Papers

Quantum Max Cut is a problem relevant to computer science and many-body quantum physics due to its links to classical Max Cut and the anti-ferromagnetic Heisenberg Hamiltonian. We prove a lower bound to quantum Max Cut of a graph in terms of the Lovász theta function of its complement. For a graph with $m$ edges, $\text{qmc}(G) \geq \tfrac{m}{4}\big( 1 + \tfrac{8}{3\pi}\tfrac{1}{\vartheta(\bar{G}) -1} \big)$, with the bound achieved by a product state. The proof can be strenghtened by the vector chromatic number and extends a result by Balla, Janzer, and Sudakov on classical Max Cut. A relaxed bound follows from $\vartheta(\bar{G}) - 1 \leq \Delta$ for graphs with maximum degree $\Delta$, making it interesting for practically relevant quantum many-body systems. We also extend results by Carlson et al. and Shearer and show that $\text{qmc}(G) \geq \frac{m}{4} + \frac{2m^{3/4}}{3 \pi}$ for all triangle-free graphs with $m$ edges.

We study in this paper the quantum phase transition (QPT) from normal phase (NP) to superradiant phase (SP) for $N$ three-level atoms in a single-mode optical cavity for both Hermitian and non Hermitian Hamiltonians, where the $\Xi$-type three-level atom is described by spin-$1$ pseudo-spin operators. The long standing gauge-choice ambiguity of $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ called respectively the Coulomb and dipole gauges is resolved by the time-dependent gauge transformation on the Schrödinger equation. Both $\mathbf{A\cdot p}$ and $\mathbf{d\cdot E}$ interactions are included in the unified gauge, which is truly gauge equivalent to the minimum coupling principle. The Coulomb and dipole interactions are just the special cases of unified gauge. Remarkably three interactions lead to the same results under the resonant condition of field-atom frequencies, while significant difference appears in red and blue detunings. The QPT is analyzed in terms of spin coherent-state variational method, which indicates the abrupt changes of energy spectrum, average photon number as well as the atomic population at the critical point of interaction constant. Crucially, we reveal the sensitive dependence on the initial optical-phase, which is particularly useful to test the validity of three gauges experimentally. The non-Hermitian atom-field interaction results in the exceptional point (EP), beyond which the semiclassical energy function becomes complex. However the energy spectrum of variational ground state is real in the absence of EP, and does not become complex. The superradiant state is unstable due to the non-Hermitian interaction induced photon-number loss. Thus only the NP exists in the non-Hermitian Dicke Model Hamiltonian.

We present exact solutions of the Schrödinger equation for a quantum system with complex mass subjected to a complex Morse potential in the extended complex phase space. The normalized eigenfunctions and corresponding eigenspectra are derived within a non-Hermitian framework, ensuring consistent probability densities. Conditions for the reality of the spectra are established and used to analyze the dependence of eigenvalue behaviour on potential parameters. The study reveals distinct regimes of spectral characteristics arising from the interplay of complex mass, the Morse parameter, and eigenvalues, leading to the emergence of five classes of non-Hermitian quantum states. By analysing the energy eigenspectra, normalization conditions, and probability density profiles across parameter space, we identify regimes corresponding to real-spectrum Hermitian-like matter, quasi-stable or resonant states, purely complex quantum matter, non- physical, non-normalizable states, and a quasi-classical determinate regime in which the probability density becomes spatially static. One of these systems exhibits a non-dissipative, collisionless state with long-range gravitational-like characteristics, suggesting a theoretical analogue for dark matter within a non-Hermitian quantum framework. Further, the five identified classes of matter may be interpreted as distinct matter phases of a single quantum system governed by complex mass and Morse parameters. This classification elucidates the boundary between physical and non-physical regimes in complex quantum systems and provides a unified approach for interpreting stability, resonance, and emergent classicality arising from complex parameters.

Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] has been demonstrated to be an efficient and accurate electronic structure method for studying the ground-state properties of large multi-reference (MR) systems at absolute zero. To explore the thermal equilibrium properties of large MR systems at finite electronic temperatures, in the present work, we propose the finite-temperature (FT) extension of TAO-DFT, denoted as FT-TAO-DFT. Besides, to unlock the dynamical information of large MR systems at finite temperatures, FT-TAO-DFT is combined with ab initio molecular dynamics, leading to FT-TAO-AIMD. In addition, we also develop FT-TAO-DFT-based quantum mechanics/molecular mechanics (QM/MM), denoted as FT-TAO-QM/MM, to provide a cost-effective description of the thermal equilibrium properties of a QM subsystem with MR character embedded in an MM environment at finite temperatures. Moreover, the FT-TAO-DFT, FT-TAO-AIMD, and FT-TAO-QM/MM methods are employed to explore the radical nature and infrared (IR) spectra of n-acenes (n = 2–6), consisting of n linearly fused benzene rings, in vacuum and in an argon (Ar) matrix at finite temperatures. According to our calculations, for n-acenes at 1000 K or below, the electronic temperature effects on the radical nature and IR spectra are very minor, while the nuclear temperature effects on these properties are noticeable. For n-acene in an Ar matrx at absolute zero, the Ar matrix has minimal impact on the radical nature of n-acene, while the co-deposition procedure of n-acene and Ar atoms may affect the IR spectrum of n-acene.

The nonintegrable transverse-field Ising model is a common platform for studying ergodic quantum dynamics. In this work, we introduce a simple variant of the model in which this ergodic behaviour is suppressed by introducing a spatial inhomogeneity in the interaction strengths. For this we partition the chain into two equal segments within which the spins interact with different coupling strengths. The ratio of these couplings defines an inhomogeneity parameter, whose variation away from unity leads to constrained dynamics. We characterize this crossover using multiple diagnostics, such as the long-time saturation of out-of-time-ordered correlators, level-spacing statistics, and the spectral form factor. We further examine the consequences for operator growth in Krylov space and for entanglement generation in the system's eigenstates. Together, these results demonstrate that introducing a macroscopic inhomogeneity in coupling strengths provides a minimal, disorder-free route to breaking ergodicity in this specific model of interacting spins.

Optically addressable spin defects are excellent candidate platform for quantum sensing and quantum network. Nuclear spins coupled to color centers naturally enable long lived quantum memories and local qubits registers. To fully leverage this potential precise characterization of the surrounding nuclear-spin environment augmented with refined DFT models is required. In this work, we report angstrom-level 3D localization of 25 nuclear spins around a single V2 center in 4H Silicon Carbide. Utilizing specially placed robust nuclear memory as a highly efficient readout ancilla for readout, we apply correlation based spectroscopy and by selecting multi-spin chains up to length four, we access and characterize extended nuclear spin cluster. Using the coupling map we reconstruct their couplings to the central electron spin and neighboring nuclei. This work paves the way towards advanced quantum register applications on Silicon Carbide platform.

This work studies a $\mathcal{PT}$-symmetric non-Hermitian spin–boson model, consisting of a non-Hermitian two-level system coupled to a continuous bosonic bath. The static properties of the system are analyzed through a projection method derived from the displacement operator. We find that only a single exceptional point (EP) emerges, in contrast to non-Hermitian spin–boson models with finite modes, which typically exhibit multiple EPs. Notably, only a single real eigenvalue is found before the EP, which differs markedly from typical non-Hermitian systems where a pair of real eigenvalues precedes the EP. The time evolution of observables is further investigated via the Dirac–Frenkel time-dependent variational principle. Compared to its Hermitian counterpart, the non-Hermitian model exhibits distinct dynamical signatures, most notably the emergence of oscillations with periodic amplified amplitude. In the $\mathcal{PT}$-unbroken phase, the system exhibits sustained oscillatory dynamics with suppressed decoherence, whereas in the $\mathcal{PT}$-broken phase, additional dissipative channels accelerate decoherence and drive rapid convergence toward a stable steady state. These results shed light on how $\mathcal{PT}$ symmetry protects coherent light–matter interactions in non-Hermitian quantum systems.

