cavity field. We obtain the numbers and form of the dark states in certain excitation-number subspaces for the two-, three-, and four-atom cases, as well as in the single-excitation subspace for a general $N$-atom case. We also suggest to characterize the dark states by inspecting the populations of some specific quantum states, which can be detected in experiments. Furthermore, we analyze the dark-state effect in a realistic case, where both the atomic dipole-dipole interaction strengths and the atom-cavity-field coupling strengths depend on the position of the atoms. Our findings pave the way for studying dark-state physics and applications in the cavity-Rydberg-atom platform.

In this note, we show that the well-known leading low-temperature correction to the Heisenberg-Euler Lagrangian in a constant electromagnetic field arising at two loops can be efficiently extracted from its one-loop zero-temperature analogue. Resorting to the real-time formalism of equilibrium quantum field theory that explicitly separates out the zero-temperature contribution from the finite-temperature corrections the determination becomes essentially trivial. In essence, it only requires taking derivatives of the Heisenberg-Euler Lagrangian at one loop and zero temperature for the field strength. As a bonus, we then effectively dress the low-temperature contribution at two loops by one-particle reducible tadpole structures. This generates a subset of higher-loop contributions to the Heisenberg-Euler Lagrangian in the limit of low temperatures. We extract their leading strong-field behavior at a given loop order, and finally resum these to all loop orders.

Decoding Bivariate Bicycle (BB) quantum error correction codes typically requires Belief Propagation (BP) followed by Ordered Statistics Decoding (OSD) post-processing when BP fails to converge. Whether BP will converge on a given syndrome is currently determined only after running BP to completion. We show that convergence can be predicted in advance by a single modulo operation: if the syndrome defect count is divisible by the code's column weight w, BP converges with high probability (100% at p <= 0.001, degrading to 87% at p = 0.01); otherwise, BP fails with probability >= 90%. The mechanism is structural: each physical data error activates exactly w stabilizers, so a defect count not divisible by w implies the presence of measurement errors outside BP's model space. Validated on five BB codes with column weights w = 2, 3, and 4, mod-w achieves AUC = 0.995 as a convergence classifier at p = 0.001 under phenomenological noise, dominating all other syndrome features (next best: AUC = 0.52). The false positive rate scales empirically as O(p^2.05) (R^2 = 0.98), confirming the analytical bound from Proposition 2. Among BP failures on mod-w = 0 syndromes, 82% contain weight-2 data error clusters, directly confirming the dominant failure mechanism. The prediction is invariant under BP scheduling strategy and decoder variant, including Relay-BP - the strongest known BP enhancement for quantum LDPC codes. These results apply directly to IBM's Gross code [[144, 12, 12]] and Two-Gross code [[288, 12, 18]], targeted for deployment in 2026-2028.

Ground-state cooling is a prerequisite for exploring macroscopic quantum effects in mechanical motion of massive objects. Here we construct a polarization-angle-controllable coupled cavity-levitated-nanoparticle system in which two nanoparticles trapped by individual tweezers are coupled to a single-mode field in a cavity. We also study the simultaneous ground-state cooling of six mechanical displacement modes of the two levitated nanoparticles through the coherent scattering mechanism. By deriving the Hamiltonian of the system and performing the linearization, we obtain a linearized seven-mode Hamiltonian, which can exhibit the coupling structure and cooling mechanism. We confirm the physical condition for the appearance of dark modes, which will suppress the simultaneous ground-state cooling of these mechanical modes. We also find that, by properly tuning the polarization angle $\theta $ between the cavity field and the optical tweezer fields, the coupling channels can be controlled on demand and simultaneous ground-state cooling of these six motional modes of the two nanoparticles can be realized. Our work paves the way for generation and manipulation of collective macroscopic quantum effects in multiple levitated nanoparticles.

