Papers

We develop a block-encoding compiler that treats matrix product operators as compressed, virtual-path linear combination of unitaries programs. The compiler constructs conditional PREP and local SELECT stages directly from a parent matrix product operator, establishing tensor networks as structured quantum intermediate representations that can be efficiently compiled to block-encoded circuits. We apply the construction to real-time evolution in the Heisenberg chain and two perturbed Heisenberg-family models. Across the regimes studied, the compressed, approximately unitary propagator MPOs retain mild bond dimension and LCU normalization. Relative to an LCU that explicitly lists the $\mathcal{O}(N^K)$ Pauli-product branches of an order-K truncated Taylor polynomial, our virtual-transition implementation replaces combinatorial branch enumeration by a circuit complexity scaling as $\mathcal{O}(\alpha_{\rm MPO}N\chi^2)$, approaching $\mathcal{O}(N\chi^2)$ when $\alpha_{\rm MPO}$ remains mild. We numerically characterize how truncation order, bond-dimension budget, and system size affect approximation error, normalization, and compiler cost. These results demonstrate how classically compressed tensor-network representations can serve as quantum compiler intermediate representations for block encoding and opens new avenues to accelerate quantum algorithms.

We present a method for performing distributed quantum computing with controlled approximations for circuits that are weakly coupled via a single qubit. Exact distributed quantum computing requires exponential classical information to reconstruct the quantum process. However, we show how the classical cost is reduced to polynomial if the quantum procedure can be partitioned between a qubit that is weakly coupled to the other qubits. We demonstrate our method for a layered circuit based on the circuits used for the quantum approximate optimization algorithm.

Bell- and contextuality-type inequalities have become practical probes of many-body quantum correlations, often involving only few-body correlators and quantities with a direct Hamiltonian interpretation such as an energy density. Here we investigate the mechanism by which translation-invariant Hamiltonians generated from representative families of contextuality witnesses organize their ground-state structure in infinite one-dimensional systems. For the witness families considered, maximal quantum violation is realized by ground-state sectors with commensurate enlarged unit cells: the Hamiltonians are invariant under one-site translations, while the optimal ground states are $p$-periodic with $p>1$. At the corresponding classical-bound points, the ground-state sectors are highly degenerate and support many commensurate periods. Along the interpolation paths analyzed in this work, entering the contextual regime is accompanied by the lifting of this classical period degeneracy in favor of a quantum-selected period. We also identify finite periodic-boundary-condition benchmarks at the selected periods: for each model studied, the finite-ring witness reproduces the same classical bound and quantum value as the corresponding infinite-chain witness, and in several cases the resulting finite inequalities are tight. These reductions turn the infinite-chain contextuality certification into compact energy-estimation benchmarks requiring only local correlator measurements. We establish the mechanism analytically in representative two- and three-body witness models and corroborate it more broadly using translation-invariant semidefinite-program relaxations together with variational matrix-product-state calculations.

Stochastic resetting has emerged as a versatile protocol to drive quantum many-body systems to non-equilibrium steady states by interspersing unitary dynamics with measurements and resets at random times. In spite of this, a quantum hardware validation of such non-equilibrium steady states is still missing. Here, we achieve this goal by first formulating a noisy discrete-time theory where unitary gates alternate with noisy mid-circuit projective measurements and conditional resets. This noisy conditional resetting theory is then demonstrated on a superconducting quantum processor for up to $N=7$ qubits. We consider, as a paradigmatic case, the unitary dynamics of the interacting Floquet transverse-field Ising model. The stationary state of the noisy conditional resetting agrees quantitatively with the experiments, and it shows crossover behavior related to the equilibrium quantum phase transition of the model. Our results might thus pave the way for the preparation of collective stationary states on noisy quantum devices and for further developments of quantum algorithms involving mid-circuit measurements.

