Papers

Multipair emission is a principal source of false heralds in entanglement swapping with spontaneous parametric down-conversion sources. A conventional Bell-state measurement (BSM) cannot distinguish the desired arrival of one photon from each neighboring source from a mixed-polarization double emission by one source accompanied by vacuum from the other. We show that a cascaded network can resolve this ambiguity by allowing its successive swapping stations to perform different measurements. A direct-basis BSM rejects same-polarization double emissions, whereas a balanced equatorial analyzer, implemented by a four-mode Green Machine (GM), uses two-photon interference to reject mixed-polarization double emissions. At the same time, it recovers same-polarization inter-source events rejected by the BSM as resolved $\phi$-type Bell heralds. Their rejection sets jointly cover both single-source two-photon classes while retaining contributions from both useful inter-source classes. We classify the passive four-mode, number-resolving analyzers satisfying this condition and identify the BSM and GM as canonical balanced representatives. Using a Gaussian-state analysis exact to all orders of multipair emission, we evaluate three-source BSM–GM and four-source BSM–GM–BSM Pure Bell Pair sources under coupling, detector, and channel loss. The three-source network suppresses the leading infidelity, while the four-source network heralds an exact Bell state in the lossless limit, a property that holds for every alternating BSM–GM chain with four or more sources. The fidelity advantage over source-count-matched all-BSM networks persists at every loss level studied, a single-channel rate advantage appears without multiplexing, and spectral multiplexing raises the Bell-pair delivery probability toward the asymptotically deterministic limit.

Quantum indistinguishability obfuscation (qIO) aims to make a quantum circuit unintelligible while preserving its functionality. It serves as a foundational primitive for advanced applications, such as witness encryption (WE) for QMA, non-interactive zero-knowledge arguments for QMA, and attribute-based encryption for BQP. Despite its importance, constructing qIO from standard assumptions remains a major open problem. In this work, we prove that the security of WE for QMA cannot be based on any falsifiable cryptographic assumption via a restricted class of quantum black-box reductions. Because qIO for null quantum circuits implies WE for QMA, this also separates null-qIO from falsifiable assumptions. Since almost all standard cryptographic assumptions are falsifiable, our result presents a barrier to basing qIO on standard cryptographic assumptions. The reductions we rule out are restricted: the reduction must query the adversary classically, non-adaptively, at the same security parameter, and only on honestly generated ciphertexts. Moreover, our impossibility applies only to WE with classical ciphertexts, and therefore does not rule out qIO with obfuscators whose output is a quantum state. Ruling out more general reductions, as well as more general forms of WE and qIO, remains open. Our impossibility relies on the existence of a QMA-QCIP[2] gap problem, an average-case assumption postulating a QMA language that cannot be verified with two messages of classical communication.

A macroscopic manifestation of superfluidity is that objects moving through liquid helium experience negligible friction below the Landau critical velocity. How this frictionless motion breaks down at the nanoscale remains an open question. Molecules embedded in helium nanodroplets represent a well-controlled system for studying this breakdown, yet none has reached the regime of strong dissipative coupling, when energy transfer from the molecule to the superfluid dominates the observed dynamics. Molecular rotation, induced by short laser pulses, offer a suitable probe to reach rotational energies in the range of the roton gap, where superfluid helium supports a large number of elementary excitations. However, the solvation shell around a rotating molecule caps the energy reachable by a free rotor after impulsive excitation well below the roton excitation energy. Here we show that continuous driving with an ultraslow optical centrifuge overcomes this limitation: the strong field dresses the molecule into pendular states whose energies fall within the spectrum of the collective excitations of the superfluid, placing the system in the strong-dissipation regime. The resulting rapid thermalization locks the molecule to the rotating field until the rotation-induced level splittings overtake the thermalization rate, beyond which the molecular alignment is progressively lost. Our approach offers a direct measurement of the molecule-bath coupling in a quantum fluid.