Non-Hermitian physics has unlocked a wealth of unconventional wave phenomena beyond the reach of Hermitian systems, with exceptional points (EPs) driving enhanced sensitivity, nonreciprocal transport, and topological behavior unique to non-Hermitian degeneracies. Here, we present a scalable and reconfigurable silicon photonic integrated circuit capable of emulating arbitrary non-Hermitian time evolution with high precision. Using this programmable platform, we implement a two-band non-Hermitian Hamiltonian defined on a Klein-bottle topology a nonorientable parameter space that enables exceptional phases forbidden on orientable manifolds. Through an on-chip amplitude-and-phase reconstruction protocol, we retrieve the full complex Hamiltonian at multiple points in parameter space and experimentally map the associated Fermi arc where the imaginary eigenvalue gap closes. The orientation of the measured Fermi arc reveals a nontrivial exceptional topology: it implies the presence of same-charge EPs (or an EP monopole) that cannot annihilate locally on the Klein bottle. Our results demonstrate the first photonic realization of exceptional topology on a nonorientable manifold and establish a versatile platform for exploring exotic non-Hermitian and topological models relevant to classical and quantum photonics.

Standard topological invariants, such as the Chern number and Berry phase, form the bedrock of modern quantum matter classification. However, we demonstrate that this framework undergoes a catastrophic failure in the presence of essential singularities – ubiquitous in open, driven, and non-Hermitian systems ("Wild" regime). In these settings, the local geometric tensor diverges, rendering standard invariants ill-defined and causing perturbative predictions to deviate from reality by order unity ($\sim 100\%$). We resolve this crisis by introducing the Floquet-Monodromy Spectroscopy (FMS) protocol, a pulse-level control sequence, which experimentally extracts the hidden Stokes Phenomenon – the "missing" geometric data that completes the topological description. By mapping the singularity's Stokes multipliers to time-domain observables, FMS provides a rigorous experimental bridge to Resurgence Theory, allowing for the exact reconstruction of non-perturbative physics from divergent asymptotic series. We validate this framework on a superconducting qudit model, demonstrating that the "Stokes Invariant" serves as the next-generation quantum number for classifying phases of matter beyond the reach of conventional topology.

Quantum entanglement is an essential resource for quantum technologies, and the controlled swap test provides a versatile tool for its detection and quantification. Here, we propose a SWAP-based entanglement witness that applies to arbitrary two-qubit states - both pure and mixed - and provides a lower bound on the concurrence. The method is resource-efficient, robust to noise, and platform-independent. As an example, we validate the approach on a room-temperature photonic chip, where the swap test is carried out using only linear and well-established integrated optical components. The robustness of the method against photonic-hardware noise is also analysed. Our results establish a simple and reliable tool for entanglement witnessing.

Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using Schmidt spectra or Rényi entanglement entropies of the target quantum state. Conversely, one obtains bounds on TTNS bond dimensions needed to achieve a specific approximation accuracy. The result implies that efficient TTNS approximations exist if $\alpha<1$ Rényi entanglement entropies for single-branch cuts obey an area law, as in ground and low-energy states of certain gapped systems on tree graphs.

High-fidelity state transfer is fundamentally limited by time-reversal symmetry: one qubit emits a photon with a certain temporal pulse shape, whereas a second qubit requires the time-reversed pulse shape to efficiently absorb this photon. This limit is often overcome by introducing active elements. Here, we propose an alternative solution: by tailoring the dispersion relation of a waveguide, the photon pulse emitted by one qubit is passively reshaped into its time-reversed counterpart, thus enabling perfect absorption. We analytically derive the optimal dispersion relations in the limit of small and large qubit-qubit separations, and numerically extend our results to arbitrary separations via multiparameter optimization. We further propose a spatially inhomogeneous waveguide that renders the state transfer robust to variations in qubit separations. In all cases, we obtain near-unity transfer fidelity (>= 98%) that is robust against imperfections in parameter values and propagation loss. Our dispersion-engineered waveguide provides a compact and passive route toward on-chip quantum networks, highlighting dispersion as a powerful resource in waveguide quantum electrodynamics.