We study quantum property testing of directed graphs whose maximum in-degree and out-degree are bounded by a fixed constant $d$. For a proximity parameter $\varepsilon$, we prove that every property testable with $O_{\varepsilon,d}(1)$ quantum queries in the bidirectional model, where both incoming and outgoing neighbors are accessible, can also be tested in the quantum unidirectional model, where only outgoing neighbors are accessible, using $n^{1/2-\Omega_{\varepsilon,d}(1)}$ queries. This gives an almost quadratic quantum speedup over the best known generic classical transformation. Our proof has two main ingredients. First, we show that, in the bidirectional model for bounded-degree digraphs, the class of properties testable with constantly many classical queries coincides with the class testable with constantly many quantum queries. Second, we give a transformation from classical bidirectional testers to quantum unidirectional testers by designing a quantum unidirectional algorithm for estimating the frequency vector of constant-radius rooted discs. The algorithm combines quantum counting and Grover search with a correction procedure that removes false local appearances of smaller disc types inside larger neighborhoods. We further show that this transformation is essentially tight. For every sufficiently small fixed $\varepsilon>0$, there is a degree bound $d=d(\varepsilon)$ and an explicit property $P_\varepsilon$ for $d$-bounded-degree digraphs that is $\varepsilon$-testable with $O_\varepsilon(1)$ classical, and hence quantum, bidirectional queries, but requires $ \widetilde{\Omega}_\varepsilon \left(n^{1/2-f'(\varepsilon)}\right) $ quantum queries in the unidirectional model, where $f'(\varepsilon)\to 0$ as $\varepsilon\to 0$.

Efficient ground state search is fundamental to advancing combinatorial optimization problems and quantum chemistry. While the Variational Imaginary Time Evolution (VITE) method offers a useful alternative to Variational Quantum Eigensolver (VQE), and Quantum Approximate Optimization Algorithm (QAOA), its implementation on Noisy Intermediate-Scale Quantum (NISQ) devices is severely limited by the gate counts and depth of manually designed ansatz. Here, we present an automated framework for VITE circuit design using Double Deep-Q Networks (DDQN). Our approach treats circuit construction as a multi-objective optimization problem, simultaneously minimizing energy expectation values and optimizing circuit complexity. By introducing adoptive thresholds, we demonstrate significant hardware overhead reductions. In Max-Cut problems, our agent autonomously discovered circuits with approximately 37% fewer gates and 43% less depth than standard hardware-efficient ansatz on average. For molecular hydrogen ($H_2$), the DDQN also achieved the Full-CI limit, with maintaining a significantly shallower circuit. These results suggest that deep reinforcement learning can be helpful to find non-intuitive, optimal circuit structures, providing a pathway toward efficient, hardware-aware quantum algorithm design.

Quantum systems are inherently fragile to environmental fluctuations or decoherence, limiting their advantages in applications of quantum information and quantum computation. State purification offers a route to recover the purity of system under noisy conditions. Here, we demonstrate a rapid purification of initially mixed states by harnessing collective reservoir engineering in driven non-Hermitian qubit systems, together with multipartite entanglement generation in larger systems. We show that the onset of efficient purification-assisted entanglement generation is dictated by the degeneracy of collective subradiant modes, rather than by exceptional points. Moreover, the system dynamics manifests an informational Mpemba effect, i.e., a more mixed initial state reaches its steady state with unit purity at a faster rate, resembling the conventional Mpemba effect where a hotter system cools more rapidly. These results reveal a unique advantage of driven non-Hermitian quantum systems with engineered collective dissipation, enabling enhanced purification efficiency and offering new opportunities for relaxation control of non-Hermitian systems and quantum state preparations.

Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers an insightful analysis of VQAs and their progression toward the fault-tolerant regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.

Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren plateaus, non-variational QKMs employ fixed quantum feature maps, with model selection performed classically via convex optimisation and cross-validation. This separation of quantum feature embedding from classical training ensures stable optimisation while leveraging quantum circuits to encode data in high-dimensional Hilbert spaces. In this review, we provide a thorough analysis of non-variational supervised QKMs, covering their foundations in classical kernel theory, constructions of fidelity and projected quantum kernels, and methods for their estimation in practice. We examine frameworks for assessing quantum advantage, including generalisation bounds and necessary conditions for separation from classical models, and analyse key challenges such as exponential concentration, dequantisation via tensor-network methods, and the spectral properties of kernel integral operators. We further discuss structured problem classes that may enable advantage, and synthesise insights from comparative and hardware studies. Overall, this review aims to clarify the regimes in which QKMs may offer genuine advantages, and to delineate the conceptual, methodological, and technical obstacles that must be overcome for practical quantum-enhanced learning.