Qubit-efficient quantum relaxations compress classical decision variables into expectation values on substantially fewer qubits. We ask what resource tradeoffs this compression entails for quantum optimization. For the complete quadratic-Majorana encoding of $m=\Theta(n^2)$ binary variables on~$n$ qubits, we define the universal margin as the smallest correlator magnitude that can be guaranteed with prescribed signs for every target sign (bit) assignment. We show that it is exactly $\Delta_{\rm Maj}(n)=\tan\!\left(\frac{\pi}{4n}\right)=\Theta(1/n)$, whereas uniformly random sign assignments retain $\Theta(1/\sqrt n)$ target-specific margins. Arbitrary density operators and mixed fermionic Gaussian states generate the same quadratic-Majorana covariance body, so non-Gaussian state resources cannot enlarge this two-point relaxation. More generally, standard quantum random access code bounds provide general information-theoretic baselines. For any fixed family of $m$ designated binary observables on~$n$ qubits, the universal margin is at most $\sqrt{(2\ln2\,n/m)}$, and random access decoding from $N$ copies with constant success probability above $1/2$ requires $nN=\Omega(m)$. For a fixed Pauli correlation encoding required to work uniformly over all targets, maintaining a fixed nonzero decoded magnitude under smooth sign decoding therefore requires a rescaling parameter that grows as the available margin shrinks. Thus, while providing substantial qubit savings, compression can shift cost into restricted expectation value geometry, smaller expectation value magnitudes, or more demanding information recovery rather than eliminate it.

We present a generalized and efficient quantum circuit framework for implementing discrete-time quantum walks (DTQWs) on Cayley graphs of arbitrary dimension. Building on the Boundary QFT scheme of Razzoli et al., we introduce a systematic multi-stage decomposition of the shift operator for 1D Cayley graphs across three classes of generating sets: inverse-closed without involutions, inverse-closed with an involution, and non-inverse-closed. The decomposition hierarchically factorizes the QFT-diagonalized shift operator into structured block components, progressively reducing the control degree of the required rotation gates and replacing high-degree multi-qubit controlled operations with collections of lower-degree equivalents. We extend this construction to $d$-dimensional torus graphs and provide explicit circuit implementations for an 8-Cayley graph and a $\mathbb{Z}_{16} \times \mathbb{Z}_8$ torus graph as concrete illustrations. Gate complexity analysis using the linear CNOT scaling of Rosa et al. demonstrates that the decomposed implementation achieves a substantial reduction in upper-bound CNOT cost relative to the naive implementation within the regime $k \leq 64$ for inverse-closed graphs and $k \leq 16$ for non-inverse-closed graphs, where $k$ denotes the degree of the generating set. Benchmarking further reveals that this efficiency gain is largely insensitive to the system size $N$, identifying $k$ as the dominant resource parameter for the shift operator. These results provide a scalable and hardware-conscious pathway toward practical DTQW implementations on near-term quantum devices.

Lithium ferrite (LiFe) is a promising material for cavity magnonics because its large spin density enables strong coupling between magnons and microwave photons. Its potential for cavity magnomechanics, however, has remained unexplored. Here, we observe magnomechanical interactions in a single-crystal LiFe sphere using coherent microwave feedback to suppress dissipation of the cavity–magnon polariton. In the absence of sufficient feedback, the narrow mechanical response is difficult to resolve against the much broader polariton background. Increasing the feedback gain reduces the polariton linewidth and correspondingly increases the magnomechanical cooperativity, revealing a clear magnomechanically induced transparency feature. In the measurements presented here, the effective upper-polariton linewidth is reduced from $3.53~\mathrm{MHz}$ without feedback to $5.8~\mathrm{kHz}$ in the presence of feedback, while the measured cooperativity increases from $C=1.9\times10^{-3}$ to $C=0.15$. These measurements provide, to our knowledge, the first observation of cavity magnomechanics in LiFe and demonstrate coherent feedback as a practical route for accessing weak interactions that would otherwise be obscured by dissipation.

Decoherence imposes severe limits on quantum circuit depth, motivating methods to reduce circuit depth. Operator backpropagation has recently been proposed as a way to lower circuit depth by classically backpropagating observables through subcircuits. While it lowers the circuit depth, it also significantly increases the number of backpropagated observables that must be measured. This calls for an efficient measurement protocol tailored to these backpropagated observables. Moreover, errors arise both during the backpropagation procedure and during measurement, and they accumulate in the final computation. No prior work has examined how to integrate operator backpropagation with advanced measurement protocols, and how to jointly optimize the combined process. In this paper, we introduce a comprehensive framework to determine the appropriate measurement protocol to achieve a desired level of accuracy with the fewest number of measurements based on the number of qubit-wise commuting (QWC) groups formed from operator backpropagation. We analyze and categorize the primary sources of error that arise through our workflow, including error incurred from the backpropagation algorithm, truncation error, and shot noise variation. We also examine truncation strategies to reduce the number of backpropagated observables by characterizing the structure of the set of backpropagated observables.