Spin-active colour centres in 4H silicon carbide are promising candidates as building blocks for quantum information applications. To increase the photon count rate of the emitters at low temperatures, the colour centres must be integrated into nanophotonic structures and characterised under cryogenic conditions. Here, we design and fabricate waveguide structures attached with an efficient Dinosaur photonic crystal reflector at one side. The devices show broadband reflection over a range of 60 THz with a peak reflectance above 80 %. Additionally, colour centres were integrated into these structures and characterised at cryogenic conditions. The emission was collected by a tapered-waveguide-tapered-fibre interface. Although the spectral stability of the emitters must be further improved for high excitation powers, the saturation intensity in standard PLE measurements is about 104 kcps. The count rate can be further improved to about 125 kcps with a charge-resonance check measurement scheme. To highlight the relevance of our devices, we theoretically show that these count rates enable optical single-shot readout with a fidelity exceeding 98 %.

The systematic discovery of effective drug combinations is a challenging problem in modern pharmacology, driven by the combinatorial growth of potential pairings and dosage configurations. Network medicine, modeling diseases and drugs as interconnected modules of the human protein-protein interactome, has emerged as a new paradigm for understanding disease mechanisms and drug action. In this work, we propose a quantum annealing-based algorithm for identifying effective drug combinations. Underlying our approach is the biologically motivated principle of `Complementary Exposure', which posits that therapeutic drug combinations target distinct yet complementary regions of a disease module. We translate this into a quadratic unconstrained binary optimisation problem. We test our method for Diabetes Mellitus, Rheumatoid Arthritis, Asthma, and Brain Neoplasms, relying on experimentally validated drug combinations for these diseases. Our simulated quantum annealing experiments reveal that low-energy configurations align with biologically plausible combinations which may serve as prioritized candidates for subsequent experimental validation.

We study the long-time behavior of a non-interacting two-dimensional quantum gas in a weak random potential with long-range correlations. Any peaked initial momentum distribution will eventually become isotropic and broaden due to scattering events with the random potential. We derive an expression for the long-time average of the momentum distribution and test it against computer simulations. We also discuss momentum isotropization and spatial diffusion.

Silicon quantum dot spin qubits have become a promising platform for scalable quantum computing because of their small size and compatibility with industrial semiconductor manufacturing processes. Although Si/SiGe heterostructures are commonly used to host spin qubits due to their high mobility and low percolation density, the SiGe spacer creates a gap between the qubits and control electrodes, which limits the ability to tune exchange coupling. As a result, residual coupling leads to unwanted single-qubit phase shifts, making multi-qubit control more difficult. In this work, we explore swapping the roles of overlapping nanogates to overcome this issue. By reconfiguring the gate voltages, we demonstrate in situ role switching while maintaining multi-qubit control. Additionally, this method significantly improves the tunability of exchange coupling by several orders of magnitude over the traditional approach. This strategy reduces unintended single-qubit phase shifts and minimizes the complexity of multi-qubit control, supporting scalable growth with minimal experimental overhead.

Identifying whether a mixed quantum state is uniquely determined among all states (UDA) by its local marginals is a basic problem in quantum information theory. We establish necessary and sufficient conditions under which several classes of multipartite mixed states are UDA by their $k$-partite marginals. We also prove structural properties based on ranges and marginals, and formulate a recursive procedure for the determination of UDA states. We show that sufficiently high rank rules out unique determination from fixed-order marginals, implying that almost all multipartite mixed states are not UDA from such marginals. Finally, we completely characterize the additivity of bipartite UDA states, three-qubit and several families of $n$-qubit product UDA states. These results clarify the boundary between UDA and non-UDA mixed states and provide a framework for local-marginal reconstruction and related certification tasks.