The Dirac operator on a lattice cannot be both local and free of fermion doubling, at least not without breaking fundamental symmetries. Non-local, symmetry-preserving discretizations that avoid doubling have a quantum circuit representation as a linear-combination-of-unitaries (LCU) in which both the number of terms and their norm (the subnormalization factor) grow with the lattice size, compromising the efficiency of a quantum algorithm. We show that the tangent-fermion discretization escapes this obstruction when the Dirac equation is written as a generalized eigenvalue problem with a local operator pencil: Each member of the pencil has an exact LCU, with term count that is independent of lattice size and with subnormalization factor of order unity, on a par with elliptic operators. This provides an efficient block-encoding primitive for Dirac spectra and Green functions without fermion doubling.

Optically addressable shallow donors in ZnO combine efficient spin-selective optical transitions with the potential for long spin coherence in an isotopically purifiable host lattice, making them an attractive platform for spin-photon quantum technologies. A key missing capability, however, has been coherent control beyond the small-angle rotations accessible with ultrafast optical pulses. Here we demonstrate coherent microwave control of implanted $^{115}\mathrm{In}$ donors in ZnO. Resonant optical pumping initializes and reads out the donor electron spin. Pulsed optically-detected magnetic resonance resolves the ten hyperfine transitions associated with the coupled $^{115}\mathrm{In}$ nuclear spin (I = 9/2) and reveals optical-pumping-induced nuclear spin polarization. We observe coherent Rabi oscillations with a maximum Rabi frequency of $\Omega/2\pi = 36.2 \pm 0.7$\;MHz, corresponding to a $\pi$-pulse time of 13.8$\pm$0.3\;ns, and characterize the spin coherence using Ramsey, Hahn echo and dynamical-decoupling measurements. Unexpectedly, the measured coherence is substantially shorter than reported in previous optical studies of donor spins in ZnO at high magnetic field. Control experiments rule out several simple explanations including microwave heating and instantaneous diffusion from the driven donor ensemble, leaving an open question regarding the origin of decoherence at low magnetic field in microwave-controlled ZnO donors. These results establish microwave control of ZnO donor qubits with resonant optical access to specific donor species. More broadly, they demonstrate that coherent microwave control can be achieved in optically addressable spin systems with nanosecond-scale inhomogeneous dephasing, enabling field-, temperature-, and materials-dependent studies of coherence-limiting mechanisms and the development of optically interfaced electron-nuclear spin registers.

We discuss here how non self-adjoint Hamiltonians, and their related Heisenberg-like dynamics, can be used to model a political system consisting in a coalition $\C$ of different parties (forming a government) and by their (original) supporters $\Sc$. Our aim is to model how the opinion of these supporters changes depending on the efficiency, competence and coherence of the coalition $\C$, as these are perceived by $\Sc$ during their action while governing. After a rather general introduction we propose three specific models, and we describe and comment the dynamical behaviour of the { full} system, $\Sc\cup\C$. The role of the so-called balanced Hamiltonians, recently introduced by the authors in connection with integrals of motion, is discussed in details.

We introduce a quantum reservoir computing online protocol that realizes amplitude encoding on quantum hardware. Our scheme combines mid-circuit measurement and reset operations to implement the partial-trace dynamics underlying amplitude encoding, while an indirect measurement scheme provides access to reservoir observables without interrupting temporal processing. In contrast to other approaches, our method preserves online operation, avoids input buffering, and keeps the runtime linear in the number of time steps. We present the theoretical formulation of the protocol and a proof-of-principle implementation on quantum hardware, and we evaluate its performance on two standard benchmark tasks. Our results show that the reservoir dynamics can be monitored through both direct measurements of the input qubits and indirect measurements of the memory qubits, enabling observation of the full system while isolating the internal evolution of the reservoir. This work provides a practical route toward scalable hardware implementations of amplitude-encoded quantum reservoir computing and opens the door to systematic experimental studies of complex quantum reservoirs.

Out-of-time-ordered correlators (OTOCs) have emerged as a diagnostic of information scrambling and quantum chaos in many-body systems. We investigate the imprints of chaos in the dynamics of OTOCs in the Heisenberg spin-$1/2$ chain with random fields. The system is parameterized to exhibit a crossover from integrable to chaotic dynamics. We demonstrate numerically that the approach to saturation of the OTOC can distinguish between integrable and chaotic regimes, with a power-law $(1/t)$ relaxation for integrable systems and a higher-degree power-law decay $(1/t^\alpha; \alpha \ge 1)$ followed by an exponential relaxation for the chaotic regime. We further show that long-range spectral statistics, such as the number variance, are more effective in characterizing quantum chaos in the regime near saturation of OTOC. We also demonstrate that the relaxation and initial scrambling regimes exhibit distinct and universal features, with the former being sensitive and the latter being robust against different realizations of random-fields. The long-time saturation of OTOC also fluctuates with different realizations, and its exact expression is derived through the Eigenstate Thermalization Hypothesis.

