Papers

Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates suffice: local input-output statistics identify channels, and every state admits an equivalent-system purification, unique up to reversible dynamics. The full complex quantum formalism follows; every consistent probability rule is realized as a POVM, so measurement no-restriction is derived rather than assumed.

Rydberg atomic quantum receivers (RAQRs) offer quantum-limited sensitivity and broadband tunability. It is not obvious whether this device-level advantage also improves network reliability, since in dense deployments, aggregate interference can push the atomic transducer out of its small-signal regime. This paper addresses the question by embedding the RAQR front end into a stochastic geometry (SG) coverage analysis. Starting with the atomic master equation and balanced coherent optical detection, we derive a third-order complex baseband model that retains both the linear gain and the leading cubic nonlinearity. A Bussgang decomposition converts the per-element nonlinear response into an equivalent linear gain plus a distance-dependent distortion noise. Using this equivalent model, we derive the post maximal-ratio combining (MRC) SINR and obtain tractable expressions for the conditional and spatially averaged coverage probabilities. The analytical results show that RAQRs outperform conventional receivers in sparse deployments. However, when the base station (BS) density becomes large, nonlinear distortion reduces this advantage and may make RAQRs perform worse. Simulation results validate the analytical expressions and confirm that the central design tradeoff is between linear gain and cubic nonlinearity.

Interstitial hydrogen and deuterium in body-centered-cubic metals constitute archetypal quantum tunneling systems. Their relevance has been renewed by the connection between hydrogenic tunneling in Nb and defect-induced decoherence in superconducting qubits, motivating a predictive microscopic theory. Existing theoretical treatments invoke an adiabatic separation between the light interstitial and the host lattice, an assumption whose validity has not been rigorously established for hydrogenic species. Here, we show that the experimentally measured tunnel splittings of O-trapped H and D in bcc Nb are quantitatively well-described within a five-dimensional (5D) Lattice-Renormalized Born-Oppenheimer (LRBO) framework. This approach treats three interstitial modes and two judiciously selected lattice modes, which includes a transition-state mode, on equal quantum footing. By recasting nested Born-Oppenheimer hierarchies within this same formalism and benchmarking against modern ab initio potential energy surfaces, we show that adiabatic separation of the light particle from lattice dynamics is satisfied only in the positive-muon ($\mu^{+}$) mass limit. In contrast, tunneling for H and D is fundamentally a collective, nonadiabatic process mediated by anharmonic lattice couplings. Finally, we show that the breakdown of adiabaticity can be anticipated from simple energy estimates involving the ground-state light-particle energy evaluated at a small number of fixed lattice configurations, providing a practical criterion for assessing the validity of adiabatic tunneling theories in other systems.

In classical thermodynamics, the Mpemba effect refers to the counterintuitive observation that hot water can freeze faster than cold water, manifesting as an anomalous crossing of dynamical trajectories. While analogues of this phenomenon have been explored in open quantum systems and spin-chain entanglement asymmetry, its connection to the finite-time decoupling of quantum correlations remains elusive. In this work, we report a distinct Mpemba effect for quantum entanglement in a dissipative quantum system associated with entanglement sudden death (ESD). By analyzing two qubits interacting with local amplitude damping reservoirs, we demonstrate that a more strongly entangled initial state can experience a faster collapse into a separable state than a more weakly entangled state. This anomalous decay stems from the competition between initial coherence and excited-state population, where the latter acts as a catalyst for ESD. We provide exact analytical derivations for the trajectory crossover and ESD time, and map the phase diagram to precisely identify the parameter regime where the effect occurs. Our results offer a new strategy for controlling the lifetime of quantum resources in dissipative environments.