The optimal control of population transfer for multi-level systems is investigated from the perspective of quantum geometry. Firstly, the general theoretical framework of optimizing the stimulated Raman adiabatic passage (STIRAP) scheme based on the dynamical quantum geometric tensor is given, and then the dynamical quantum geometric tensor and the nonadiabatic transition rate are calculated by taking the detuned $\Lambda$-type three-level system and tripod-type four-level system for example. Secondly, the transfer dynamics of the particle population of the system are investigated in detail. For a three-level system, the optimal STIRAP scheme has an efficiency of over 98% in transferring the population to the final state, while the transfer efficiency of traditional STIRAP is about 72%. The superposition states with arbitrary proportions can be efficiently prepared for a four-level system due to the decoupling of the degenerate dark states. Finally, the influences of system parameters, such as the operation time of the Rabi pulses, the amplitude fluctuation and the single-photon detuning, on the transfer process are discussed. Especially, the phenomenon of the adiabatic resonance transfer is revealed. Choosing the pulse parameters in the resonance window can reduce the infidelity of the population transfer to below $10^{-3}$. It is found that the optimal STIRAP scheme by the dynamical quantum geometric tensor provides faster and more efficient transfer than the traditional STIRAP scheme.

A dynamical bulk-edge relation in quantum walks has been theoretically proposed and experimentally observed, in which a power-law dependence of the bulk loss probability is associated with a pronounced peak of loss probability at the edge. This behavior has been proven to arise from imaginary gap closing and the non-Hermitian skin effect in the infinite limit without boundary effects. However, in a finite-size chain, we find that boundary scattering can suppress this edge burst. Meanwhile, imaginary gap opening, together with the non-Hermitian skin effect, can also induce a large loss probability at the edge. Our results provide insights into finite-size quantum dynamics.

Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this asymmetry by introducing a comprehensive framework for efficient detector estimation that reveals the fundamental limits to extractable parameter information and errors arising in detector analysis - the detector quantum Fisher information. Our development eliminates the need to optimise for the best probe state, while highlighting aspects of detector analysis that fundamentally differ from quantum state estimation. Through proofs, examples and experimental validation, we demonstrate the relevance and robustness of our proposal for current quantum detector technologies. By formalising a dual perspective to state estimation, our framework completes and connects the triad of efficient state, process, and detector tomography, advancing quantum information theory with broader implications for emerging technologies reliant on precisely calibrated measurements.

We theoretically investigate quantum measurement noise in a hybrid optomechanical system, focusing on radiation pressure back action and its impact on force sensing. The setup consists of an optomechanical cavity with a movable mirror, a fixed semi transparent mirror, an ensemble of quantum dots (QD) coupled to the cavity mode, and an intracavity optical parametric amplifier (OPA). We show how the QD induced response, together with the system nonlinearity, modifies the noise spectral density and thereby improves the force measurement sensitivity. In this setup, coherent quantum noise cancellation (CQNC) can completely remove the back action noise. In addition, increasing the OPA pump gain enables sensitivity beyond the standard quantum limit (SQL) at reduced laser power. These combined effects allow weak force sensing beyond the SQL.

Machine-learning (ML) models are increasingly used in quantum computing systems to discriminate multi-qubit readouts, mitigate correlated readout errors, and decode quantum error-correcting codes, making them an integral component of today's quantum computer control and readout stacks. This paper is the first to analyze the susceptibility of such ML models to physical fault injection, which can cause quantum computers to return incorrect results or perform wrong error correction operation. This work studies two representative architectures: (i) a fully connected neural network for 5-qubit (32-class) readout error correction (HERQULES), and (ii) a convolutional neural network used as a Deep Q-learning (Deep Q) decoder for the distance-5 Surface Code. Using the ChipWhisperer Husky for voltage glitching together with automated search over the fault parameter space, this work localizes successful fault settings to specific layers of each target ML model. On the HERQULES model, fault susceptibility is strongly layer-dependent: early layers exhibit higher misprediction rates than later layers. On the Deep Q decoder, a single trigger-aligned voltage glitch in either the first convolutional layer or the final fully connected output layer reduces decoding accuracy from 100% to as low as 21.57%. We further characterize the resulting failures at the bitstring level using Hamming-distance and per-bit flip statistics, showing that single-shot glitches can induce structured corruption rather than purely random noise. These results motivate treating ML-based quantum readout and error-correction decoding as security-critical components, and highlight the need for lightweight fault-detection and redundancy mechanisms in quantum computing pipelines.