Electronic correlations in graphene are generally considered weak due to the large bandwidth of its $\pi$ electrons. Here we show that tensile expansion of the honeycomb lattice provides a direct route to enhancing correlation effects. Using variational and diffusion quantum Monte Carlo, we compare a conventional Jastrow-Slater determinant wave function with a resonating-valence-bond (RVB) Jastrow-antisymmetrized geminal product ansatz for a series of stretched graphene lattices. We find that the energy gain of the RVB state relative to the single-determinant description increases with bond expansion up to a critical strain $\delta_{\mathrm{cr}}$, and decreases beyond it, revealing a nonmonotonic evolution of electronic correlations. The crossover is found to occur in the range $15\% < \delta_{\mathrm{cr}} < 20\%$, in agreement with mechanical stability limits. This behavior indicates a transition from a weakly correlated Dirac semimetal to a regime with enhanced non-dynamic correlation and short-range singlet pairing. Our results provide direct many-body evidence that lattice expansion drives graphene into a regime where RVB-like correlations become energetically favorable, offering a simple route to tuning correlation effects in Dirac materials.

We introduce the Biorthogonal Variational Quantum Eigensolver (B-VQE), a quantum algorithm for simulating non-Hermitian many-body systems on noisy intermediate-scale quantum (NISQ) hardware. Non-Hermitian quantum matter exhibits exceptional points, parity-time symmetry breaking, and non-Hermitian skin effects, yet existing quantum algorithms often rely on costly post-selection procedures and are not designed to capture biorthogonal eigenstates. B-VQE employs independent variational circuits to represent the left and right eigenstates of a non-Hermitian Hamiltonian and optimizes a biorthogonal objective function that directly tracks non-Hermitian phase transitions. The framework incorporates an Exceptional-Point Detector (EPD) that identifies exceptional points through a hardware-native coalescence metric and a Non-Hermitian Quantum Geometric Tensor (NH-QGT) readout that distinguishes state-topological and band-topological signatures in interacting many-body systems. To overcome the exponential overhead associated with conventional non-Hermitian simulation, we develop an importance-sampling mitigation strategy that removes the need for ancilla-based post-selection while retaining polynomial computational scaling. We validate the approach on three representative models: a non-Hermitian Hubbard chain, a non-Hermitian XXZ spin chain, and a two-dimensional non-Hermitian (t)-(J) model. B-VQE achieves relative energy errors below (5\times10^{-3}) and locates exceptional points with high accuracy on noise-free simulations while resolving phase boundaries associated with localization, quantum scars, and skin-effect physics. These results establish B-VQE as a scalable NISQ methodology for constructing non-Hermitian many-body phase diagrams and exploring topological and critical phenomena in open quantum systems.

The continuous progress of quantum technologies has spurred the exploration of their potential applications across diverse fields, particularly in combinatorial optimisation. In this work, we study a quantum-classical optimisation framework based on Pauli Correlation Encoding, an encoding scheme that can represent m binary variables using a polynomial number of qubits. To evaluate the performance of the method, we use three classical optimisation problems against the instances of the QOPTLib benchmark. The study includes an analysis of the impact of the compression order of the encoding scheme, the problem structure, and hyperparameter selection on solution quality, as well as the role of post-processing in improving performance. Additionally, we study the effect of shot-based execution and hardware noise, showing how these factors influence both the accuracy of expected value estimation and the overall dynamics of the optimisation process. The results indicate that the proposed PCE-based framework achieves competitive performance against the benchmark and, in several cases, obtains equivalent or even superior solutions, highlighting its potential as an efficient encoding strategy for quantum optimisation in the NISQ and near fault-tolerant era.

