Papers

The meticulous preparation of macroscopic Greenberger-Horne-Zeilinger (GHZ) states provides a foundational resource for quantum technologies such as metrology, cryptography, and fault-tolerant codes. While state-of-the-art measurement-based protocols offer efficient low-depth execution, their performance can be bottlenecked by conventional decoders, such as minimum weight perfect matching (MWPM) or even maximum-likelihood decoding (MLD), which optimize for $binary$ logical recovery and fail to maximize the $continuous$ long-range order characteristic of a GHZ state for two-dimensional geometries. Here we overcome this limitation by framing the decoding problem as minimum Bayesian risk inference, introducing a general paradigm that maximizes the expected ${utility}$ of the decoded state. Implementing this maximum-utility approach, we construct an algorithm that achieves the highest possible per-shot decoded quantum order and thereby establish an optimal decoding strategy for measurement-based GHZ state preparation. To improve its computational efficiency, we design a scalable two-stage decoder, which first encodes the syndromes into the edge weights of MWPM and then refines the result with a convolutional neural network trained to maximize the expected utility, at a fraction of the cost of the optimal decoder. Remarkably, we find that the first stage alone$\unicode{x2014}$which makes the matching aware of the gauge choice at no cost beyond bare MWPM$\unicode{x2014}$already performs near-optimally up to the largest sizes we study, $N=256\times256$, closing up to $87\%$ of the gap between the bare-MWPM and optimal decoding thresholds. Generalizing MWPM and MLD, the maximum-utility decoder (MUD) establishes a versatile framework that can be explicitly tailored to the operational demands of specific experiments by redefining the utility function.

While the prethermal regime of random many-body localized (MBL) systems is dominated by accidental many-body resonances, another class of resonances, originating from the underlying potential structure, is expected in large-size deterministic systems. It is known that this class of resonances can lead to single-particle critical phases that are neither localized nor extended, but the consequences in interacting systems remain unclear. In this work, we construct an asymptotically solvable model of a one-dimensional nearest-neighbor interacting spin chain, whose spatial structure induces a hierarchy of mirror-like many-body resonances. We derive two phases in the thermodynamic limit, characterized by the satisfaction and violation of a version of the weak eigenstate thermalization hypothesis (ETH). While these two phases are similar to the usual MBL and ETH phases, there exist rare eigenstates that behave like the opposite phase, interpreted as many-body scars and inverted scars. Surprisingly, the two phases can be separated by a finite-temperature phase transition, corresponding to a thermodynamic many-body mobility edge, which was often believed to be impossible. Our results also suggest the existence of delocalized rare regions in an otherwise-localized interacting Aubry-André model, even if there are no low-disorder regions like those in random systems. This challenges the common belief that there is no avalanche instability in quasiperiodic MBL.

Forecasting neural activity from short recordings remains a fundamental challenge. Reservoir computing may offer an efficient paradigm for temporal prediction, however classical reservoirs typically underperform in small-data regimes. Here we investigate whether quantum reservoir computing (QRC) can help overcome this limitation. Building on recent advances, we introduce a quantum reservoir based on a transverse-field Ising model, combined with heterogeneous quantum measurements and polynomial ridge regression. On a standard benchmark task, results show that the quantum reservoir outperforms a classical counterpart overall, with prediction accuracy strongly dependent on reservoir parameters. We further demonstrate feasibility by running the same task on quantum hardware. To assess performance on biological signals, we evaluate QRC on simulated human electroencephalography (EEG) data with a parallel reservoir architecture. On this challenging task, the tested quantum reservoir did not match the performance of the classical one, but it produced stable, convergent predictions. This is a meaningful first step toward forecasting of biologically realistic neural data using a quantum reservoir. Overall, our findings indicate that although current quantum hardware and parallel reservoir architectures do not yet surpass classical methods on complex neural signals, QRC can be executed on near-term devices and does converge with realistic EEG-like data. This work establishes a practical baseline for future algorithmic and hardware developments aimed at clinical time-series forecasting with quantum systems.