We propose and analyse a quantum thermal field-effect transistor (qtFET) composed of left-qubit, middle-qutrit, and right-qubit subsystems. In this architecture, the left qubit is coupled to the middle qutrit, which in turn interacts with the right qubit. Each subsystem interacts independently with its respective baths. The middle subsystem serves as a modulator. We have shown that the qtFET exhibits functionality analogous to that of a conventional electronic field-effect transistor (eFET). The left, right, and middle subsystems of the qtFET correspond to the drain, source, and gate of an eFET in a common gate configuration, respectively. Our results show that the qtFET can precisely modulate thermal currents, highlighting its potential as a fundamental building block for quantum thermal devices and amplifiers in emerging quantum technologies.

Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to centroid initialization, difficulty capturing non-linear structure, and poor performance in high-dimensional spaces. Recent work has proposed improved initialization strategies and quantum-assisted distance computation, but the similarity metric itself has largely remained classical. In this study, we propose a quantum-enhanced variant of k-means that replaces the Euclidean distance with a quantum kernel derived from the inner product between feature-mapped quantum states. Using the Iris dataset, we use multiple quantum feature maps, including entangled SU2 and ZZ circuits, to embed classical data into a higher-dimensional Hilbert space where cluster structures become more separable. We will also be testing using another dataset, namely the breast cancer dataset. Similarity between data points is computed through the inner product between two states. Our results show that this approach achieves improved clustering stability and competitive accuracy compared to the classical algorithm, with the SU2 feature map yielding an accuracy of 88.6 % on the Iris dataset and 91.0 % on the breast cancer dataset, despite operating on NISQ-feasible shallow circuits. These findings suggest that quantum kernels provide a richer similarity landscape than traditional distance metrics, offering a promising path toward more robust unsupervised learning in the NISQ era.

Programmable neutral-atom arrays offer a promising route toward scalable quantum computing, where coherent qubit transfer enables non-local connectivity and reduces resource overhead. However, transfer speed and motional heating remain key bottlenecks for fast and deep quantum circuits. Here, we employ a fiber array neutral-atom quantum computing architecture with site-resolved control of trap depths to realize smooth amplitude exchange between static and moving traps, thereby enabling fast and coherent qubit transfer with ultralow motional heating. With a 10 $\mu$s in situ transfer between static and moving traps, we obtain a per-cycle heating rate of 0.156(9) $\mu$K, sustain over 500 cycles with negligible atom loss, and achieve a quantum state fidelity of 0.99992(5) per cycle. For inter-site transfer between two separated static traps, the operation takes 120 $\mu$s with 0.783(17) $\mu$K heating per transfer, and remains negligible atom loss for up to 100 repeated cycles with a fidelity of 0.9998(1) per transfer. Furthermore, through experimental studies of parallel transfer, we establish a model that elucidates the relationship between array inhomogeneity and the transfer heating rate. This fast, low-heating coherent transfer capability provides a practical route for improving both speed and fidelity in atom-shuttling based quantum computing.

Deploying quantum machine learning algorithms on near-term quantum hardware requires circuits that respect device-specific gate sets, connectivity constraints, and noise characteristics. We present a hardware-aware Neural Architecture Search (NAS) approach for designing quantum feature maps that are natively executable on IBM quantum processors without transpilation overhead. Using genetic algorithms to evolve circuit architectures constrained to IBM Torino native gates (ECR, RZ, SX, X), we demonstrate that automated architecture search can discover quantum Support Vector Machine (QSVM) feature maps achieving competitive performance while guaranteeing hardware compatibility. Evaluated on the UCI Breast Cancer Wisconsin dataset, our hardware-aware NAS discovers a 12-gate circuit using exclusively IBM native gates (6 ECR, 3 SX, 3 RZ) that achieves 91.23 % accuracy on 10 qubits-matching unconstrained gate search while requiring zero transpilation. This represents a 27 percentage point improvement over hand-crafted quantum feature maps (64 % accuracy) and approaches the classical RBF SVM baseline (93 %). We show that removing architectural constraints (fixed RZ placement) within hardware-aware search yields 3.5 percentage point gains, and that 100 % native gate usage eliminates decomposition errors that plague universal gate compilations. Our work demonstrates that hardware-aware NAS makes quantum kernel methods practically deployable on current noisy intermediate-scale quantum (NISQ) devices, with circuit architectures ready for immediate execution without modification.

Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.

We revisit the longstanding issue of why no well defined probability measure exists corresponding to a classical (Kolmogorov) path integral representation of the Dirac equation in Minkowski space. Two complementary perspectives are compared: (i) Zastawniak's observation that the distributional character of the Dirac propagator (presence of derivatives of the delta distribution) obstructs the construction of a nonnegative transition kernel, and (ii) the indefinite signature of the Minkowski metric which prevents positivity of the action and yields oscillatory integrals. We show how these viewpoints can be unified as different manifestations of a single mathematical obstruction from measure theoretical point of view, and we discuss consequences for stochastic representations of relativistic first-order equations.

Phase estimation in quantum interferometry is a major scenario where the quantum advantage is significantly revealed. Recently, the optimal finite-dimensional probe states (OFPSs) for phase estimation in two-mode quantum interferometry have been provided with the absence of noise [J.-F. Qin et al., Phys. Rev. A 112, 052428 (2025)]. However, the noise is inevitable in practice and the previously obtained OFPSs may cease to be optimal anymore. Hence, the forms of the true OFPSs in the existence of various noises are still open questions. Hereby, the noise of particle loss is studied and the true OFPSs under this noise have been investigated with the numerical algorithm named constrained optimization by linear approximation. Furthermore, a two-step measurement strategy is proposed to realize the ultimate precision limit in practice. The validity of this strategy is confirmed by the numerical simulation of practical experiments.

Continuous-variable (CV) cluster states offer a promising platform for large-scale measurement-based quantum computations (MBQC). However, finite squeezing inevitably introduces Gaussian noise during MBQC. While fault-tolerant MBQC schemes exist in principle, they require the scalable incorporation of non-Gaussian resources, such as GKP states, which remain experimentally challenging. Consequently, a central question at this stage is how finite squeezing fundamentally constrains the intrinsic computational power of CV cluster states themselves. In this work, we address this question by analyzing the classical complexity of measurement-based linear optics (MBLO) implemented with such states, motivated by its near-term feasibility and recent experimental progress. We develop an explicit MBLO framework and examine how the squeezing level governs the complexity of the classical simulation of the resulting output states. Specifically, we identify squeezing-level thresholds that delineate classically tractable and intractable regimes, thereby revealing a squeezing-driven complexity phase transition. These findings advance our understanding of the squeezing resources necessary for meaningful quantum computation in current experimental regimes. Furthermore, they underscore the critical need to either scale the squeezing level or integrate error-correction schemes to achieve reliable, large-scale quantum computation with CV cluster states.

Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum chromodynamics, in which the optic theorem and the renormalization group equation can be solved by a unique contour integral written in two different "dual" ways related between themselves by a complex map in the complex plane of Mellin variable. The inverse integral transformation should be modified to be applied for these contour integral solutions. These modified inverse transformations may be used in security protocols for quantum computers. Here we do a brief review of the basic integral transforms and propose their modification for the extended domains.

Ghost imaging was first demonstrated with entangled photon pairs and well-known for its peculiar properties. The signal beam that illuminates the object possesses no spatial resolution, whereas the reference beam, which never interacts with the object, is spatially resolved. Either beam alone cannot retrieve the image, which can only be obtained when the signal and reference beams are correlated. Here we will report a ghost imaging experiment with even more peculiar properties, in which the image can be reconstructed when no photon interacts with the object or even no photon in neither signal nor reference beam. All the photons interacted with the object are discarded. Only the time bins with zero photon are employed to retrieve the image, a process referred to as "ghost imaging with zero photons" hereafter. The reason why ghost image can be retrieved with zero photons is jointly determined by photon-number projection measurement and photon statistics of thermal light. The results are helpful to resolve the debate on the physics of ghost imaging and understand the relation between quantum and classical correlations.