Transitioning quantum magnetometry from laboratory environments to real-world applications has been limited by a persistent trade-off between sensor miniaturization and magnetic sensitivity. While bulky systems can achieve high sensitivity, endoscopic probes commonly suffer from inefficient fluorescence collection and reduced performance. Here we resolve this trade-off and present a miniaturized diamond quantum magnetometer with a 6 mm diameter endoscopic sensor head, achieving a magnetic-field sensitivity of 91 pT/sqrt(Hz) with a 2 kHz measurement bandwidth in a magnetically unshielded environment. The fluorescence collection bottleneck is overcome by separating excitation and collection into different cores of a fused multi-core fiber bundle, coupled to the diamond through a custom high-numerical-aperture micro-objective. A compact FPGA-based backend performs microwave control, lock-in detection and real-time resonance tracking, enabling robust operation during magnetic-field imaging. To demonstrate the practical utility of the miniaturized sensor, we image the magnetic field of a commercial lithium-ion pouch cell during charge and discharge and reconstruct depth-integrated current-density maps of the current flow. These results show that endoscopic diamond magnetometers can combine high sensitivity with a probe geometry suitable for confined, unshielded measurements, opening new avenues in battery technology and beyond.

Realizing scalable Quantum-to-the-Home (QTTH) faces a bottleneck: link asymmetry in broadcast continuous-variable quantum access networks (CV-QANs) hinders the selection of a globally optimal modulation variance. We demonstrate a downstream broadcast CV-QAN connecting a Quantum Line Terminal (QLT) to multiple Quantum Network Units (QNUs) over commercial fiber. Operating within a trusted local network domain, we establish a multi-user utility model to select the optimal shared variance, balancing network efficiency and user fairness. Supported by robust digital signal processing, our 1:16 field trial achieves Mbit/s-level asymptotic secure key rates, bridging theoretical protocols with Fiber-to-the-Home reality and guiding future scalable access architectures.

We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as ${\cal O}(M^a)$ with $a<1/2$, where $M$ is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.

End-to-end entanglement distribution is a key capability of upcoming quantum networks, enabling applications like distributed quantum computing, quantum sensor networks, and secure communications. Hence, its realistic and efficient simulation is crucial for quantum network design and for assessing the ability of a network to run certain applications. This work provides tools to scale-up and improve the realism of entanglement generation simulations in quantum networks. This is achieved by deriving analytical results that directly return the success probability, the output state and corresponding fidelity of a selected entanglement generation protocol, while accounting for a variety of noise sources affecting the protocol. These results are then integrated and streamlined in an upgraded version of SeQUeNCe, one of the most popular quantum network simulators. The resulting simulator features increased scalability by reducing computation time by more than 60%, while allowing for a variety of realistic noise sources, including imperfect mode matching, dark counts, and imperfect memory initialization. The simulator is also benchmarked with real experimental data and is capable of replicating the average entanglement generation time and the final state fidelity of a selected experiment. Altogether, the results can enhance current quantum network simulation capabilities towards large-scale networks, paving the way for the future quantum internet.

The photon blockade (PB) effect is a hallmark non-classical phenomenon in quantum optics and finds important applications for building quantum sources, while the control of PB by the non-Hermitian exceptional points remains largely unexplored. In this work, we theoretically investigate universal photon blockade in a microcavity harboring chiral exceptional points (CEPs) for building multiplexing quantum sources with nonreciprocal photon statistics. The results reveal that the presence of the CEPs leads to a stark contrast in the photon statistics of two whispering-gallery modes with opposite propagating directions. That is, one mode exhibits a strong PB effect while the other displays either sub-Poissonian or super-Poissonian distribution. Our findings thus may pave the way for advanced applications of photon blockade, and provide a theoretical foundation for the selective generation of single-photon and two-photon emission

Superconducting qubits offer a versatile platform for quantum simulation. In this architecture, quantum information can be encoded in the bosonic modes of a microwave cavity, offering an alternative to conventional qubit-based encoding schemes. These cavity bosonic modes can be manipulated using a single ancillary qubit. In this work, we investigate the quantum simulation of two- and three-flavor neutrino oscillations using Fock-basis encoding of a cavity mode. We design pulse sequences for implementing the required unitary operations through selective number-dependent arbitrary phase (SNAP) and displacement gates. Pulse-level control is employed to realize high-fidelity gate operations on the encoded cavity mode. The resulting neutrino oscillation probabilities obtained from quantum simulation exhibit close agreement with the corresponding theoretical predictions, demonstrating the feasibility of cavity-based bosonic encoding schemes for quantum simulation.