A local deterministic model can reproduce Bell-inequality violations only if the hidden state depends on the measurement settings. Hall found the minimum such dependence for the singlet state [Phys. Rev. Lett. 105, 250404 (2010)] and posed the corresponding problem for the Mermin state [Phys. Rev. A 84, 022102 (2011)]. This paper solves it, for the $n$-party GHZ-Mermin scenario at every $n \geq 3$, with the marginals reproduced as well as the correlators. The minimum measurement-dependence fraction is $F_{\min}(n) = R/[2(R+1)]$, with $R = 2^{\lfloor (n-1)/2 \rfloor}$ the Mermin violation ratio: $1/3, 2/5, 4/9, 8/17, \ldots$, always below $1/2$. The lower bound follows from Mermin's inequality by a general overlap bound; the upper bound is an explicit model, uniform on the hidden-variable classes that violate the fewest constraints, with closed-form counts; a reduction theorem shows that for Mermin scenarios the marginals impose no additional dependence. The Mermin values are also certified by integer-arithmetic enumeration through $n = 22$. The formula was stated as a conjecture in the first version of this paper and was first proved, by a different route, by Wang, Yao and Chen; the proof here was obtained independently and the two agree. Every minimal contradiction of size $k$ among stabilizer constraints has correlator-only minimum $1/(k-1)$. With the marginals included the minimum is the same on every core of the $C_5$ ring cluster, on the size-4 and size-5 cores of $C_4$ and on every four-core of $C_6$, but larger on the size-6 and size-7 cores of $C_4$ and on 112 of the 1,920 five-cores of $C_6$, with exact certificates on both sides in every case.

In this paper, we apply the covariant phase space formalism to the perturbative canonical quantization of the Pais-Uhlenbeck oscillator, with the acceleration-squared term treated as a perturbation. We quantize this model by constructing the symplectic form on the low-energy solution space. We then compute the energy spectrum and the unequal-time commutator in a perturbative way, and obtain the results that agree with the expansion of the exact low-energy theory. The perturbation method bypasses the standard Ostrogradsky construction and naturally decouples the Ostrogradsky ghost. This work extends our previous perturbative quantization scheme to genuine higher-derivative theories.

In Online Shadow Tomography, we are given copies of an unknown $d$-dimensional quantum state $\rho$, an adversary (adaptively) proposes a sequence of bounded observables $A^{(1)},\ldots,A^{(m)}$, and after each $A^{(t)}$ is given we must estimate $\mathrm{Tr}(A^{(t)}\rho)$ to within $\pm \epsilon$. This is the direct quantum generalization of the classical problem of Adaptive Data Analysis. Prior results for online Shadow Tomography were suboptimal in all three parameters $m, d, \epsilon$, lagging behind the best known and classical rates, for which there is some evidence of optimality. In this work, we finally close this gap, giving a pair of algorithms matching the classical rates. Our first algorithm is the first to achieve $o(\log^2 m)$-dependence together with $\mathrm{poly}(\log(d)/\epsilon)$; moreover, it improves all three exponents even in the Offline Shadow Tomography setting. Our second algorithm is known to be optimal among bounds independent of $d$, and improves the best prior result by a $\sqrt{m} \log m$ factor. The key to our proof is a new framework for quantifying post-measurement damage, based on the quantum Efron-Stein decomposition.

We study the sample complexity of estimating and testing fundamental unitarily invariant properties of unknown quantum states; namely, the tasks of spectrum estimation, von Neumann entropy estimation, and rank-testing. For $d$-dimensional states, and for every $\gamma>0$, we prove a sample complexity lower bound of $\Omega(d^{2-\gamma})$ for spectrum estimation to constant sorted total-variation error, entropy estimation to constant additive error, and rank-testing to constant trace distance. Our hard instances are constructed from sandwiched products of Haar-random projectors, suitably normalized using a novel technique that lets us derive explicit expressions for high-order tensor moments of the resultant states. These moments can be expressed as symmetric functions of Jucys–Murphy elements of the symmetric group algebra. To show that two such mixtures are indistinguishable, we analyze the log-likelihood ratio and perform moment-matching, i.e., we set its low-order Jucys–Murphy components to zero. Indistinguishability is then obtained by bounding an $f$-divergence through the high-order components; the non-zero high-order terms and concentration of functions of Haar-random unitaries also imply separations in typical spectra, entropies, and ranks, proving all our lower bounds.

