Papers

Hybrid quantum neural networks are increasingly explored for classification, yet it remains unclear how their performance and quantum behavior scale with circuit depth and qubit count. We present a controlled scaling study of hybrid quantum-classical classifiers along two axes: (1) increasing the number of quantum layers L at fixed qubits Q, and (2) increasing the number of qubits Q at fixed depth L. Across multiple datasets, we evaluate predictive performance using Accuracy, PR-AUC, Precision, Recall, and F1, and track quantum-specific metrics (QCE, EEE, QGN) to characterize how quantum properties evolve under scaling. Our results summarize scaling trends, saturation regimes, and dataset-dependent sensitivity, and further analyze how quantum metrics relate to predictive performance. This study provides practical guidance for selecting (Q,L) in hybrid QNN classifiers and establishes a consistent evaluation protocol for scaling analysis.

Entanglement is a key quantity for characterizing quantum correlations in particle scattering processes, but its direct evaluation is computationally demanding on quantum hardware. In this work, we investigate whether fermion density profiles, which are easier to access, can serve as proxies for entanglement by framing the problem as a classification task across multiple entanglement thresholds. Using the fermion scattering in the Thirring model as a test bed, we compare Quantum Convolutional Neural Networks (QCNNs) with classical CNNs of comparable parameter counts, and find that QCNNs achieve consistently competitive or superior accuracy with faster convergence and lower variance. Notably, we observe that increasing the model size does not improve the performance within the architectures studied here, and larger models appear to be more sensitive to the choice of encoding. Instead, a compact 4-qubits QCNN provides the best results, suggesting the importance of trainability and encoding choices over model scaling. These findings demonstrate the potential of quantum and quantum-inspired machine learning models for extracting nontrivial quantum information from accessible observables, with implications for high-energy physics and quantum many-body systems.

Expectation values of measurement operators, interpreted as measurement probabilities, arise frequently throughout quantum algorithms. When quantum states are randomly distributed, their expectation values are also randomly distributed. In this work, with the goal of understanding non-unitary dynamics, we generalize previous derivations for distributions of expectation values [Campos et al., Phys. Lett. A 377, 1854 (2013)] to the case of sets of measurement operators and random mixed quantum states within variable sized environments. Using combinatorics approaches, we derive expressions for their moments. We proceed to construct empirical distributions of simulated Haar random brickwork quantum circuits with local depolarizing noise, and compare their form to a proposed effective global-depolarizing-like model with variable effective noise scales and environment dimensions. The fitted effective distributions reproduce peak behaviour across circuit depths, noise scales, and system sizes, while deviations in the distribution tails arise from local noise effects. The fit effective model parameters are also shown to vary smoothly and consistently with circuit depth and noise scale. Finally, sets of non-symmetric measurement operators are shown to exhibit distinct multi-modal distributions relative to uni-modal distributions for symmetric measurement operators, opening up questions about their simulability.

We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $\rho$, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of $\rho$. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $\sigma$, decide whether $\rho=\sigma$ or $\|\rho-\sigma\|_1\geq \epsilon$. Additionally, we focus on the case of limited quantum communication between distributed nodes and the central node. We show that when each communication channel is limited to only $n_q\leq \log d$ qubits, then the sample complexity of distributed state certification is $\mathcal{O}(\frac{d^2}{2^{n_q}\epsilon^2})$ when public randomness is available to all nodes. Moreover, under the assumption that the channels used by the distributed nodes are mixedness-preserving, we prove a matching lower bound. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $\Omega(\frac{d^3}{4^{n_q} \epsilon^2})$ lower bound in the private-coin setting under the same assumption as above. Our lower bounds leverage a recently introduced quantum analogue of the celebrated Ingster-Suslina method and generalize arguments from the classical setting. Together, our work provides the first characterization of distributed quantum state certification in the regime of limited quantum communication and establishes a general framework for distributed quantum inference with communication constraints.