Variational Quantum Algorithms (VQAs) potentially offer a pathway to practical quantum advantage, but their optimization is heavily hindered by barren plateaus and numerous local minima. While classically simulable Clifford circuits can warm-start VQAs to accelerate convergence, existing heuristic-based initialization methods struggle to scale within vast combinatorial search spaces. To overcome this bottleneck, we propose CRiSP (a Clifford Reinforcement Learning agent for State Preparation), a framework that formulates discrete prefix selection as a sequential decision-making problem. CRiSP utilizes Neural-Guided Monte Carlo Tree Search, driven by a Transformer-based policy trained via self-play, to insert learned Clifford gates before fixed parameterized rotations. This enables the construction of high-quality initial states entirely through polynomial-time classical stabilizer simulation without altering the underlying circuit architecture. By integrating a curriculum learning strategy that progressively expands the search horizon, the agent efficiently scales to deep circuits. Evaluated on QAOA benchmarks of up to $22$ qubits and $1{,}370$ parameters, CRiSP outperforms state-of-the-art Clifford initialization methods by a mean of $3.17\times$ (max $45.02\times$) in average energy accuracy and $2.44\times$ (max $16.01\times$) in best-achieved energy accuracy. Assessments on VQE tasks further demonstrate the framework's robustness and generalizability.

We generalize the stabilizer formalism for entanglement-assisted quantum error-correcting codes with noisy ebits (EAQECCs-Ne) from the binary case to the general $q$-ary case, where $q$ is a prime power. By leveraging the structure of the generalized Pauli group over $\mathbb{F}_q$ and symplectic geometry over $\mathbb{F}_q^{2n}$, we establish a unified framework for constructing EAQECCs-Ne for qudit systems. Equivalent formulations in terms of symplectic geometry over $\mathbb{F}_q$ and additive codes over $\mathbb{F}_q^{2n}$ are derived. We further construct several families of $q$-ary EAQECCs with noise ebits and analyze their performance compared to optimal stabilizer codes. Our results demonstrate that under certain noise conditions, the proposed EAQECCs-Ne can outperform standard stabilizer codes with equivalent error-correcting capability, offering a promising approach for fault-tolerant quantum computation in high-dimensional quantum systems.

Distributed quantum learning (DQL) has emerged as a promising paradigm to scale quantum-enhanced machine learning by interconnecting multiple quantum devices. However, for efficient real-world deployment, it is essential to characterize how DQL converges under practical scenarios while simultaneously safeguarding multi-device quantum infrastructures from evolving security threats. Addressing these aspects in an integrated manner is key to ensuring both performance and resilience in large-scale DQL systems. Therefore, this paper presents a new DQL study where our innovation lies in: (i) conducting a holistic convergence analysis for DQL under practical settings, i.e., partial device participation, non-convex loss functions, and heterogeneous data distributions, (ii) developing a novel multi-layered post-quantum cryptographic architecture with a quantum neural network-powered adaptive mechanism that monitors conditions, evaluates threats, and adjusts parameters across three National Institute of Standards and Technology (NIST)-compliant levels. Our theoretical framework and empirical validation reveal two key insights: (i) the derived convergence bound uncovers a fundamental trade-off between convergence rate, measurement shots, and the size of the participating device subset; and (ii) findings from our evaluations on a physical testbed modeling quantum control architectures expose the performance limitations of static post-quantum security, while confirming that our adaptive framework effectively mitigates these overheads to preserve overall system efficiency. Specifically, the hardware experiments demonstrate that our dynamic security mechanism reduces total security execution time by approximately 49% relative to static high-security baselines, while maintaining a threat detection accuracy of over 91%. Furthermore, extensive simulations validate our theoretical analysis.....

The analytic properties of the Jost functions are fundamental in quantum scattering theory and in the analytic continuation of the scattering matrix into the complex energy plane. In this work, the analyticity of the Jost functions is investigated from the perspective of parameter-dependent ordinary differential equations. Starting from the radial Schrödinger equation for a short-range central potential, a first-order differential system is derived for the coefficient functions associated with the Ricatti–Bessel and Ricatti–Neumann solutions. The multivalued dependence on the energy variable is shown to originate from the square-root relation between energy and momentum. By explicitly factorizing the momentum-dependent branching terms, the scattering problem is transformed into a differential system whose coefficients are single-valued analytic functions of the complex energy. Using the classical theory of analytic dependence of solutions of ordinary differential equations on parameters, it is shown that the transformed Jost functions are single-valued analytic functions of the energy variable for finite radial distance. The geometric interpretation of the factorization procedure is also discussed in terms of the topology of the associated Riemann surface.