Planted noisy $k$XOR and the strong refutation of random $k$XOR are governed by a conjectured trade-off between signal strength and time: Level $\ell$ of the Kikuchi hierarchy should achieve the smooth curve \begin{equation*} m\ \gtrsim\ \rho^{-2}n^{k/2}/\ell^{k/2-1}\ \text{clauses} \quad\Longleftrightarrow\quad \text{solvable in time }n^{O(\ell)}, \end{equation*} where $\rho$ is the bias of the planted signal or, for refutation, the target advantage. However, every spectral analysis of sparse $k$XOR to date loses polylogarithmic factors against this curve, a loss that enters the exponent of the running time. We show that a normalized variant of the Kikuchi hierarchy achieves the sharp conjectured trade-off, with no logarithmic loss, at every arity $k\ge3$. At the scale above, our algorithms achieve strong detection, weak recovery, and strong refutation; an additional cleanup step boosts weak recovery to exact recovery, and the refutation certificates yield sum-of-squares proofs of degree $O_k(\ell)$. We also prove matching lower bounds in the same model. The inference and refutation upper bounds transfer to more general planting laws and predicates. Finally, we give a quantum algorithm that achieves a quartic speedup over the classical spectral algorithms for detection and weak recovery. The proofs rest on two key ingredients: a normalization of the sparse Kikuchi matrix, and a sharp count of the closed walks in its trace expansion. We use a closely related trace-walk count to prove Feige's 2008 hypergraph Moore bound conjecture in a companion paper.

Fermionic Gaussian states form a central class of classically tractable quantum states, while fermionic non-Gaussianity provides the resource required to go beyond free-fermion dynamics. A key challenge is to quantify this resource through monotones that are both mathematically rigorous and experimentally accessible. Here, we show that the fermionic entropy, defined through the squared Frobenius norm of the correlation matrix, is a strong pure-state Gaussian monotone. Its simple closed-form expression also makes it directly measurable: we show that the associated fermionic purity can be unbiasedly estimated up to additive error $\varepsilon$ using $O(\varepsilon^{-2})$ two-copy measurements, independently of the system size. Moreover, we prove that the fermionic entropy obeys asymptotic continuity and, as a direct consequence, establish its operational meaning as the upper bound to the asymptotic rate of non-Gaussianity distillation. We further derive a linear sample complexity bound for tolerant testing of fermionic Gaussian states, providing a quadratic improvement over the state of the art. As a further application of our results, we study unitary designs generated by Matchgate circuits supplemented with Majorana-local non-Gaussian gates. We prove that a linear number of such gates is necessary even to achieve an approximate state $2$-design with error below $0.4\%$. Combined with known nearly linear upper bounds for relative-error designs, this determines the optimal doping level, up to logarithmic factors, across all relevant design notions and reveals the extensive non-Gaussianity cost required to generate Haar-like quantum dynamics in this architecture.

Phonons hold promise for storing and transferring quantum information, including in mechanically-mediated quantum interconnects between superconducting qubits and light. Phononic crystal cavities confine gigahertz sound to micron-scale volumes well matched to near-infrared light. So far, these devices have typically been suspended to suppress phononic radiation loss into the substrate, but suspension limits thermal anchoring leading to excess noise. Release-free phononic crystals have emerged as a way to address this challenge – but had yet to be shown compatible with strong electromechanical interactions. Here, we demonstrate a release-free phononic crystal cavity strongly coupled to a high-impedance microwave resonator, with an electromechanical coupling rate $g_\mathrm{em}/(2\pi) \approx 30\,\text{MHz}$ that exceeds both the mechanical and microwave loss rates, leading to a cooperativity up to $\mathcal{C} \approx 180$ on resonance. In addition, our lithium niobate phononic crystals reach quality factors above $10^4$ at millikelvin temperature on both silicon and sapphire substrates. Our results establish release-free phononic crystals as compact, scalable interfaces between microwaves and gigahertz sound for emerging sensing, communication, and computing systems.