We investigate the quantum phases of a half-filled generalized interacting Su-Schrieffer-Heeger model with intracell, nearest-neighbor, and next-nearest-neighbor intercell hoppings, together with an on-site inter-sublattice interaction. In the noninteracting limit, the model hosts one topologically trivial phase and two symmetry-protected topological (SPT) phases, distinguished under periodic boundary conditions by different winding numbers and under open boundary conditions by two-fold and four-fold entanglement-spectrum degeneracies, respectively. When interactions are introduced, these free-fermion SPT phases evolve into distinct interacting topological phases that retain characteristic signatures such as entanglement-spectrum degeneracy structures, boundary modes, and nonzero string order parameters. For strong repulsive interactions, a symmetry-breaking phase with unequal but spatially uniform sublattice densities appears between the trivial and topological regimes. For strong attractive interactions, period-2 and period-4 charge-density-wave phases emerge from particle clustering. At intermediate attractive interactions, the competition between interaction-induced localization and hopping-induced delocalization gives rise to a Luttinger liquid phase, a paired Luttinger liquid phase, and a gapless symmetry-protected topological (gSPT) phase. The gSPT phase is characterized by a gapless charge mode together with symmetry-protected current-carrying edge states. We further characterize the gapless phases and the associated quantum phase transitions through central charges and critical exponents.

Quantum advantage, broadly understood as the ability of quantum systems to significantly outperform their classical counterparts, underpins current interest to quantum technologies and is a topic of active investigation. In many situations, its existence is subject to debate, and the areas of supremacy of large-scale quantum systems are not well defined. Here, we uncover a novel niche where quantum advantage can be clearly defined and proven. We study a time-optimal transfer of excitations in the lattice involving both nearest-neighbor and longer-range couplings. We prove that the quantum-mechanical property of a particle to propagate along several trajectories simultaneously speeds up the transfer process, which takes a shorter time compared to any particular trajectory and thus provides a clear example of quantum advantage.

We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} , \cdots , H_{i_M}\}$ (for all $i$) are classically known, we present a procedure (with three variants) in which these operators are classically diagonalized, and then this information is fed into three possible quantum procedures to obtain the block-encoding of $H$. The evolution operator $\exp(-iHt)$ is then obtained using the standard block-encoding/quantum singular value transformation framework. In the case where $\{H_i\}_{i=1}^K$ commute pairwise, our method can be trivially extended to the case with time-dependent coefficients. We provide a detailed discussion of the efficient regime of our hybrid framework and compare it with existing quantum simulation algorithms. Our algorithm can serve as a useful complement to existing quantum simulation algorithms, thereby expanding the reach of quantum computers for practically simulating physical systems. As a side contribution, we will show how the recent technique called randomized truncation to a quantum state developed by Harrow, Lowe, and Witteveen [arXiv preprint arXiv:2510.08518, 2025] can be applied to the context of quantum simulation and particularly quantum state preparation, for which the latter can be of independent interest.

We study non-Hermitian quantum mechanics of an inverted triple-well potential within the exact WKB framework. For a single classical potential, different Siegert boundary conditions define three distinct quantum problems: the PT-symmetric, resonance, and anti-resonance systems. For each case, we derive the exact quantization condition and construct the associated trans-series solution. By identifying the resurgent structures and cancellations in these non-Hermitian setups, we obtain the median-summed series, clarifying when the spectra are real or complex in accordance with the physical properties of each system. Establishing explicit links to the semi-classical path integral formalism, we elucidate the roles of bounce and bion configurations in these non-Hermitian systems. This analysis predicts PT-symmetry breaking, which we also verify numerically. Using the median quantization conditions, we prove the existence of this symmetry breaking and establish an exact equation for the exceptional point, which emerges as a remarkably simple algebraic relation between the bounce and bion actions. We further show that the median-summed non-perturbative correction to the spectrum vanishes at the exceptional point, while the resurgent structure survives through a universal minimal trans-series. For the resonance and anti-resonance systems, we find that the exact median-summed spectra are related by complex conjugation, representing time reversal in this setting, are necessarily complex, and do not exhibit an exceptional point. Although their spectra differ significantly from the PT-symmetric case, they share the same minimal trans-series. By maintaining explicit links with the path integral saddles and the formal theory of resurgence, our analysis provides a unified and general perspective on the quantization of non-Hermitian theories.

Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and impair their error correction capabilities. Although defect adaptive methods for surface codes have been extensively studied, other topological codes such as color codes still lack a systematic framework for handling defects. To address this issue, we propose a universal superstabilizer scheme applicable to data qubit defects in arbitrary stabilizer codes. Based on this scheme, we develop concrete repair methods for isolated defects of both internal data qubits and ancilla qubits in color codes defined on square lattices. Furthermore, for ancilla qubit defects, we present two optimization schemes. One scheme reuses neighboring ancilla qubits, and the other employs iSWAP gates. Unlike conventional approaches that directly disable neighboring data qubits and thus cause resource waste, both of our schemes avoid such waste and consequently achieve a lower logical error rate.Integrating the above techniques, we construct a comprehensive defect adaptive architecture for color codes to handle various defect clusters. We also show that our scheme supports a full transversal Clifford gate set and lattice surgery operations. These results provide a systematic theoretical pathway for deploying robust and low overhead color codes on defective quantum hardware.

Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable protocols remain rare, mainly because Hamiltonian engineering in higher dimensions lacks the geometric intuition available for qubits. Here we present a general framework for dynamical decoupling in qudit systems, based on Lie group representation theory. By extending the group theory approach to dynamical decoupling, we show how decoupling groups can be systematically identified among the finite subgroups of SU(d) by analyzing their access to the irreducible components of the operator space. As an application, we construct new pulse sequences for interacting qutrit systems based on finite subgroups of SU(3), and show how subgroup factorizations and group orientations can be exploited to obtain shorter and more experimentally practical protocols for spin-1 systems with large zero-field splitting. We further show that the same symmetry-based framework yields quantum error-correcting codes: whenever a finite subgroup of SU(d) acts as a decoupling group for the relevant set of operators, the associated one-dimensional symmetry sectors define codespaces satisfying the Knill-Laflamme conditions, thereby unifying dynamical decoupling and quantum error correction in multi-level quantum systems.

Consider a rectangular grid of qubits in 2D with single-qubit and nearest-neighbor two-qubit operations subject to local stochastic Pauli noise. At different length scales, this setup describes both a single quantum computing device with geometrically limited connectivity between qubits arranged on a disc, and planar networks composed of quantum repeater stations of constant size. We give a protocol which robustly generates entanglement between distant qubits in this setup. For noise below a constant threshold error strength, it generates a constant-fidelity Bell pair between qubits separated by an arbitrarily large distance $R$. To generate distance-$R$ entanglement, a rectangular grid of qubits of dimensions $\Theta(R)\times \Theta(\mathsf{poly}(\log R))$ suffices. Our protocol applies quantum operations in one shot, establishing a Bell state in a constant time up to a known Pauli correction. In contrast, existing entanglement generation protocols either require local quantum devices controlling a number of qubits growing with the targeted distance, or are not single-shot, i.e., have a distance-dependent execution time. The protocol leverages many-body entanglement in networks and provides the first example of a short-range entangled state in 2D with long-range localizable entanglement robust to local stochastic Pauli noise. As an immediate corollary, we construct a 2D-local stabilizer Hamiltonian whose Gibbs states possess long-range localizable entanglement at constant positive temperature.

We investigate the overall optomechanical force experienced by a macroscopic lossy object in free space under external quantum illumination. To this end, utilizing the Modified Langevin Noise Formalism (MLNF), we derive the time-averaged expectation value of the Maxwell stress tensor for a non-equilibrium scenario in which the incoming scattering field is prepared in an arbitrary mixed quantum state, while the medium-assisted field is maintained in local thermal equilibrium. In the limit of full radiation-matter thermal equilibrium, our expression exactly recovers the well-known fluctuation-dissipation relation governing the Casimir effect, and, under coherent illumination, it yields the standard classical radiation pressure. We demonstrate that by driving the scattering field with an anisotropic, multimode squeezed vacuum state, the spatial profile of the electromagnetic quantum fluctuations can be engineered to exhibit broken rotational symmetry, thereby inducing a purely quantum mechanical force acting on the object. Such mechanical interaction is generated in the strict absence of a mean field, $\langle\hat{\mathbf{E}}\rangle=0$, and its non-classical nature is evidenced by its reliance on second-order field correlations $\langle\hat{\mathbf{E}}^2\rangle$, unlike classical optical radiation pressure governed by the squared mean field $\langle\hat{\mathbf{E}}\rangle^2$. Applying this exact formulation to a homogeneous lossy sphere, we demonstrate the experimental feasibility of the effect using realistic material parameters and optical estimations. Ultimately, we establish a general formalism for macroscopic quantum optomechanics that operates beyond the constraints of thermal equilibrium, enabling the prediction of regimes where the purely quantum force circumvents classical mean fields and shot noise while preserving the object's macroscopic quantum coherence.