Complex quantum networks can support a diverse set of long-range entanglement distribution schemes ranging from linear repeater protocols to multipath entanglement purification strategies. As a result, a network's resourcefulness, that is its ability to facilitate quantum communication, depends on the deployed distribution scheme. In this work, we analyse and compare the resourcefulness of quantum networks across a broad range of network topologies, including both regular and random networks, under two distinct entanglement distribution schemes. The first relies on entanglement swapping along a single path connecting a source-target pair, while the second exploits entanglement purification using multiple paths between the same source and target nodes. The resourcefulness of the network is quantified using a recently described metric [1] that averages over the maximum teleportation fidelity between arbitrary source-target pairs in the network. We present algorithms for estimating this metric under constraints of edge-usage and ordering of paths. Our results not only demonstrate the sensitivity of the average maximum teleportation fidelity metric to the choice of entanglement distribution protocol, but also highlight the significant improvements enabled by network purification schemes. In particular, purification-based approaches can substantially enhance average teleportation fidelity, thereby improving the overall teleportation capability of quantum networks.

We analyze how memory in disorder facilitates quantum communication in many-body scar systems. We consider three distinct types of disorder, viz., memoryful, and memoryless uniform and Gaussian, and compare their respective performances in facilitating quantum state transfer. Using the maximum transfer fidelity and fidelity area as figures of merit, we find that memoryful disorder yields a better performance than the memoryless disordered channels. Furthermore, the maximum transfer fidelity exhibits an initial parabolic decay with disorder strength, followed by a linear decrease, for all the disorder models considered. We introduce a degree of scarness, and show that it is higher for memoryful disorder in comparison to memoryless disorders, implying a role of scarness in the quantum state transfer protocol. We further perform a scaling analysis, revealing that memory effect in disorder is not only beneficial for short-distance but also long-distance quantum state transfer. Finally, we show that the state yielding the maximum transfer fidelity has larger inverse participation ratio for memoryful disorder in comparison to the other two disorders, highlighting the role of nonergodicity in enhancing state transfer.

Tin vacancy (SnV) centers in diamond are promising solid state qubits for integrated quantum photonics. Here, we fabricate and characterize a diamond on Al2O3 dual taper waveguide structure containing SnV centers, demonstrating optical coupling between the diamond nanobeam and the underlying Al2O3 waveguide. The devices are realized using a bilayer fabrication approach compatible with wafer scale lithography. Clear guided SnV- emission is observed in all optically active devices, indicating effective optical coupling in the integrated structure. These results demonstrate a scalable fabrication approach toward integrating diamond color centers with photonic waveguides.

We study covert block-activity information transmission over a thermal-loss bosonic channel, where messages are encoded in weight-constrained activity patterns that Bob must recover through block-local decisions by prescribed deadlines. Shared circular Gaussian displacement modulation makes Willie's averaged lost-light state exactly thermal, with a strictly convex relative-entropy cost in signal energy, whereas a fixed Gaussian receiver at Bob yields a Gaussian mean-shift divergence linear in energy. This asymmetry produces an exact finite-block energy–information frontier and a detector-independent latency converse, matched in order by a block-reset cumulative-sum detector. For block covertness budget $\delta_b$ and error target $\epsilon_b$, the required active length scales as $\delta_b^{-1}\log^2(1/\epsilon_b)$ up to an explicit channel–receiver factor. Lifting this local law to communication yields the matching transmission limit $\log M=\Theta(\sqrt n/\log n)$ for the symmetric coordinatewise architecture under a fixed total covertness budget, maximal-message covertness, vanishing maximal error, and local deadlines. A relaxed full-horizon reference with the same modulation family and fixed measurement supports $\Theta(\sqrt n)$, showing that covertness and the selected measurement alone do not impose the extra logarithmic factor. Finally, public quadrature phase-shift keying codebooks selected by $O(\sqrt n)$ secret bits remove ideal continuous shared randomness without changing the payload order.