Quantum integrability is a cornerstone of the exact theory of interacting quantum spin chains. In its standard formulation, however, one starts from R-matrices satisfying the Yang–Baxter equation, rather than from the Hamiltonian itself. It has therefore remained unclear how Yang–Baxter solvability can be characterized directly at the Hamiltonian level, and how it is related to the existence of local conservation laws. Here we prove that, in a broad standard setting, the Reshetikhin condition is not only necessary but also sufficient for Yang–Baxter integrability, thereby reducing the hidden algebraic structure of integrability to a Hamiltonian-level conservation law. Since the Reshetikhin condition is equivalent to conservation of the total energy current, this Hamiltonian-level criterion is also experimentally accessible. This result establishes a quantum counterpart of the Liouville–Arnold theorem for isotropic spin chains, stating that Yang–Baxter solvability is equivalent to an infinite hierarchy of local conserved quantities. Our result also simplifies substantially the search for integrable spin chains by replacing the search for R-matrices with a direct criterion on local Hamiltonians.

We consider an elastic helical nanoribbon that can take on various conformations, and study the effect of placing a quantum particle on its curved surface. Using a modified Canham-Helfrich model for the elastic energy, we write down the local elastic potential for the ribbon in terms of its bending rigidity, mean curvature $M$ and Gaussian curvature $K$. The Schrödinger equation of a particle confined to a rigid curved surface is found using da Costa's formulation. It has a purely quantum geometric potential which depends on $M$ and $K$. The Schrödinger equation of a particle on an elastic curved surface will therefore have a total potential comprising quantum and elastic potentials. We compute $M$ and $K$ for a helical ribbon and derive the total potential which depends on the conformation and is thus geometric in nature. Defining a dimensionless quantity $R_H$, we study the behavior of the total geometric potential as $R_H$ is varied. In the absence of an electron, the elastic potential is positive and has a single positive maximum for all conformations. Further, a binormal helical ribbon conformation has the lowest potential, while the normal ribbon has the highest, with those of the intermediate ribbons lying in between these. Intriguingly, when a quantum particle is placed on the elastic ribbon, above a certain critical value of $R_H$, the presence of the quantum geometric potential reverses this order. But localized states for the particle are not supported. Only above a second critical value of $R_H$, localized states appear for all conformations. The injection of an electron on any given conformation of the elastic ribbon will induce a conformational transition to the normal ribbon conformation.

The proposal is to probe Majorana modes in the system when its parameters are tuned to bring it into a disentangled ground state, which occur on the parametric curves known as disorder lines (DL). In such state certain correlation functions do not depend on separation. The exact results are presented for the XY spin chain in transverse field, also called the Kitaev chain in the Majorana representation. The single Majorana modes are shown to be localized near the ends of the chain, as in the states off the DL, while the disentangled $n$-particle Majorana modes ($n \geq 2$) penetrate into the bulk without attenuation. The predicted bulk-edge effects can be detected in the specially engineered optical chains and lattices.

A key enabling feature of future quantum networks is interoperability between platforms that operate at different wavelengths and with different qubit encodings. We demonstrate an interface that converts atom-photon entanglement from polarization encoding at an atomic wavelength to time-bin encoding in the telecom C-band. Atom-entangled photons at 854 nm are generated from a single $^{40}$Ca$^+$ ion. After quantum frequency conversion to 1550 nm, the photonic polarization qubit is converted into a time-bin qubit using a fiber-based Mach–Zehnder-like encoder. Full quantum tomography of the final state verifies that the process preserves entanglement with 96.3(4.2)% fidelity. Together with the independent work of Ferrari et al. [arXiv:2607.07805 (2026)], this is the first demonstration of polarization-to-time-bin conversion of photons entangled with a single atomic quantum memory. The telecom-compatible interface enables robust qubit transmission over optical fibers and provides a key building block for heterogeneous quantum networking architectures.