We present numerical simulation of a six-qubit quantum reservoir network with an output implemented on a 5-dimensional decoherence-free subspace (DFS), working as a classifier between entangled and product states of the input quantum system, fed to the reservoir during a finite learning time. Since the dynamics of DFS is not affected by external fluctuations, no cooling is required, and the proposed model seems a promising candidate for future quantum artificial intelligence systems working at room temperatures and free of huge energy consumption.

Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize quantum resource usage in near-term algorithms. Quantum resources should only be used when they are truly essential for quantum advantage, and not wasted on operations that can be efficiently handled by classical computation. In this work, we focus on de-quantizing quantum operations to classical computation whenever possible. The approach we propose for this is hybrid quantum-classical constant propagation, an optimization which reduces quantum operations by trading them for fast, reliable classical instructions. This is done by tracking between quantum and classical states to identify and eliminate unnecessary quantum gates and controls. We formalize a hybrid state model for quantum-classical constant propagation, implement our optimizations in the open-source MQT Core tool, and evaluate them on benchmark circuits. The obtained results show that quantum-classical constant propagation can reduce costly multi-qubit operations, making quantum programs more practical and robust for near-term devices. This opens the door to new hybrid compiler strategies that leverage the best of both quantum and classical worlds.

The cost of simulating quantum many-body systems - on classical or quantum hardware - scales with the number of variational parameters, so progress at fixed computational budget hinges on more parameter-efficient ansätze. Configuration Interaction (CI) is widely dismissed as parameter-heavy; we show this verdict is an artifact of the orbital basis. Co-optimizing the orbital basis with a sparse CI wavefunction - a method we call Core-Optimized Orbitals (COO) - absorbs a large fraction of the dynamical correlation directly into the single-particle basis, cutting the determinant count by several orders of magnitude beyond the already compact TrimCI ansatz on which it builds. On [Fe$_4$S$_4$] (54e, 36o), a billion-determinant TrimCI+COO wavefunction reaches accuracy that would require $3\!\times\!10^{14}$ determinants in a localized basis. At matched accuracy, it is $8\times$ more compact than the largest unrestricted-DMRG benchmark ($25\times$ with PT2). Across the iron-sulfur series - from [Fe$_2$S$_2$] (30e,20o) to the P-cluster (114e,73o) - TrimCI+COO is $10$-$100\times$ more compact than SU(2)-adapted DMRG with entanglement-minimized orbitals at matched accuracy. A tunable Hubbard-on-graph model factorizes the advantage into an orbital-basis gain and an ansatz gain, the latter capturing multi-center entanglement that resists MPS localization. COO therefore changes the picture of CI efficiency: sparse CI with optimized orbitals can outperform state-of-the-art tensor networks on strongly correlated multi-center systems.

We study transport across the Aubry-André-Harper localization transition in the presence of non-Markovian dissipation. For a single particle initially at the center of the chain, we show that bath memory (i.e., finite decay time of bath correlations) plays distinct roles in the two phases. In the extended phase, bath memory qualitatively reshapes the dynamical generator, thereby producing transport patterns that cannot be reduced to a simple rescaling of time. By contrast, in the localized phase, the bath activates motion between localized states and bath memory mainly renormalizes the dynamical timescales. Our results identify localization as a simple filter of non-Markovian effects: memory restructures transport in the extended regime, but survives mainly as a timescale renormalization in the deeply localized regime.

Quantum scars enable memory and recurrent dynamics, but their fate under dissipation remains poorly understood. Here, we show that distinct quantum scars can respond qualitatively differently to the same dissipative channel. We consider a collective spin model coupled to a lossy cavity and, guided by its classical limit, identify scars associated with two unstable structures: a saddle point on a dissipation-free invariant manifold with vanishing cavity field and an unstable superradiant fixed point with finite photon occupation. The former is immune to photon loss in the classical limit and exhibits persistent quantum revivals, whereas the latter couples directly to the dissipative channel, but exhibits slow dynamics. Remarkably, the superradiant scar also supports chaos-assisted quantum tunneling between two symmetry-related, macroscopically distinct semiclassical configurations, despite the presence of dissipation. Our results identify an experimentally accessible setting for exploring dissipative scarring and chaos-assisted tunneling in cavity QED.