The realization of Coulomb coupled electron-hole double layers in 2D semiconductor heterostructures has enabled the thermodynamic and transport studies of equilibrium exciton fluids without a magnetic field. By doping the exciton fluid with additional electrons/holes, an equilibrium fluid of trions - three particle bound states of electrons and holes - further emerge, providing the platform to explore new transport phenomena associated with such composite particles. Here we report the observation of a Hall effect for trions in MoSe2/WSe2 heterobilayers, which support Coulomb-coupled electron and hole fluids with tunable densities. The Hall effect arises from a Lorentz force on trions under a perpendicular magnetic field. It is manifested in both Hall drag measurements and standard Hall effect measurements on just one of the semiconductor layers. For negatively charged trions, an electron Hall effect is observed even in a hole doped WSe2 monolayer due to the presence of trion drags. The trion Hall effect also disappears when the trions are ionized at elevated temperatures and/or high trion densities. Our work opens the door for realizing quantum oscillations and the quantum Hall effect for trions.

Quantifying coherence is an essential endeavor in both quantum foundations and quantum technologies. In this paper, we study the coherence measures in terms of the diagonal states in the strictly incoherent operations framework. Specifically, we propose a coherence measure in terms of fidelity and provide its analytical expression. The relations between the proposed coherence measure and some other coherence measures are derived. Furthermore, we prove its monotonicity under incoherent operations. As an application, we explore the role of the proposed coherence measure in characterizing the waveness in the multi-path interferometer. As a result, some wave-particle dualities in terms of fidelity are presented. This work not only deepens the interpretation of the diagonal states on characterizing quantum states, but also promotes the quantitative description of the wave-particle behaviors in the multi-path interferometer.

We present a holographic dual of a two dimensional conformal field theory with non-hermitian but Parity-Time (PT) symmetric boundary conditions, by applying the AdS/BCFT duality and by introducing an imaginary valued scalar field localized on an end-of-the-world brane. We find that as we increase the strength of the non-hermitian PT symmetric interactions, the system experiences a spontaneous PT symmetry breaking. We also consider its Wick rotated setup as a new quantum quenched state and show that its growth of entanglement entropy can be larger than the standard results obtained from standard Cardy states.

We characterize three-qubit controlled unitary gates of Schmidt rank three, establishing necessary and sufficient conditions for such gates to have Schmidt rank three. We construct explicit examples and analyze their entanglement capabilities, showing that gates with Schmidt rank three can generate output states ranging from fully separable to maximal GHZ-class states. Within this classification, we present a parameterized gate family that produces an output W-class state whose bipartite tangles for subsystems AB and AC are modulated as simple trigonometric functions of a single phase parameter. The examples also include gates implementable with only three CNOT gates, showing that this lower bound is achievable. Decompositions that achieve the minimum possible CNOT count for several other cases are provided as well. Our results bridge Schmidt rank classification, entanglement structure, and resource-efficient circuit synthesis.

We introduce the notion and reveal remarkable properties of quantum complexity resource contained in a mixed multimode Gaussian state and providing universal quantitative characterization of its quantum advantage. The notion is based on convex optimization, multimode photon number statistics, Hafnian Master Theorem, and #P-hard complexity. We consider pulsed OPAs targeting maximal quantum complexity resource and thousands of multipartite-entangled squeezed modes of output light via nonlinear, spatio-temporally nonadiabatic generation inside OPA and optimized extraction out of OPA. We show that such figure of merit is more realistic than Bloch–Messiah supermodes and guides to multimode OPAs opening new paths to important applications in quantum information science such as generation of 3D cluster states for one-way photonic quantum computing and demonstration of quantum advantage.