Qubit loss occurs when the physical carrier of a qubit leaves the computational system without directly revealing the event's location. Such errors are a major obstacle to fault-tolerant quantum computation on platforms including photonic, neutral-atom, and trapped-ion systems. Loss locations are commonly identified using additional hardware operations such as leakage-detection units (LDUs), which introduce space-time overhead and may themselves become a source of error. We investigate whether qubit loss on stabilizer codes can instead be inferred from syndrome data obtained through standard repeated stabilizer measurements. Under a non-entangling model for gates involving a lost qubit, we derive a sufficient condition for loss detectability in general stabilizer codes. The condition is based on the emergence of anticommutation between stabilizer checks after their support on the lost qubits is removed. By using that condition, we formulate the exact loss-inference problem using the observed set of non-deterministic checks together with its maximum-likelihood formulation. We then relax the problem to the minimum set cover problem with a greedy heuristic algorithm. We evaluate the resulting inference and loss-correction protocols on the rotated surface code via circuit-level noise simulations for trapped-ion and neutral-atom platforms. On both platforms, inference-based and adaptive protocols reduce the logical error rate relative to a noisy-LDU baseline in the low-to-moderate loss-rate regime relevant to near-term hardware, while requiring fewer space-time overheads.

The proliferation of power electronics in multi-terminal transmission grids has increasingly led to harmonic distortions and dynamic instabilities. While Resonance Mode Analysis (RMA) provides deep insights into these system resonances, evaluating the critical modes of large-scale grids presents a severe computational bottleneck. Classical iterative techniques must continuously diagonalize massively high-dimensional, non-Hermitian admittance matrices across a wide frequency spectrum, a process that rapidly exhausts classical memory and processing limits. To overcome this scaling barrier, we propose a novel quantum-classical hybrid methodology that natively maps the transmission grid's admittance matrix onto a Quantum Processing Unit (QPU). Because the grid's matrix is non-Hermitian, standard quantum eigensolvers are insufficient; thus, we employ the Real Variance-based Variational Quantum Eigensolver (RVVQE) algorithm to accurately extract the complex eigenvalues that represent the system's modes. Validated against a standard 5-bus transmission system, the quantum-derived critical-resonance modal impedances demonstrate near-perfect alignment with the exact classical frequency responses. Crucially, by encoding the grid's state logarithmically into quantum memory, this methodology bypasses classical RAM limitations. The successful implementation of the RVVQE framework not only bridges the mathematical topologies of dissipative electrical grids and open quantum systems but also provides a profoundly scalable architecture capable of diagnosing resonance instabilities in massive, continental-scale networks that currently exceed classical computational boundaries.

The physical properties of a quantum system, whether pure or mixed, are described fully by its density matrix. Recovery of the density matrix through projective measurements – referred to as quantum state tomography – is a cornerstone of quantum optics and metrology. The implementation of this approach in transmission electron microscopy, in particular for the characterisation of an electron beam after inelastic scattering, has remained a longstanding challenge as a result of the complexity of scanning high-dimensional phase spaces, with the number of required measurements growing quadratically with space dimensionality. Here, we introduce a simplified approach by restricting tomography to the electron orbital angular momentum (OAM) subspace. By using an electron optical device known as an OAM sorter, we discretise the phase space into a finite set of measurable states, thus significantly reducing the experimental and computational burden. The resulting measurements suffice to probe essential features of inelastic scattering. We demonstrate the technique by studying the inelastic scattering of a structured electron probe exciting volume plasmons in a carbon film. The combined use of a structured beams and OAM-resolved quantum tomography reveals symmetry-breaking effects and offers insight into the coherence and evolution of the scattered quantum states. Analysis of the diagonalised density matrices further reveals the nature of the induced state transitions, demonstrating the power of the approach for quantum tomography of electron scattering.