Metastable quantum many-body dynamics could facilitate the organisation of microscopic degrees of freedom into macroscopic structures. However, the conditions under which this occurs are not well understood. Here we study false-vacuum decay in a 2D quantum Ising model and show that the initial correlation structure can qualitatively change this behaviour. Compared with product-state initialisations, correlated false-vacuum states suppress the proliferation of small true-vacuum domains and favour the formation of macroscopic connected clusters. Tree tensor network simulations of lattices up to $25 \times 25$ further reveal that nucleation proceeds predominantly from the boundary. Finite-size scaling demonstrates the dominant connected cluster remains an extensive fraction of the system even as its size increases. By suppressing this edge-assisted nucleation pathway through boundary pinning, we generate large magnetisation fluctuations consistent with macroscopic superposition. This mechanism relies on the 2D nucleation barrier and is absent in 1D systems or product-state quenches. Our results identify correlated state preparation and boundary engineering as complementary techniques for controlling metastable quantum dynamics.

Models of interacting complex systems provide the fundamental statistical physics reference frame for the study and the understanding of associative memories, machine learning, and the dynamics of neural networks. On the other hand, simulating complex multi-synaptic interactions on a classical hardware is computationally demanding due to the super-linear scaling of the system complexity. Photonic quantum technologies provide a promising solution to these limitations by leveraging on their inherent speed and parallel processing ability in order to simulate complex networks. Recently, a connection between multiphoton processes and generalized $p$-body Hopfield models has been theoretically established. Here, we design and demonstrate an experimental platform that exploits single photons distributed across a set of optical modes, in which controlled arrays of binary phase shifters act as Ising-like neurons. We focus specifically on a fully connected Hopfield Hamiltonian with four-body local interaction terms, realized via two-photon processes. Through quantum simulations on programmable photonic processors, the study identifies three distinct regimes: a memory retrieval phase, a spin-glass memory "black-out" phase, and a paramagnetic phase. Experimental results confirm successful memory retrieval at low storage capacities and temperatures, where the system consistently relaxes to fixed points with high memory overlap, effectively reconstructing the stored patterns. Future research will extend the platform design to investigate networks with local or dilute interactions, while advances in the realization of scalable photonic circuits will enable architectures that encompass very large numbers of interacting spins.

Many applications of Green's functions (GFs) require their evaluation over intervals or at multiple points, motivating quantum algorithms that return an efficiently computable functional representation rather than mere point estimates. We introduce a robust quantum Arnoldi method (ROQAM) that achieves this goal. Its robustness is derived from formulation in terms of orthogonal polynomials, which preserves the upper-Hessenberg structure of the projected matrices despite finite-precision estimation. We also show that as the iteration depth increases, the precision required for matrix-element estimation can be reduced. Resource estimates for the spectral function of a quantum impurity model indicate that ROQAM outperforms pointwise estimation via quantum singular value transformation by multiple orders of magnitude. Finally, we show that the ROQAM can be used to estimate GFs at nonzero temperatures using only a single Krylov subspace.