Variational quantum algorithms (VQAs) are among the leading approaches for near-term quantum computing, yet their performance can degrade in barren plateau regimes characterized by vanishing gradients. A widely held intuition is that increasing circuit expressivity, often associated with random-state behavior, leads to a loss of trainability. Existing results show that sufficiently random circuits can lead to barren plateaus. Here we show that standard statistical signatures of randomness can emerge well before this regime, without degrading trainability. We demonstrate this behavior in structured variational circuits applied to the one-dimensional cluster-Ising model and a generalized toric code Hamiltonian. To characterize state complexity, we analyze Porter-Thomas statistics, entanglement-spectrum level statistics, and inverse participation ratios. Across both models, increasing circuit depth drives these diagnostics toward random-state-like or random-matrix-like behavior, while variational optimization remains effective, with no evidence of exponential gradient suppression in the regime studied. We interpret this behavior in terms of locality. Spectral correlations develop at relatively shallow depth through locally generated structure, while global state randomization and the associated concentration-of-measure effects are not yet realized. These results show that commonly used statistical diagnostics of complexity do not by themselves determine trainability. Instead, they point to a separation between different aspects of complexity in finite-depth variational circuits.

Atom interferometers are among the most sensitive instruments for precision measurements and tests of fundamental physics. Their performance, however, is ultimately limited by quantum projection noise when uncorrelated atomic ensembles are employed. Cavity-assisted generation of entangled states has proven to be a promising route toward quantum-enhanced interferometry beyond the standard quantum limit. In this work, we present the realization and characterization of a monolithic bow-tie cavity developed to achieve a strong collective atom-light coupling with strontium atoms. Unlike conventional standing-wave Fabry-Pérot resonators, the traveling-wave geometry of the bow-tie cavity provides homogeneous atom-light coupling over the entire atomic ensemble, making it particularly suitable for entanglement-enhanced atom interferometry with freely falling atoms. The monolithic cavity architecture presents several scientifically relevant features such as high mechanical stability, high finesse, robustness against mirror misalignment, optical and atomic access and the option of generating squeezed states through different strategies. The cavity was realized for operation on the strontium $(5s^2) ^1S_0-(5s5p) ^3P_1$ transition at 689 nm and achieves a finesse of $\mathcal{F}=5.7\times 10^4$ while keeping the transmission of a single mirror sufficiently large to allow for efficient atomic information extraction. In this geometry, the cavity supports two foci with waists of 164 $\mu$m and 31 $\mu$m which gives access to different regimes of atom-cavity coupling. For ensembles containing up to $10^5$ atoms, the cavity is expected to enable a Wineland squeezing parameter $\xi^2$ of 24 dB through cavity-feedback squeezing, and 28 dB through quantum non-demolition measurements, demonstrating its potential as a platform for next-generation quantum-enhanced atom interferometers.

The detection of hyperuniformity relies critically on accurate characterization of the small-wavenumber behavior of the static structure factor of the system. In practice, however, measurements are performed on finite subsystems or through incomplete observations that effectively mask portions of the underlying configuration. Inspired by a recent numerical study [Y. Liu, X. Li, J. Tian, X. Yan, G. Zhang, J. Chem. Phys. 164, 094102 (2026)], we develop a unified theoretical framework that quantifies how finite windows and spatially correlated binary masks modify the observed structure factor. We show that the measured structure factor $S_{obs}(k)$ is the convolution of the intrinsic structure factor with the spectral density of the observation function, whether it is a compact window or an extended random mask. For generic hyperuniform systems with small-$k$ scaling $S(k)\sim k^{\alpha}$, finite observation window induces a universal quadratic leakage term at sufficiently small wavenumbers (i.e., $k \lesssim 1/L$), leading to an apparent $k^{2}$ scaling independent of the true exponent. The true hyperuniform exponent $\alpha$ can only be measured in the intermediate regime $1/L \ll k \ll q_c$. In stealthy hyperuniform systems, where the intrinsic structure factor possesses a spectral gap, all observed small-$k$ power arises entirely from this convolution mechanism. For spatially correlated masks, we derive the corresponding convolution relation in terms of the mask spectral density and identify conditions under which hyperuniform signatures are suppressed, preserved, or distorted. Our results establish quantitative criteria for reliably extracting intrinsic scaling exponents and distinguishing genuine hyperuniform order from measurement-induced artifacts.