We have studied the fidelity of spatial entanglement between dissociated atom and ion from two photon dissociation of hydrogen molecular ion H 2 + . Two processes for two photon dissociation of molecular ion have been considered (i) sequential two photon (STP) absorption and (ii) correlated two photon (CTP) absorption by the molecular ion. We compared the results for fidelity of spatial entanglement (FSE) between dissociated atom and ion for these two types of dissociation. In a previous study in our group [1] we have shown that when an atom interact with nonlocal mode of electromagnetic field (which has been derived field theoretically), simultaneous phase-correlated two pho1 ton absorption by the atom occurs within a very short time {\delta}t << {\omega} , where {\omega} is the laser frequency, and the rate of this correlated two photon absorption is linear in intensity. This will happen when the photon flux in the interaction region is high i.e. laser intensity is higher than 10 10 W/cm 2 . In this work we have extended this formalism to study the correlated two photon dissociation of molecular ion and to explore the effect of correlation between two simultaneous photo-absorption processes on the fidelity for spatial entanglement of dissociated atom and ion. Dependence of fidelity for spatial entanglement on the photon frequency has been studied for both the STP and CTP dissociation, to show that photon frequency can be used as control parameter to achieve maximum fidelity. Saturation of fidelity with the increase in time at which fidelity was calculated shows the robustness of the processes considered here. A scheme for detection of spatial entanglement between ion and atom has been suggested.

We prove that the $\mathrm{iSWAP}$ gate maximises the spectral gap of the Hermitian second-moment operator on every connected graph with at least three vertices, among all two-local unitary circuit ensembles. We further prove that the polyhedral cone defined by asymmetric four-point inequalities is invariant under the transpose of the $\mathrm{iSWAP}$ semigroup, yielding a componentwise comparison certificate for its positive Perron–Frobenius eigenvector. These results resolve a conjecture of Kong, Li, and Liu.

Strong light-matter coupling gives rise to polaritons through coherent and periodic energy exchange between electromagnetic cavity fields and material excitations. While this interaction is typically inferred from spectral mode splitting, its dynamics remain largely unexplored. Here, using phase-resolved terahertz time-domain spectroscopy, we observe Rabi oscillations of Landau polaritons formed by coupling the cyclotron resonance in a GaAs/Al$_{0.36}$Ga$_{0.64}$As two-dimensional electron gas with Fabry-Perot cavity modes. By employing cross-polarized spectroscopy and magnetic-field differential, we resolve the temporal beating of the cyclotron resonance oscillations. Remarkably, we find that the Rabi oscillations do not start immediately after excitation of the cyclotron resonance, but after a delay corresponding to one cavity round-trip time. This demonstrates that the strong-coupling regime sets up only after the formation of the cavity mode field. Our results provide direct insight into the dynamics of hybrid light-matter states in the THz regime.

We study a class of Friedrichs Hamiltonians, that is, operators describing an excited state coupled to a bath through a rank-one perturbation, in the case where the bath Hamiltonian has purely discrete spectrum. We consider sequences of such Hamiltonians for which the spectral measures associated to the coupling functions by the bath Hamiltonians converge weakly to a limiting measure that is absolutely continuous with a Hölder continuous density near the excited energy. Under this assumption, we show that the survival probability of the excited state decays in an approximately exponential manner on suitable time scales and under favourable conditions, with a decay rate given by Fermi's golden rule for the limiting measure. The error is estimated in terms of the coupling strength and the Lévy distance between the discrete spectral measures and the limiting measure. As an application, we treat a two-level atom coupled to a massless bosonic field confined to a large cavity in the rotating-wave approximation.

We present a comprehensive framework for evaluating the phase sensitivity of spectrally multimode SU(1,1) interferometers probed with a coherent-vacuum input, under both number and homodyne detections. The optical parametric amplifiers (OPAs) are simulated using a periodically polled thin-film lithium niobate waveguide. The theoretical model incorporates the intrinsic multimode spectral nature of waveguide-based OPAs. Under the assumptions of identical OPAs and Schmidt-mode-independent phase shifts, we have shown that the multimode SU(1,1) interferometer is equivalent to a collection of independent single-mode interferometers in the Schmidt basis that operate in parallel, each associated with a Schmidt mode of the parametric process. We further present an optimized waveguide design based on asymmetric group-velocity matching to realize a practical OPA with nearly factorizable joint spectral amplitude (JSA). The Schmidt coefficients extracted from the numerically simulated JSA are incorporated into the theoretical model to evaluate the phase sensitivity. The results show that the sensitivity under a multimode condition depends strongly on the measurement scheme. For number detection, the degradation in sensitivity arises from the redistribution of the available nonlinear resource among the Schmidt modes, whereas homodyne detection exhibits an additional coherence penalty that can be substantially reduced by optimally shaping the local oscillator. Moreover, we show that the performance degradation can be to a large extent mitigated by optimizing the spectrum of the injected signal coherent state and, in the case of homodyne detection, the spectrum of the local oscillator. Altogether, this work provides a unified theoretical and numerical framework for analyzing and optimizing realistic multimode SU(1,1) interferometers with waveguide-based OPAs for quantum-enhanced sensing applications.