We investigate the critical behavior of momentum-space entanglement entropy at dynamical quantum phase transitions (DQPTs) in translationally invariant two-band insulators and superconductors. By analyzing the Su-Schrieffer-Heeger model, the quantum XY chain, and the Haldane model, we establish that the geometric DQPT condition $\hat{\textbf{d}}_{\textbf{k}}^{i} \cdot \hat{\textbf{d}}_{\textbf{k}}^{f} = 0$ manifests as exact degeneracy $p_{\textbf{k}^{*}}=1/2$ in the entanglement spectrum defined with respect to the post-quench eigenbasis, yielding a maximal momentum-space entropy of $\ln 2$. In one dimension, critical momenta appear as isolated points, whereas in two dimensions they form continuous one-dimensional manifolds, reflecting the dimensional dependence of the underlying critical structure. Importantly, alternative bipartitions such as the sublattice basis produce qualitatively different behavior: the entropy becomes explicitly time-dependent and attains a minimum at DQPT critical times, underscoring the essential role of basis selection. Our results establish that momentum-space entanglement entropy, when evaluated in the appropriate eigenbasis, provides a robust, time-independent diagnostic of DQPTs and offers a unified geometric perspective linking entanglement, topology, and non-equilibrium criticality.

Efficiently simulating many-body quantum systems with Coulomb interactions is a fundamental question in quantum physics, quantum chemistry, and quantum computing, yet it presents unique challenges: the Hamiltonian is an unbounded operator; its Hilbert space dimension grows exponentially with particle number; and the Coulomb potential is singular, long-ranged, and non-smooth, violating the regularity assumptions of many prior state-of-the-art many-body simulation analyses. In this work, we establish rigorous error bounds for Trotter formulas applied to these systems. Our first main result shows that for general initial conditions in the domain of the Hamiltonian, second-order Trotter achieves a $1/4$ convergence rate with explicit polynomial dependence of the error prefactor on the particle number. The polynomial dependence on system size suggests that the algorithm remains quantumly efficient, even without introducing any regularization of the Coulomb singularity. Such a worst-case rate has been observed in prior work for the hydrogen ground state, demonstrating its physical relevance. We further establish one-step local error lower bounds of order $5/4$ for both formulas, showing that the local exponent is sharp. Our second main result identifies a set of physically meaningful conditions on the initial state under which the convergence rates improve, with the full first-order and second-order rates recovered at sufficiently high angular momentum. Our theoretical findings are consistent with prior numerical observations. Our third main result establishes improved convergence rates for many-body fermionic Coulomb systems with initial data of different Sobolev regularity. In particular, even without imposing any additional regularity beyond the natural domain of the Hamiltonian, both the first- and second-order Trotter formulas converge with rate $1/2$, rather than the general $1/4$ rate.

Precise environmental-noise characterisation in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Non-parametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra, (ii) control filter functions are no longer encumbered by time-ordering. In particular, we show that this approach enables the seamless generalisation of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that effectively remove time-ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in general probabilistic process theories, which include both classical probabilistic models and quantum instrument models as special cases. We show how many aspects of quantum-like cognition can be described diagrammatically in process theories, before using our approach to assess the arguments for quantum-like models. While standard Bayesian classical models are insufficient, we prove that any sequential decision data can in fact be given a more general form of classical instrument model, and see that even simple deterministic models can exhibit all cognitive effects. Restricting attention to instruments induced by measurements, such as classical Bayesian and quantum POVM models, rules out such a result, but is challenged by the fact that such instruments cannot account for certain effects. Finally, we argue that to strictly rule out classical instrument models one should make use of parallel composition in the modelling of joint decisions, and find real world cognitive data violating Bell inequalities.