As quantum computers advance toward the regime of MegaQuOp machines executing millions of gates, a decoding system capable of real-time error correction in such a device will be crucial. Recent efforts have been focused on decoding an error-corrected memory or a small number of logical operations. Here we demonstrate an end-to-end real-time decoding stack for a universal fault-tolerant trapped-ion quantum computer architecture capable of decoding real workloads with millions of logical gates over hundreds of logical qubits. The complete pipeline, including on the fly detector error model generation, decoding of all logical qubits, logical operations, and magic-state factories, runs on a single CPU. We benchmark the decoder on practically relevant quantum applications spanning up to 408 logical qubits, and up to one million $T$ gates. Assuming a trapped-ion architecture with 1 to 5 ms cycle time, the decoding delay stretches the computation by less than $0.3\%$ at $p_{\mathrm{CNOT}}=10^{-4}$ and less than $12\%$ at $p_{\mathrm{CNOT}}=5\times 10^{-4}$ for all workloads studied. These results demonstrate real-time decoding at MegaQuOp scale on a single conventional CPU.

Quantum simulation of strongly correlated fermionic systems is among the most promising near- term applications of quantum computing, but its practical efficiency depends critically on the choice of fermion-to-qubit mapping and on the connectivity of the underlying hardware. In this work we address this problem in the context of the two-dimensional Hubbard model, simulated on IBM superconducting quantum processors with heavy-hexagon connectivity. We numerically benchmark the Jordan-Wigner, Bravyi-Kitaev, and Bonsai transformations, evaluating their Pauli weight and SWAP overhead across seven heavy-hexagon chips of increasing size. We show that, while the Bravyi-Kitaev mapping initially exhibits a lower Pauli weight, this advantage is eliminated once routing costs are taken into account, confirming the Bonsai mapping as the most hardware-efficient baseline transformation for this architecture. We then use the Bonsai mapping to construct the qubit Hamiltonian of the 2D spinful Fermi-Hubbard model, introducing a simulated annealing algorithm that optimizes the assignment of Majorana strings to lattice sites, reducing the cost function by nearly 50% percent. Finally, we simulate on quantum hardware the time evolution of fermionic states up to 6x6 lattices, confirming the viability of the Bonsai encoding for hardware-aware large-scale two-dimensional simulations.

Programmable quantum devices nominally act on a Hilbert space whose dimension grows exponentially with the number of constituents, but the presence of noise makes it unlikely that they remain coherent across all of this immense Hilbert space. Then, what is the effective coherent quantum dimension that should be associated with such imperfect devices? To answer this question we here introduce an operational basis-independent framework which imposes a dimension bottleneck on the programmable transformations. Concretely we ask how strongly the quantum information they process can be compressed. Formalizing this idea we identify three inequivalent notions, termed $d$-compressibility, $d$-simulability and $d$-embeddability, which differ in the causal structure used to impose the bottleneck and form a strict hierarchy. The framework unifies several existing notions: joint measurability and simulability of quantum measurements, and the absolute dimensionality of state ensembles, are recovered as special cases. We illustrate the hierarchy with noisy qubit measurements in complementary bases, and we determine the white-noise thresholds at which the set of all noisy unitary channels in dimension $n$, a noisy universal quantum processor, becomes $d$-compressible, $d$-simulable and $d$-embeddable. The thresholds confirm the expectation – maintaining coherence across the full Hilbert space becomes increasingly demanding as the nominal dimension $n$ increases.