We develop a complete theoretical framework for open quantum systems coupled to scale-invariant environments. We show that such environments are universally described by unparticle baths characterized by a single scaling dimension $d_{\mathcal{U}}$. This work provides the proof of the uniqueness theorem, the formalism of the resulting non-Markovian dynamics, and applications to several physical systems. From the uniqueness theorem, we derive the non-Markovian memory kernels, the exact noise kernel including vacuum and thermal contributions, and a fractional generalization of the Caldeira-Leggett master equation for arbitrary $d_{\mathcal{U}}$. The scaling dimension governs a rich phase structure, including a thermalization transition at $d_{\mathcal{U}}=3/2$, the Ohmic boundary at $d_{\mathcal{U}}=2$, and a decoherence transition at $d_{\mathcal{U}}=5/2$ in the thermal regime, beyond which long-time quantum coherence is protected. Three realizations are studied. For the quantum Ising model at criticality, coupling to the energy operator in $(1+1)$ dimensions gives $d_{\mathcal{U}}=3/2$, producing $1/f$ noise, while the $(2+1)$D case yields $d_{\mathcal{U}}\approx1.413$ from the conformal bootstrap. In inflationary cosmology, massless scalar and graviton baths in de Sitter spacetime give $d_{\mathcal{U}}=2$, predicting linear decoherence growth consistent with the quantum-to-classical transition. For high-energy astrophysical neutrinos, the decoherence rate $\Gamma_{\mathrm{decoh}}\propto \mathcal{B}(E,T_{\mathcal{U}})L^{5-2d_{\mathcal{U}}}$ provides an observable signature of the scaling dimension. We also compare the framework with Caldeira-Leggett and Lindblad approaches, analyze the validity regimes, and discuss experimental implications for trapped-ion simulators, neutrino telescopes, and superconducting qubits.

We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for many-body wave functions known analytically in the occupation-number basis, systematic lower bounds to the QFI can be mapped onto expectation values over a classical probability distribution defined by the wave function amplitudes. This mapping enables efficient estimation via Markov-chain Monte Carlo sampling, with a computational cost that scales as a `slow' exponential ($e^{b L}$ with $b \lesssim 0.6$) and remains manageable for system sizes well beyond exact diagonalization. We specify this framework to Jastrow-Gutzwiller wave functions. We characterize their metrological content by identifying the observables that maximize the QFI and the corresponding scaling with $L$. Then, we analyze the QFI under three physically motivated noise channels: local dephasing, local amplitude damping, and global depolarizing. We compare polynomial and Krylov-based lower bounds across these channels, relating their behavior to the effective rank of the noisy density matrix and to the structure of the operator generating the parameter encoding. The framework extends naturally to other analytically known wave functions and to a broader class of information-theoretic quantities beyond the QFI.

Dynamical quantum phase transitions (DQPTs) are an exciting paradigm of out-of-equilibrium criticality in many-body systems manifested in nonanalytic behavior in the return rate to the initial state following a sudden quench. While previous work has tried to distinguish between distinct types of DQPTs, such as regular and anomalous, or manifold and branch, a comprehensive understanding of why each type appears in a given scenario is still lacking. In this work, we propose a unified framework addressing this gap in terms of the energy structure of different product state configurations. In particular, while manifold DQPTs are governed by resonances within the initial state manifold, branch DQPTs are governed by resonances with a transitional manifold of states dynamically connected to the initial manifold by low-order processes. We show that the (ir)regularity of branch DQPTs is related to the multiplicity of this transitional manifold, and we also observe exotic periods of extended degeneracy in the return rate (beyond the conventional level crossing of a DQPT) which are also conditioned on the structure of this transitional manifold. We demonstrate this by studying quenches of two different configurations in the 1 + 1D Z_2 LGT to various parameter regimes. Our findings provide a dynamical mechanism underlying branch DQPTs and frames DQPTs as probes of resonant connectivity in constrained Hilbert spaces, paving the way to a more complete understanding of the multifaceted nature of dynamical criticality.

Random circuit sampling (RCS) remains one of the most competitive frameworks for demonstrating quantum advantage in near-term noisy intermediate-scale quantum (NISQ) hardware. Unfortunately, absent error-correction, existing benchmarks to characterize these experiments, like linear cross-entropy, have been classically spoofed due to noise. Because of this, there are interesting regimes, like shallow-depth random quantum circuits, where sampling is plausibly classically intractable, but no existing benchmark can distinguish between a noisy quantum computer and an adversarial classical spoofer. In this paper, we demonstrate that the nonlinear cross-entropy provides a sample-efficient benchmark for shallow-depth all-to-all random quantum circuits whose score cleanly separates noisy quantum computers from state-of-the-art classical spoofers, even in the presence of depolarizing noise. Further, we develop a binary classifier based on the notion of heavy output generation that features logarithmic sample complexity at short depth. Our evidence comes from exact analytic expressions for all-to-all Brownian circuit ensembles derived using replica tricks, and numerical simulations that corroborate these results for discrete Haar-random unitary circuits.