We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.

We investigate the light statistics of an ensemble of independent motionless two-level atoms in a product state. We identify the conditions under which the cold atomic ensemble emits thermal light statistics characterized by the Gaussian Moment Theorem. For the theorem to hold, we derive for each correlation order two conditions on the atom number and the ratio of coherent to incoherent light emission. We further discuss their validity for atoms either in a pure or mixed state. Our results contribute to the understanding of the generation of thermal light by two-level atoms without interactions among the emitters.

Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit $n \to 1$. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of JT gravity coupled to a large-$c$ bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-$n$ information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the $n=1$ limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.

Nonlinear optical processes, mediated by multiphoton interactions rather than single-photon response, are routinely exploited to enable a range of light-based functionalities in devices and applications. Nonlinear effects are enhanced through higher intensity fields, which is a limiting strategy owing to potential radiation damage. An alternative strategy relies on the fluctuation redistribution typical of quantum light, but experimental demonstrations at the most fundamental level have been limited. Here we report experimental nonlinear tunnelling ionization of isolated atoms, a pivotal nonlinear process that drives high-harmonic generation and forms the basis of attosecond science, boosted by quantum light – bright squeezed vacuum (BSV). A BSV light with an average pulse energy of 300 nJ achieves an effective intensity equivalent to that of a coherent light with 7.1 {\textmu}J, demonstrating a more than 20-fold quantum boost in nonlinear effect from BSV light. This boost is revealed by matching the peaks of the photoelectron momentum spectra produced by the BSV and coherent light using angular streaking. Furthermore, we demonstrate control of the effective intensity of the BSV by tuning the correlation function at fixed average pulse energy, establishing a robust method to tailor nonlinear processes via quantum statistics rather than classical intensity scaling. These findings may facilitate the development of quantum-controlled strong-field dynamics using tailored quantum light sources.

Amplitude Amplification offers a provable speedup for search problems, which is leveraged in combinatorial optimization by Grover Adaptive Search (GAS). The protocol demands deep circuits that are challenging with regards to NISQ capabilities. We propose a nested Amplitude Amplification protocol for the binary knapsack problem that splits the decision tree at a tunable depth, performing a partial amplification on the first variables before executing a global GAS on the full search space. The partial amplification is implemented by an Inner Iteration Finder that selects the rotation count maximizing marked-subspace amplitude. The resulting biased superposition serves as the initial state for the outer Amplitude Amplification. Using the Quantum Tree Generator for feasible-state preparation and an efficient classical amplitude-tracking scheme, we simulate the protocol on knapsack instances of sizes intractable by statevector simulation. Our results show that the nested approach reduces the cost of improving an incumbent solution compared to baseline GAS, particularly for a specific subset of knapsack instances. As combinatorial problems in domains such as semiconductor supply-chain planning grow in scale, methods that reduce circuit cost are an important step toward eventual quantum advantage for such applications.

Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.

Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number $N$, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.

The quantum Rabi model has been a useful and pedagogical quantum model in the past decades, sufficiently simple to be solved analytically and intuitively understood, while sufficiently complex as to provide highly non-trivial eigenstates and a practical description of quantum optical platforms for quantum technologies. The Dirac equation, especially when restricted to 1+1 dimensions, is a simple toy model as well, but its easy diagonalization enabled historically to connect the electron spin to the fermionic statistics, among others. Both models share a symmetry at the purely mathematical level, namely, the spectra of each one has a dual equivalent under energy sign change, that I name a mirror dual symmetry. Usually, one quantizes these equations by assuming a ground state energy for the bosonic mode. But there is another option for the interpretation of the Hamiltonian, as I will argue, that is to assume a total symmetry principle, namely, that the total energy is zero at all times, for either the quantum Rabi model or the Dirac equation, and impose the constraint that every positive energy excitation has a mirror excitation of negative energy. This possibility, which was, apparently, ignored in the times when Paul Dirac was studying the implications of his equation, would avoid the worries in the scientific community that the negative energy solutions would decay until minus infinity, thus obviating the necessity to build a highly artificial Dirac sea, and instead impose what has always been successful in Physics, which is the enforcement of symmetry principles. Assuming a total symmetry principle, many of the problems of current Physics, such as renormalization of quantum gravity, dark matter, and dark energy, may possibly be automatically solved. One obvious result would be the automatic cancellation of the zero point energy.