We develop a geometric framework for constructing and organizing Kochen–Specker configurations in real four-dimensional space. The construction uses finite grids on pairs of smooth quadrics related by Euclidean polarity. Their incidence geometry directly produces orthogonal measurement contexts and parity proofs of quantum contextuality, yielding infinite families of configurations and a geometric interpretation and extension of a previously known cyclic construction. For a distinguished subfamily, the same geometry admits a canonical completion determined by secant lines. The first two instances of this completion recover the exceptional root configurations of types $F_4$ and $H_4$, while the smallest case also recovers the Cabello configuration and its embedding in the Peres configuration. Thus several prominent four-dimensional contextual configurations, previously obtained from different constructions, arise from a single projective-geometric mechanism.

Geometry of quantum states is a fundamental research area with applications ranging from topological materials in condensed matter to variational algorithms in quantum information. Due to their relative simplicity, pure states are often studied, while mixed states are generally needed, for instance to have nonzero temperatures or other statistical mixtures. Mixed-state geometry, however, is much more challenging and has so far lacked any overall structure that relates distance and curvature, like the Kähler structure does for pure states. This work introduces that missing structure. We show that it has the physical meaning of fluctuation-dissipation—by identifying distance with fluctuations and curvature with linear response—and becomes the known structure for pure states, but is non-Kähler otherwise. This paints a simple picture that unifies fluctuation-dissipation and geometry of quantum states. It also applies on parameter spaces, as encountered in condensed matter or estimation theory. Our picture implies that the geometry contains all linear responses and fluctuations, proves the usual fluctuation-dissipation relation, explains that quantum geometry is present in any sum rule, and allows one to geometrically characterize generic transport behaviors.

We experimentally investigate how symmetry-protected topological order in a one-dimensional cluster state is transformed by measurement and decoherence in a five-qubit superconducting array. We first characterize the state's nonlocal string order and show that controlled dephasing selectively suppresses one symmetry sector while leaving the other robust, consistent with average symmetry-protected topological order. We then measure one sublattice in a tunable basis and show that the remaining qubits are driven between a long-range-entangled GHZ state and a paramagnetic state. When the measurement record is discarded, the conventional long-range correlator vanishes while a nonlinear fidelity correlator remains finite, providing a finite-size signature of strong-to-weak spontaneous symmetry breaking. These experiments demonstrate how conditioning, averaging, and decoherence reveal distinct manifestations of order encoded in the same underlying cluster state, and establish a superconducting-circuit setting for probing mixed-state symmetry and topology.

Correlations allowed by quantum mechanics can defy any classical explanation, with Bell nonlocality standing as their most profound and operationally powerful manifestation. While nonlocality has been demonstrated across a wide range of platforms, in many-body systems it has remained limited to ensembles of qubits, leaving the observation of higher-dimensional multipartite Bell correlations an open challenge. Here we report the observation of qutrit Bell correlations in a spin-1 $^{87}$Rb Bose-Einstein condensate via the violation of a Bell witness based on collective spin observables only. Exploiting spin-exchange collisions in an ensemble of $N \simeq 3.1 \times 10^{4}$ atoms, we generate spin-nematic squeezing of $-11.8(7)$ dB and observe a violation that surpasses the minimum bound achievable by a collection of $N$ qubits, providing direct evidence of genuine multipartite qutrit Bell correlations. Our results establish spinor Bose-Einstein condensates as a viable platform for investigating high-dimensional Bell correlations in the many-body regime, and demonstrate that coarse-grained collective measurements suffice to certify the dimensionality of quantum correlations at macroscopic scales.

Electromagnetic fluctuations can transfer not only energy but also angular momentum, leading to forces, torques, heat currents, and friction in out-of-equilibrium setups. In enclosing configurations, we show that if at least one of two objects is rotationally symmetric, the torque is bounded by heat transfer, since both arise from photon transfers with angular momentum $\hbar n$ and energy $\hbar\omega$. With only one object assumed to be rotationally symmetric, it may be possible to obtain a nonzero torque with reciprocal media, but nonreciprocal media are required to break the symmetry between $n$ and $-n$ and produce a nonzero torque if both objects are rotationally symmetric. We then specialize to concentric cylinders with a nonreciprocal dielectric response and use Rytov fluctuational electrodynamics to express heat transfer and torque in terms of an angular-momentum-resolved flux density, $\Phi_n(\omega)$. We also analyze the conditions for stable levitation of the inner cylinder using the proximity force approximation, in the process obtaining a new analytic formula for the normal Casimir force between dilute plates at different temperatures. Finally, to find the extracted work in a contactless engine setup, we compute the fluctuation-induced friction for a slowly rotating inner cylinder, and we find a bound between torque, friction, and heat transfer. Due to this bound, the efficiency of the heat engine remains bounded by the Carnot limit.