Relaxation and condensation of an isolated low-energy Bose gas provide an ideal setting for the study of the universal features of far-from-equilibrium many-body dynamics and the emergence of long-range order. Conceptually, the emergence of such order involves two steps: the formation of local coherence, on a system-specific microscopic lengthscale, and the spreading of coherence, over lengthscales much larger than any microscopic scale. The latter is understood in terms of universal phase-ordering kinetics, or coarsening, characterized by an algebraic growth of the coherence length. Here, for a homogeneous Bose gas with tunable interactions, we show that the former also has a universal description, within the framework of weak wave turbulence (WWT). Specifically, the initial transport of particles to low momenta corresponds to an inverse turbulent cascade that is, in agreement with the WWT theory, characterized by a power-law momentum distribution, with exponent $\gamma = 2.4(1)$, and transport times ${\propto} (na)^{-2}$, where $n$ is the gas density and $a$ the $s$-wave scattering length.

Mediative Fuzzy Logic was conceived as a practical scheme for reconciling hesitant or conflicting assessments in fuzzy control and decision-making. However, its logical and semantic foundations remain underdeveloped, especially beyond operational type-1 settings. This article develops a unified account of the type-1 core together with interval type-2, granular type-3, and quantum extensions. We characterize the mediative operator as a convex aggregation controlled by hesitation and contradiction, model mediative truth values as independent truth-falsity pairs in a continuous bilattice-like structure, and introduce a propositional system extending a standard t-norm-based fuzzy logic with a mediative connective. We establish soundness, paraconsistency, and conservativity over the underlying fuzzy base for formulas without mediation, and formulate coherent semantic extensions to interval type-2 truth values, granule-indexed local evaluations, and effects and density operators on Hilbert spaces. An autonomous-braking sensor-fusion example illustrates how the framework supports transparent, conservative, and safety-first decisions under incomplete, heterogeneous, and mildly contradictory evidence. Under suitable assumptions, the higher-level formulations reduce to the type-1 case, clarifying coherence across levels and reliably supporting future work in intelligent decision systems.

We develop a bottom-up open effective field theory (EFT) for non-Abelian gauge theories within the Schwinger–Keldysh formalism. Instead of integrating out the environment completely and starting from a nonlocal influence functional, we retain the slow environmental response variables explicitly and construct a local system-environment EFT. The environmental sector is described by a dynamical color-frame variable, Stückelberg-like field, and an associated color-current sector, which gives the nontrivial interactions and dissipation between the system and the environment. The resulting construction provides a gauge-covariant Markov embedding of nonlocal and non-Markovian color response. After integrating out the retained environmental variables with retarded boundary conditions, the reduced system theory acquires nonlocal dissipative kernels and stochastic sources. We show that the hard thermal loop response arises naturally as a particular realization of the retained environmental response. Our framework provides a local open-EFT description of color transport, memory effects, and fluctuation-dissipation structure in non-Abelian plasmas, and offers a systematic starting point for dissipative Yang–Mills EFTs with dynamical environments.

Quantum processes with indefinite causal order – so-called causally nonseparable processes – can exhibit various advantages over quantum circuits with a fixed or a well-defined causal structure. A natural question is how much nonclassicality is required for a process to display causal nonseparability. Here we address this by investigating how many systems can be dephased (or decohered) before this property vanishes. First, for bipartite processes with open past and future we show that if all systems are dephased, or if only the future system is kept undephased, then the process becomes causally separable. However, if any single system other than the future system remains undephased, then there exist processes that retain causal nonseparability. Next, we demonstrate a similar behaviour in the multipartite case, when restricted to the physically motivated class of quantum circuits with quantum control (QC-QCs). Namely, dephasing all systems or keeping only the future system undephased renders any QC-QC causally separable; while causal nonseparability can persist if any non-future system is left undephased.

We consider the problem of single-photon transmission through an atomic medium, using quantum channel fidelity to describe the resulting information loss. We find that the normalized fidelity decreases monotonically with coupling strength, establishing a performance bound for quantum communication through such media. Our results hold for several channel types and for deterministic and random media.