The development of large-scale superconducting quantum computing requires efficient in-situ control methods that allow high-fidelity operations at millikelvin temperatures. Superconducting circuits based on Josephson junctions offer a promising solution due to their high speed, low power dissipation, and cryogenic nature. Here, we report a superconducting quantum controller that enables direct chip-to-chip interconnection with qubits at 10 mK and high-fidelity, all-digital manipulation. Randomized benchmarking reveals a uniformly high average Clifford fidelity of 99.9% with leakage to high energy levels on the order of $10^{-4}$, and an estimated average gate operation energy of 0.121 fJ, demonstrating the potential to resolve the control bottleneck in superconducting quantum computing.

In several articles, this author has advocated an alternative approach towards quantum foundation based upon a set of postulates, and based upon the notions of theoretical variables and of accessible theoretical variables. It is shown in this article that this basis can be considerably simplified. In particular, the assumption that there exists an inaccessible variable $\phi$ such that all the accessible ones can be seen as functions of $\phi$, can be dropped. This assumption has been difficult to motivate in the previous articles. From this, I get a simple basis for the main Theorems.The essential assumption is that there in the given context exist two different maximal accessible variables, what Niels Bohr would have called two complementary variables. From this, the whole Hilbert space formalism may be derived. It is also discussed in some detail how this Hilbert space can be chosen. The resulting theory is a purely mathematical theory, but it leads to quantum mechanics by letting the variables be physical variables. Other applications of the main theory are also considered. The mathematical proofs are mostly deferred to the Appendix.

Parameterized stable homotopy theory organizes local systems of spectra over homotopy types, governed by a "yoga" of six functors. To provide semantics for the recently developed Linear Homotopy Type Theory (LHoTT), good model categories of these spectra are required, preferably monoidal with respect to the external smash product. We focus on the case of parameterized $H\mathbb{K}$-module spectra ($\infty$-local systems), motivated by recent applications of parameterized homotopy to topological quantum computing. While traditionally treated via dg-categories, we leverage combinatorial model structures on simplicial chain complexes to construct the first dedicated global model structure for $\mathbb{K}$-linear $\infty$-local systems, which offers better control than existing models for general parameterized spectra. In particular, when restricted to base 1-types, our model structure is monoidal with respect to the external tensor product, making it a candidate target semantics for the multiplicative fragment of LHoTT.

Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence and imaginarity resources. We establish a lower bound on the circuit cost by the Tsallis relative $\alpha$ entropy of cohering power, which is shown to be tighter than the one presented by Bu et al.[Communications in Mathematical Physics 405, no. 7 (2024):161] under restrictive conditions. As a consequence, we obtain the relationships between the circuit cost and the coherence generating power via probabilistic average in terms of skew information/relative entropy, and present explicit bounds of the circuit cost for typical quantum gates. Moreover, we derive lower bounds on the circuit cost via the imaginaring power of the circuit, induced by the Tsallis relative $\alpha$ entropy and relative entropy. We demonstrate that imaginarity can yield nontrivial constraints on the circuit cost even when coherence-based lower bounds are zero (e.g., for the $T$ gate), which implies that imaginarity may provide advantages under certain circumstances compared with coherence. Our results may help better understand the connections between quantum resources and circuit complexity.

We propose a quantum machine learning framework for estimating classical covariance matrices using parameterized quantum circuits within the Pauli-Correlation-Encoding (PCE) paradigm. We introduce two quantum covariance estimators: the C-Estimator, which constructs the covariance matrix through a Cholesky factorization to enforce positive (semi)definiteness, and a computationally efficient E-Estimator, which directly estimates covariance entries from observable expectation values. We analyze the trade-offs between the two estimators in terms of qubit requirements and learning complexity, and derive sufficient conditions on regularization parameters to ensure positive (semi)definiteness of the estimators. Furthermore, we show that the barren plateau phenomenon in training the variational quantum circuit for E-estimator can be mitigated by appropriately choosing the regularization parameters in the loss function for HEA ansatz. The proposed framework is evaluated through numerical simulations using randomly generated covariance matrices. We examine the convergence behavior of the estimators, their sensitivity to low-rank assumptions, and their performance in covariance completion with partially observed matrices. The results indicate that the proposed estimators provide a robust approach for learning covariance matrices and offer a promising direction for applying quantum machine learning techniques to high-dimensional statistical estimation problems.