The topology of the electronic structure for an avoided crossing and a conical intersection (CI) is different and is characterized by the presence of the geometric phase in the electronic wavefunction in the latter. Using the linear Jahn-Teller model, we show that an avoided crossing can be created from the conical intersection while preserving the nontrivial topology of the latter by adding a Pauli $\sigma_y$ term to the Hamiltonian. Analogously to solid state systems, we derive a half-integer topological invariant as the integral of the Berry curvature over the CI nuclear branching space. We investigate the influence of electronic topology on chemical dynamics by conducting fewest-switches surface hopping simulations and find distinct hopping rates on identical eigensurfaces but with different topologies. Our work extends the influence of topology on molecular excited state dynamics beyond the Berry phase that can be practically realized through electron-nuclear and spin-orbit coupling.

In a recent breakthrough, Yamakawa and Zhandry (J. ACM 2024) constructed a proof of quantumness in the quantum random oracle model (QROM) in which the quantum prover samples a codeword preimage of a publicly computable function H. They conjectured that given any H, a successful prover must sample their preimage from a high-entropy distribution over possible answers. If true, this would give a certifiable randomness protocol in the quantum random oracle model. As partial evidence for their conjecture, Yamakawa and Zhandry proved the security of their certifiable randomness protocol assuming the Aaronson-Ambainis conjecture. We prove the security of the certifiable randomness protocol of Yamakawa-Zhandry unconditionally, without relying on the unproven Aaronson-Ambainis conjecture, against low query-depth quantum adversaries: specifically, adversaries that make up to o(\log \lambda) adaptive quantum queries to the random oracle.

We introduce masked auto-correlation, a new primitive for the cryptanalysis of symmetric-key primitives, together with a quantum attack pipeline built on it. For a permutation $f$, output masks $\alpha,\beta$, and an input difference $w$, masked auto-correlation (MAC) measures the correlation between the masked outputs $\alpha\cdot f(x)$ and $\beta\cdot f(x\oplus w)$. The associated masked differential-linear (MDL) approximations strictly generalize several classical techniques; ordinary linear cryptanalysis, differential-linear cryptanalysis, and the differential-linear connectivity table all arise as special cases. Our central object of study is the problem of finding mask pairs with large masked cross-correlation – those that yield powerful distinguishers – which we call MAC Fishing. We give a constant-query quantum algorithm that samples such pairs according to their squared correlation, and we prove an exponential classical lower bound of $\Omega(N/\log N)$ queries, by adapting the hardness of Fourier Fishing. To our knowledge this is the first result pairing a quantum upper bound with a classical lower bound for the core task of identifying high-correlation approximations, making quantum algorithms an absolute necessity. Building on this, we analyse the distribution of masked auto-correlation for random permutations, and then construct capacity-based distinguishers and key-recovery attacks, both classically and with a quadratic quantum speed-up using amplitude estimation. We validate our claims with experiments on reduced-round mini-AES.

Measurement-based quantum computing (MBQC) is a powerful model for quantum computation, but dedicated software tools that bridge its theoretical foundations with practical research workflows remain limited. We present Graphix, a software framework for MBQC written in Python that provides a unified environment for developing, integrating, and exploring measurement-based protocols and algorithms. Graphix establishes a modular, extensible, and user-friendly architecture for the compilation and simulation of quantum computations in the MBQC model with abstractions closely aligned with the theoretical formulations of MBQC. Through examples drawn from recent research on MBQC, we demonstrate Graphix's ability to reproduce and extend previous results. Graphix thus provides a software infrastructure for MBQC, supporting education and research while enabling collaborative development and accelerating the transition toward practical implementations.