Inferring a Hamiltonian from a single quantum trajectory is generally non-unique. This ambiguity limits inverse use of projective quantum geometry. Here we show that a nearest-neighbour structural prior makes the problem locally identifiable. For a smooth real time-dependent Jacobi Hamiltonian initialized at a ladder endpoint, the physical-time projective jet through order M+1 reconstructs the first M couplings, their logarithmic rates, and diagonal energy differences, up to an overall scalar-energy gauge. A canonical osculating-frame representation encodes the same data in a gauge-fixed connection. Pair-driven bosonic dynamics provides a direct realization because the vacuum evolves on the even-Fock Jacobi chain. In a nonstationary test, shallow reconstructions fit early projective data yet strongly overpredict later occupation growth; adding the projective order that resolves each hidden nonlinear layer restores the self-limited dynamics. The result supplies an inverse local counterpart to forward Krylov/Lanczos constructions and specifies when phase-resolved short-time state information identifies a sparse driven Hamiltonian.

Optomagnonic modulation techniques are an emerging platform for information transfer from the microwave to the optical domain. However, these techniques focus largely on the spectral domain of the transduced signal. Given the potential of the field to bridge the gap between microwave and optical signals, analyzing and studying the interactions real-time in temporal domain becomes equally essential. In this work, we exploit the optomagnonic modulation in a YIG microsphere to demonstrate and study microwave to optical real-time dynamic transfer on a time scale comparable to the decay of magnons. We inductively excite magnons in the microwave domain and use magnon-based Brillouin light scattering to transduce the signature of excited magnonic waveforms to the optical domain. The square type modulation of the magnons is retrieved in the corresponding optical sidebands. Our work enables real-time measurement of the magnonic dynamics and therefore direct access to lifetime measurements of the magnonic mode. Providing insight into the temporal dynamics of magnons, this work can open up new promising research directions such as in magnon coupled superconducting qubits or magnon-based Brillouin memory.

Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $\epsilon$ in Heisenberg-limited time $T=\Theta(1/\epsilon)$. Standard gate-based implementations of QPE require deep controlled time-evolution circuits and are not native to analog hardware. Here, we present a simple adiabatic protocol for QPE that achieves (up to logarithmic factors) the optimal Heisenberg-limited scaling $T = O\left( \frac{1}{\epsilon} \log\left(\delta^{-1}\right)\right)$ in both the precision $\epsilon$ and failure probability $\delta$. By encoding eigenvalues in populations of computational basis states rather than complex phases, our approach is naturally robust against certain dephasing errors. The adiabatic protocol only requires the ability to couple a single ancilla qubit to the system Hamiltonian as well as pairwise couplings within the ancilla register.

We identify a sharp interaction-degree threshold for the classical simulation of QAOA with $2$-local cost functions. At degree~$3$, classical sampling from depth-$1$ QAOA, even within multiplicative error $2^{n^{s}}$ for any fixed $s < 1$, would collapse the polynomial hierarchy to its third level. At degree $2$, exact classical sampling from depth-$p$ QAOA on $n$ qubits runs in time $n^{O(1)}$ whenever $p = O(\log n)$. The hard degree-$3$ instances have trivially optimizable cost functions, so sampling hardness does not by itself imply a quantum optimization advantage.

We introduce the Motte model, a software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each disjoint layer of gates accompanied by a pairwise or k-local quantum state tomography of the device. We prove that the model is equivalent to the coupling-graph-restricted circuit model, and hence universal for BQP, with only polynomial overhead: emulating a depth-D circuit on N qubits requires O(D^2 N log N) elementary operations. Because the gate applied at each step is fixed exactly by the tomographic report, this emulation is robust to both the sampling and readout noise of the tomography. The model formalizes an idiom shared by existing work that ranges from quantum imaginary time evolution for the study of quantum systems to the use of quantum computers for procedural generation in games. It therefore provides a natural interface for designing quantum software entirely in terms of physically observable quantities, relevant for the NISQ era and into fault-tolerance, with gate and decoherence noise lying outside the present scope.