We analyze the time evolution of the nearest-neighbour tight-binding chain in the presence of a single onsite defect. Such a defect was shown to generate non-trivial transport behavior recently in the article Acharya et al J. Stat. Mech. (2026) 043102. The authors have used a defect technique inspired by classical random walk methods to obtain exact analytical expressions for the occupation probability and subsequently the mean and mean-squared displacement (MSD). Here we derive the same results using a spectral decomposition approach. Starting from the secular equation, we obtain the self-consistency condition for the eigenvalues and construct the corresponding normalized eigenvectors. This approach naturally separates the Hilbert space into dark subspace, whose states have zero amplitude at the defect site and remain unaffected, and bright subspaces, whose states get modified because of the defect. Using this eigenvalue decomposition, we provide a spectral origin of non-monotonicity in the MSD. Numerical calculations for finite chains show that the analytically estimated critical defect strength is in excellent agreement with the defect strength that minimizes the MSD.

We give a bounded-error quantum algorithm that, given a prime $p$, a divisor $q\mid(p-1)$, and an integer $0<n<p$, computes $n!\bmod p$ in expected time $\widetilde{O}(q^c+\sqrt{p/q})$ for some absolute constant $c\ge 1$. When $p-1$ has a divisor of size $q\approx p^{1/(2c+1)}$, this gives the exponent $c/(2c+1)<1/2$. To our knowledge, this is the first algorithm to break the exponent $1/2$ barrier for modular factorials under such a divisor promise. The main technical ingredient is a quantum algorithm that reconstructs the relevant Jacobi sum exactly in compact algebraic form, with polynomial dependence on $q$ and $\log p$. We further extend the same asymptotic bound to the computation of $n!\bmod p^2$, uniformly over $0\le n<p^2$. At $n=p-1$, this determines the Wilson quotient $\frac{(p-1)!+1}{p}\pmod p$. We conjecture that the condition $q\mid(p-1)$ is a technical limitation of the present method rather than an inherent obstruction, and that a uniform quantum algorithm exists for all primes.

Quantum error correction (QEC) codes can correct twice as many erasure errors as Pauli errors. Because of this scaling advantage, there is significant interest in developing qubits whose dominant error channel can be converted into erasures via mid-circuit erasure checks. However, such erasure checks come with hardware overhead in practice. End-of-the-line three-state readout, in which one simultaneously measures a qubit's erasure status and computational state, is an alternative to mid-circuit erasure checks that is generally simpler to implement. In this work, we systematically study the conditions required to enable erasure performance—the doubled error-correction capacity—in the surface code with and without mid-circuit erasure checks. We introduce the moonwalking surface code, the time-reversal of the walking surface code, as a zero-overhead circuit with superior handling of leakage and erasure. Specifically, we show that it enables erasure-like logical error rate scaling when combined with three-state measurement if leaked qubits cause two-qubit gates to be skipped and an appropriate decoder is used. Our decoder, based on a branch-and-bound algorithm, specifically incorporates the noise structure of the skip-gate leaked-qubit effect.

We study how much of the proto-area response can be inferred from the bulk von Neumann entropy. In the perturbative holographic code setting considered by CCKLP and Witten, we keep the recovery frame fixed and analyze the response averaged over the GUE at second order in the encoding perturbation. Near the maximally mixed bulk spectrum, the response is fixed by the entropy through quadratic order. For $d_1\geq3$, spectral information first enters at cubic order through the third centered moment, so states with the same entropy can have different responses. We determine the resulting response range on small equal-entropy level sets and obtain its sharp leading $D^{3/2}$ dependence, including the coefficient. The corresponding minimax error for prediction from entropy alone is one half of this range. For $d_1=2$, the entropy instead determines the response exactly.