We ask how passive conducting geometry determines the spatial structure of electric-field noise seen by trapped ions. From a boundary-potential covariance and the Dirichlet Green function we construct the $N$-ion electric-field cross-spectral matrix and its blockwise motional Kossakowski generator. In a parallel slab, billiard unfolding turns the electrostatic response into a return-depth measure and yields an exact return-pair functional for arbitrary stationary surface spectra. For every finite equal-height ion array, the passive cover increases the normal-field covariance matrix in the positive-semidefinite ordering and decreases the tangential-field covariance matrix in the same ordering: all collective normal-field coordinates acquire more absolute noise, while all collective tangential coordinates acquire less. At $h=2d$ the local-noise single-ion ratios are exactly $\zeta(3)$ and $\eta(3)$. Diagonalizing the equal-frequency covariance identifies collective environmental noise eigenchannels and a geometry-dependent noise rank; within a degenerate frequency block these become the Lindblad jump channels. In a ten-ion example, closing the cover to $h=2d$ lowers the participation rank from 5.61 to 5.11 while increasing the leading channel's share from 23.7% to 28.6%; a primitive Mølmer-Sørensen calculation shows how the projected covariance sets the weak-heating gate exposure. Beyond parallel walls, specular paths emerge as large-$q_z$ saddles of the screened boundary operator. Across 16 curved covers, the fitted electrostatic decay exponent correlates at 0.9991 with the independently computed shortest specular excess length, while separate tests resolve focusing and competing saddles.

Fidelity susceptibility is a useful probe of quantum phase transitions and quantum metrology, but its direct evaluation on a quantum device is challenging. By integrating Krylov-subspace methods with a resolvent-based reformulation, we present a method for certifying fidelity susceptibility using randomized single-copy measurements across repeated ground-state preparations. The resulting approximations form monotone lower bounds to the exact fidelity susceptibility and converge geometrically. We also present applications to metrology and linear static susceptibilities.

The state frame potential is a standard diagnostic of how closely a quantum state ensemble approximates Haar randomness. In this work, we study the problem of estimating the state frame potential of order $t$ to within additive error $\varepsilon$ under three progressively weaker access models: (i) query access to a multi-state-preparation oracle, (ii) general sample access, and (iii) single-copy sample access. In the query model, we establish a near-optimal query complexity of $\widetilde{\Theta}(\sqrt{t}/\varepsilon)$, yielding a quadratic improvement in the dependence on $t$ over the previous best result of Nakata, Takeuchi, Kliesch, and Darmawan (PRX Quantum 2025). In the general sample model, we establish the optimal sample complexity $\Theta(t/\varepsilon^2)$. In the single-copy sample model, we present a store-and-estimate approach whose sample complexity depends on the Rényi entropy of the ensemble weights. As an application, we use the single-copy algorithm to assess the randomness of projected state ensembles, where the entropy term becomes the observational Rényi entropy associated with measuring one subsystem.

Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies, as existing Lindblad estimation methods are typically limited to small system sizes due to the computational complexity of repeatedly solving the Lindblad equation during optimization. Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a stochastic simulation method, the Tensor Jump Method (TJM), with gradient-free optimization of a least-squares cost-function defined on time series of local-observable expectation values. We demonstrate the approach on two noise models in the Ising model: a site-resolved (local) model, in which independent dissipation rates are learned for each site up to $N_{\mathrm{site}}=16$, and a spatially homogeneous (global) model with only seven parameters, scaled to $N_{\mathrm{site}}=160$ sites.We complement these numerical results with a series of exact, provable guarantees: the Frobenius variance of the TJM density-matrix estimator is shown to equal $(1-\mathrm{Tr}[\rho^2])/N_{\mathrm{traj}}$, an exact purity-based characterization of the stochastic estimation error; the corresponding purity evolution is proven to be monotonically non-increasing for Hermitian jump operators; and, under a finite covariance distance assumption, the standard deviation of the cost-function is shown to decrease with system size, so that fewer trajectories are needed to reach a fixed target accuracy as the system grows. Together, this combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices and for guiding future work on error mitigation and quantum error correction.