Quantum entanglement routing in dynamic Low Earth Orbit (LEO) satellite networks is important for achieving scalable and high-fidelity quantum communication. However, the dynamic characteristics of satellite network topology, limited quantum resources, and strict coherence time constraints pose significant challenges to reliable entanglement routing. An entanglement distribution analysis model for this unique environment is critical and helpful for entanglement routing research. We address the fundamental challenge of establishing and maintaining quantum entanglement links between satellites operating in free space, where links are subject to both transmission losses and quantum memory decoherence. This paper presents a comprehensive Markov chain model with a state space defined by link storage age and physical distance for analyzing entanglement distribution in noisy dynamic LEO satellite quantum networks. We construct transition matrices that capture system dynamics under varying request arrival rates, and derive analytical expressions for key performance metrics, including request satisfaction rate, average waiting time, link utilization efficiency, and average consumed link fidelity. Our analysis reveals that the critical trade-offs of higher request rates lead to faster link consumption with higher fidelity but potentially lower satisfaction rates, while lower request rates allow longer storage times at the cost of lower fidelity of increased decoherence effect. Moreover, this paper proves it is reasonable to leave out polarization rotation when the transmission distance is very short (40-50 km). In summary, this work provides theoretical foundations for designing and optimizing quantum entanglement distribution strategies in satellite networks, with applications to global-scale quantum communications.

An augmented system model provides an effective way to model non-Markovian quantum systems, which is useful in filtering and control for this class of systems. However, since a large number of ancillary quantum oscillators representing internal modes of a non-Markovian environment directly interact with the principal system in these models, the dimension of the augmented system may be very large causing significant computational burden in designing filters and controllers. In this context, this paper proposes an $\mathscr{H}_2$ model reduction method for the augmented model of linear non-Markovian quantum systems. We first establish necessary and sufficient conditions for the physical realizability of the augmented model of linear non-Markovian quantum systems, which are more stringent than those for Markovian quantum systems. However, these physical realizability conditions of augmented system model pose non-convex constrains in the optimization problem of model reduction, which makes the problem different from the corresponding classical model reduction problem. To solve the problem, we derive necessary conditions for determining the input matrix in the reduced model, with which a theorem for designing the system matrix of the ancillary system in the reduced system is proved. Building on this, we convert the nonlinear equality constraints into inequality constraints so that a semidefinite programming algorithm can be developed to solve the optimization problem for model reduction. A numerical example of a two-mode linear quantum system driven by three internal modes of a non-Markovian environment validates the effectiveness of our method.

Multipartite entanglement enables secure group key distribution among multiple users while providing immunity against hacking attacks targeting source devices, thereby realizing source-independent quantum conference key agreement (SI-QCKA). However, previous experimental demonstrations of SI-QCKA have encountered substantial technical challenges, primarily due to the low efficiency and scalability limitations inherent in the generation and distribution of multipartite entanglement. Here, we experimentally demonstrate a scalable and efficient SI-QCKA protocol using polarization-entangled photon pairs in a three-user star network, where Greenberger-Horne-Zeilinger correlations are realized via a post-matching method. We achieve a secure group key rate of $2.11 \times 10^{4}$ bits/s under the single-user channel transmission of 1.64 $\times$ $10^{-1}$ in a symmetric channel loss network. Additionally, we conduct six sets of experiments to investigate the impact of varying channel transmission and random basis selection probabilities on secure key rates. Our work establishes an efficient pathway for SI-QCKA and demonstrates potential scalability for future large-scale multi-user quantum networks.

The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging and closely related to the classical difficulty of choosing suitable neural-network topologies, which is computationally hard. This work investigates automated quantum-circuit construction for regression tasks and introduces a genetic-algorithm framework that discovers Reduced Regressor QNN architectures. The approach explores depth, parametrized gate configurations, and flexible data re-uploading patterns, formulating the construction of quantum regressors as an optimization process. The discovered circuits are evaluated against seventeen classical regression models on twenty-two nonlinear benchmark functions and four analytical functions. Although classical methods often achieve comparable results, they typically require far more parameters, whereas the evolved quantum models remain compact while providing competitive performance. We further analyze dataset complexity using twelve structural descriptors and show, across five increasingly challenging meta-learning scenarios, that these measures can reliably predict which quantum architecture will perform best. The results demonstrate perfect or near-perfect predictive accuracy in several scenarios, indicating that complexity metrics offer powerful and compact representations of dataset structure and can effectively guide automated model selection. Overall, this study provides a principled basis for meta-learning-driven quantum architecture design and advances the understanding of how quantum models behave in regression settings–a topic that has received limited exploration in prior work. These findings pave the way for more systematic and theoretically grounded approaches to quantum regression.