The entanglement entropy of quantum systems typically exhibits both ultraviolet and infrared (IR) divergences. In the low-frequency limit, the IR divergence is intimately tied to the unbounded spatial delocalization of zero-modes, a pathological feature common to both coupled harmonic oscillators and massless scalar fields. In this work, we demonstrate that this infinite growth is naturally resolved by invoking the Extended Uncertainty Principle (EUP), which introduces large-length-scale geometric corrections to the canonical commutation relations. By exactly solving the simple harmonic oscillator under the EUP framework, we establish the existence of an intrinsic geometric confinement that enforces a strict upper bound on the position variance, limits spatial delocalization, and introduces an intrinsic localization length scale related to the background Ricci scalar. We extend this regularizing mechanism to many-body systems by evaluating the entanglement entropy and entanglement spectrum of a one-dimensional harmonic chain and a massless scalar field. We show that the EUP-induced spatial bounds prevent the accumulation of low-lying long-wavelength modes, keeping the entanglement spectrum discrete and evenly gapped even in the strictly massless limit. This non-vanishing modular gap effectively caps the local entanglement temperature of the vacuum. Consequently, the entanglement entropy saturates to a finite value, providing a robust, geometric resolution to the zero-mode IR divergence problem in quantum field theory.

We introduce a variational framework for approximating the time-evolution operator $\hat{U}(t)$ within a physically motivated operator manifold, reformulating quantum dynamics as a tractable problem in operator space using stationary action principle. For periodically driven systems, the resulting approximate evolution operator directly yields an effective Floquet Hamiltonian, offering a non-perturbative alternative to conventional expansion-based methods. The framework is systematically improvable by enlarging the operator pool and naturally incorporates symmetries and physical constraints. When the operator manifold is chosen from the terms of a truncated Magnus expansion, the variational procedure effectively resums the Magnus series within the restricted space, significantly enhancing accuracy. We benchmark the approach on the driven Rabi model, the driven Lipkin-Meshkov-Glick model, and the one-dimensional driven Ising chain, yielding effective Floquet Hamiltonians that are systematically more accurate than low-order Magnus expansions, particularly in regimes where the latter converge poorly, and illustrating applicability to systems with exponentially large Hilbert spaces. Although we focus here on Floquet systems, the formalism applies equally to generic time-dependent Hamiltonians, providing a versatile tool for non-equilibrium quantum dynamics.

A general implementation of the equation-of-motion (EOM) formalism for correlated many-body states is presented and applied to the description of collective excitations in atomic nuclei. While EOM approaches are traditionally formulated on top of independent-particle reference states, the present work extends the method to correlated reference states generated by modern many-body solvers. This formulation enables a consistent treatment of ground-state correlations and excited-state dynamics within a unified framework. Particular emphasis is placed on collective nuclear excitations employing chiral nuclear Hamiltonians in an ab initio context. The approach is motivated by the renewed interest in EOM techniques across several fields, including quantum chemistry and quantum computing, where they provide efficient and systematically improvable descriptions of excitation spectra. The present results demonstrate that the EOM framework offers a flexible and powerful tool for the microscopic description of nuclear spectroscopy beyond the traditional mean-field paradigm.

Deterministic exact inversion of an arbitrary $d$-dimensional unitary requires {$\Theta(d^2)$} coherent forward calls in the worst case. We ask how this cost changes for Hamiltonian evolution $U(x)=\exp(i\sum_j x_jH_j)$ when the generators are known but the parameters are hidden. For one-parameter families with a fixed eigenbasis, we show that additive relations among the distinct eigenvalues determine the optimal query number exactly, and we construct the corresponding inversion protocol. For general families, we prove that repeated symmetry sectors do not affect the exact query complexity and give an automatic construction for combining inverses from inequivalent active sectors. We also give a sufficient phase-alignment condition under which family-specific structure can reduce the query number. These results establish structure-dependent bounds for reversing the unknown dynamics arising in Tavis-Cummings out-of-time-order correlator protocols, collective-spin echo verification, and passive multimode links, without requiring prior knowledge or explicit estimation of the underlying coupling strengths.