The symmetry-resolved Krylov complexity is a useful tool for studying the chaotic properties of systems endowed with symmetries. We investigate the conditions under which an invariant Hermitian operator would have the symmetry-resolved Krylov complexity in a charge subspace identical to the Krylov complexity of the full operator, and find a necessary and sufficient condition that ensures this matching at all temperatures. Further, we study the Krylov complexity of the Uncoloured Tensor Model, a disorder-free kin of the SYK Model, which has a plethora of symmetries. We identify charge subspaces of the same operator in which equipartition holds, as well as those where it doesn't, along with observations on the underlying mechanism behind these. We also find that, within the computational limits, the Krylov complexity, averaged over the symmetry subspace, is bounded above by that of the operator in the full space.

When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace distance between two quantum states, computing it for any two general density matrices remains computationally demanding. In this paper, we propose a quantum algorithm based on the exponentiation of the density matrix and the improved quantum phase estimation (IQPE) to determine the trace distance for both pure and mixed states, with a time complexity of $O(N^2/\varepsilon^6)$ where $N$ is the number of qubits of the given states and $\varepsilon$ is the simulation or estimation precision error. We demonstrate its ability to predict the quantity with proof-of-principle simulations and also quantum hardware computations on the IBM quantum computers, confirming its promise for near-term quantum devices.

The natural gradient descent optimisation technique is an efficient optimising protocol for broad classes of classical and quantum systems that takes the underlying geometry of the parameter manifold into account by means of using either the Fisher information metric of the classical probability distribution function or the Fubini-Study tensor of the associated parametrised quantum states in the consequent update rules. Even though the natural gradient descent procedure utilises the geometry of the space of probability or states, it is, however, insensitive to the measure of parametrised distance on the space of possible outcomes when the corresponding optimising problem is considered for the expectation value of a classical or quantum observable with respect to the probability distribution or the quantum state. In this work, we introduce a generic optimising principle, where the intrinsic geometry of the space of outcomes has been taken into account suitably, either by using an ambient space construction with a base statistical manifold with the usual Fisher information metric (or the Fubini-Study tensor), where the loss hypersurface is embedded to, or by means of a first-principle construction from the overlap of nearby quantum states on the projective Hilbert space. This construction as well as a family of conformal variants yields a form of loss-aware natural gradient updates that rescale the effective step size while preserving the descent direction. We benchmark the resulting optimisers on variational quantum circuit examples and on a classical neural network task, finding that, while the standard natural gradient remains the most robust on average, the proposed conformal schemes can improve best-case convergence in favourable regimes.

Quantum memories for optical states are essential resources for quantum communication and information processing. We propose a quantum memory protocol based on coherent photon-phonon transduction in a Brillouin-active optical waveguide supporting traveling acoustic modes. A pulsed pump drives an effective beam-splitter interaction between optical and acoustic fields, enabling the mapping of a propagating optical quantum state onto a traveling phononic excitation and its subsequent retrieval on demand. Using a continuum optoacoustic model, we show that the protocol enables broadband quantum state storage in a distributed medium without relying on discrete cavity modes. Analytical and numerical results demonstrate high-fidelity storage and retrieval of squeezed and entangled states under experimentally realistic parameters. The memory bandwidth is set by the Brillouin interaction and can reach hundreds of MHz. Our results identify continuum Brillouin optomechanical systems as a scalable platform for broadband quantum memories and multimode quantum signal processing.

We present a layered and modular network architecture that combines Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC) to provide scalable end-to-end security across long distance multi-hop, trusted-node quantum networks. To ensure interoperability and efficient practical deployment, hop-wise tunnels between physically secured nodes are protected by WireGuard with periodically rotated pre-shared keys sourced via the ETSI GS QKD 014 interface. On top, Rosenpass performs a PQC key exchange to establish an end-to-end data channel without modifying deployed QKD devices or network protocols. This dual-layer composition yields post-quantum forward secrecy and authenticity under practical assumptions. We implement the design using open-source components and validate and evaluate it in simulated and lab test-beds. Experiments show uninterrupted operation over multi-hop paths, low resource footprint and fail-safe mechanisms. We further discuss the design's compositional security, wherein the security of each individual component is preserved under their combination and outline migration paths for operators integrating QKD-aware overlays in existing infrastructures.