We introduce Quantum Index Algebra (QIA) as a finite, index-based algebraic framework for representing and manipulating quantum operators on Hilbert spaces of dimension $2^m$. In QIA, operators are expressed as structured combinations of basis elements indexed by Boolean codes, allowing products, commutators, and conjugations to be computed through finite rules on discrete indices rather than through dense matrix arithmetic. This representation unifies combinatorial index structure, explicit matrix realization, and transformation properties under Walsh-Hadamard-type transforms within a single formalism. Using QIA and its associated block-matrix realization, we reformulate the Bernstein-Vazirani hidden-string problem in its phase-oracle form entirely within a real, finite-dimensional algebraic setting. We show that, under structured oracle access, the QIA procedure reproduces the Bernstein-Vazirani algorithm exactly and achieves the same asymptotic query complexity and circuit depth as the standard quantum algorithm. In particular, the hidden string is recovered by symbolic manipulation of a sparse algebraic representation of the oracle rather than by numerical simulation of quantum amplitudes. Our results demonstrate that the apparent quantum speed-up in this setting is a consequence of operator structure rather than Hilbert-space dimensionality alone. QIA thus provides a precise language for separating genuinely quantum resources from those arising from algebraic and combinatorial structures and offers a new perspective on the classical simulability of structured quantum circuits.

This paper introduces a new Boolean-based methodology for constructing Segment Display Problems (SDPs) in the quantum domain and solving them using Grover's quantum search algorithm. In the classical domain, the SDPs are typically solved using various techniques, such as human deduction, heuristic search, and methods for solving Boolean satisfiability (SAT) and constraint satisfaction problems (CSPs) that are based on different problem design models. In this paper, our newly introduced methodology proposes a quantum-based approach for solving such SDPs, by building their quantum oracle using binary reversible circuits and our previously proposed step-decreasing structures shaped operators (Stesso). To demonstrate the usability of this proposed method, we experimentally solve an SDP instance of the matchstick problem using Grover's algorithm with a noisy simulated quantum computer implemented in Qiskit.

The operational resource theory (ORT) measure is a nonclassicality measure for bosonic states, notable for its resource-theoretic properties and connection to metrology. However, it can be difficult to evaluate, being linked to an optimization problem for mixed states. Here, we present ORT measure calculations for mixed states with photon-number coherence. We give exact formulas governing the ORT measure of a broad class of rank-two mixed states, and numerical solutions for some higher-rank states. We also compare the nonclassicality of these states to their metrological power, thus showing in what regimes the metrological power manages to saturate the ORT bound. Throughout, we consider the role of coherence. In particular, we show that nonclassicality and metrological power never increase under bosonic dephasing, but may plateau in a manner similar to entanglement sudden death. Nevertheless, lowering photon-number coherence more freely can sometimes yield more nonclassical and metrologically useful states.

Band flattening has been identified as key ingredient to correlation phenomena in Moiré materials and beyond. Here, we examine strongly repulsive fermions on a ladder – a minimal platform for unconventional $d$-wave pairing – and show that flattening of the lower band through an additional diagonal hopping term produces non-Fermi liquid behavior, evidenced by the violation of Luttinger's theorem, as well as axial $d$-wave pairing correlations. Alternatively, plaquette ring exchange can also generate pairing, albeit with a distinct diagonal $d$-wave pairing symmetry. Hence, our finding showcases a competition of different unconventional pairing channels, and demonstrates via a simple model how band geometry can induce fermionic pairing. This offers broadly relevant insights for correlated flat-band systems, ranging from ultracold atoms to strongly interacting electrons in solids.