Entanglement criteria based on variances or Fisher information are well developed for compact collective spin algebras, but their extension to non-compact dynamical sectors is less straightforward. In particular, double-quantum (DQ) observables associated with effective SU(1,1) structures can lead to formally unbounded classical fluctuation estimates unless additional physical constraints are imposed. In this note, we develop a thermodynamic witness framework in which the classically accessible fluctuation sector is strictly bounded by finite-temperature detailed-balance conditions and motionally narrowed sequence-transfer limits. By analyzing the quantum dynamical semigroup of the spin-bath interaction, we demonstrate that spontaneous transient pair correlations generated by a stationary incoherent bath are contractively capped near an amplitude of \(10^{-9}\). Furthermore, classical coherent sequence amplification is empirically bounded to \(\mathcal{O}(10^{-2})\) in motionally narrowed tissue. The resulting functional provides a concrete, theoretically derived bounding framework against which macroscopic DQ anomalies (e.g., fractional amplitudes on the order of \(10\%\) to \(15\%\)) can be rigorously classified as classically inexplicable, provided macro-scale structural stability (constant \(T_2^*\)) is empirically verified.

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We provide evidence for these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP = BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

We analyze fermionic entanglement and correlation measures in the ground and the low temperature thermal state of the water molecule as a function of the internuclear distance in the context of the full configuration interaction approach. The aim is to obtain a general entanglement based characterization of the electronic eigenstates. We consider first the spin-up - spin-down partition and the associated Schmidt decomposition, examining the total up-down entanglement of the electronic wave function. We then consider the one- and two-body entanglement derived from the one- and two-body reduced density matrices (DMs), which measure both the deviation of the state from a Slater Determinant (SD) as well as the up-down correlation at the two-body level. All blocks of these DMs are examined. We also introduce and analyze new measures like the up-down two-body mutual information and two types of two-body negativities, the latter measuring the "inner" entanglement of the reduced two-body DMs, i.e., their deviation from a convex mixture of SDs. Finally, the dissociation limit is also analyzed, considering both the exact ground state (GS) as well as the thermal state in the zero temperature limit, representing the projector onto the "GS band" of almost degenerate lowest lying eigenstates.

Dynamic control of visible light is crucial for technologies such as holographic displays and adaptive optics. Passive metasurfaces can shape wavefronts at the subwavelength scale and active metasurfaces promise to extend this functionality into the temporal domain. However, existing metasurfaces for dynamic phase manipulation typically cannot deliver phase modulation across a broad range without causing variations in the scattering amplitude. Here, we use an inverse-design pipeline to numerically demonstrate a hybrid-2D excitonic metasurface platform offering independent amplitude and phase control in the visible regime. Harnessing the gate-tunable excitonic response of monolayer WS2 retrieved from experiments, we design a pi-phase modulator with a uniform amplitude profile. Adding a second tunable monolayer, we achieve independent control of the amplitude and phase over the full 0-2pi phase range, which we leverage for a reconfigurable beam-steering metadevice. Our results demonstrate how hybrid-2D excitonic metasurfaces enable electrically tunable wavefront shaping in the visible regime.

A foundational result in relativistic quantum information theory due to Peres, Scudo, and Terno, is that von Neumann entropy is not Lorentz invariant. Motivated by the "It from Qubit" paradigm, here we show that Lorentzian symmetries of quantum information emerge naturally in a pre-spacetime setting, without any reference to external variables such as position or momentum. In particular, we derive the natural action of the restricted Lorentz group $\text{SO}^+(1,3)$ on the internal degrees of freedom of a single qubit from a simple, information-theoretic principle we refer to as preservation of linear entropy. It is then shown that the Lorentz invariance of the linear entropy of a relativistic qubit is a special case of a much more general phenomenon, namely, that any spectral invariant of an operator we term the '$W$-matrix' is an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant scalar. Consequently, the linear $n$-partite quantum mutual information is shown to be an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant for all $n$-qubit states. Finally, we show that the correlation function associated with a pair of qubits in the singlet state yields the Minkowski metric on the space of qubit observables, whose symmetry group is the full Lorentz group $\text{SO}(1,3)$. In accordance with the "It from Qubit" paradigm, our results thus establish the natural emergence of relativistic spacetime structure from intrinsic properties of quantum information.