Absolute nuclear magnetic shielding constants and relative chemical shifts are second-derivative response properties that underpin the interpretation of Nuclear Magnetic Resonance (NMR) spectra and provide critical insights into the structural and electronic environments of diverse chemical systems. However, their accurate computation is often constrained by the need for method-specific, analytical response implementation, and therefore is particularly challenging for non-variational, correlated wavefunction methods where analytical second derivatives are frequently unavailable. Here we present a scalable framework that computes NMR shielding tensors through finite magnetic field differentiation of complex-valued, gauge-including atomic-orbital (GIAO) based self-consistent field (SCF) calculations. By combining hybrid MPI and OpenMP parallelization and resolution-of-identity (RI) approximation-based Coulomb (J) and Exchange (K) implementation and mixed numerical/analytical derivatives computational scheme, we achieve very good efficiency for hybrid density functional theory (DFT) NMR shielding, relative to existing state-of-the-art analytic implementations across realistic chemical systems of various sizes. Forward differentiation with optimal step sizes derived from rigorous error analysis retains favorable numerical errors much smaller than experimental uncertainty or intrinsic DFT errors. The results demonstrate that RI-accelerated finite magnetic field calculations can obtain DFT-level NMR shielding constants very precisely, providing a scalable foundation for extensions to more advanced quantum chemistry methods in future work.

The minimal operator systems over ${\rm Mat}_k(\mathbb C)_+$, $k\geqslant2$, and the Lorentz cones $\mathcal L_m$, $m\geqslant4$, are not subhomogeneous. For the $2\times2$ cone we construct extreme positive maps of arbitrarily large output dimension. Positive retracts give the remaining cases. Equivalently, for fixed $k\geqslant2$ and $d$, there exist $s>d$ and an entangled positive operator on $\mathbb C^k\otimes\mathbb C^s$ such that every compression of the second factor to $\mathbb C^d$ is separable.

Similarity in many decision systems is governed not by distance alone but by interactions among variables. In fraud and anomaly detection, small local perturbations can cross interaction-sensitive decision boundaries while leaving ambient distance almost unchanged. Motivated by this setting, we introduce a thin-slab interaction model and an interaction-driven quantum kernel constructed from entangled Pauli-string feature maps. The feature map explicitly encodes sparse high-order block interactions. We show that the resulting fidelity kernel is positive semidefinite, admits an exact block-factorized formulation, and induces a geometry sensitive to changes in interaction regime. Across balanced and imbalanced synthetic experiments spanning third-, fourth-, sixth-, and eighth-order interactions, the proposed kernel consistently outperforms linear, radial basis function, Laplacian, and polynomial kernels, as well as an engineered-interaction linear baseline supplied with the planted block products. On real fraud-detection benchmarks, it achieves the highest mean accuracy and F1 on Credit Card Fraud Detection and ranks second on IEEE-CIS Fraud Detection. Executed on a 156-qubit IBM Quantum processor in a fourth-order setting, the hardware-estimated kernel matches the noise-free simulator within seed-to-seed variability and retains its advantage over the baselines. These findings show that quantum-kernel performance depends on alignment between feature-map geometry and the underlying predictive structure, rather than on Hilbert-space dimension alone. Because the prescribed block-factorized kernel can also be evaluated exactly on a classical computer, the results establish predictive and representational value rather than computational quantum speedup.

Topological states of matter, such as quantum Hall states, are characterized by the absence of local order parameters. In the continuum, their topological order has been reinterpreted as the condensation of nonlocal composite bosons, but this condensation and the resulting long-range correlations have so far eluded direct confirmation beyond the simplest trial states. Here, we apply tensor-network methods to lattice Hamiltonians hosting quantum Hall states, revealing this exotic order directly in interacting ground states and demonstrating both the long-range correlations and the condensation of composite bosons. These correlations define a nonlocal order parameter that identifies phase transitions between trivial and topological phases, for both bosonic and fermionic models. The corresponding operators are accessible through site-resolved, local measurements on an extensive number of particles, making them directly probable in quantum simulators. Our work opens new avenues for microscopic studies of topological quantum matter beyond the reach of traditional solid-state approaches.

We study the dynamics of the cumulants of the entanglement Hamiltonian in interacting integrable models following global quantum quenches. Building on recent results based on space-time duality, we show that these cumulants are exactly given by the cumulants of currents of suitable conserved charges evaluated in the macrostate selected by the initial state. This establishes a direct connection between entanglement dynamics and transport, providing a transport counterpart to the quasiparticle picture that successfully describes the evolution of the von Neumann entropy. In the free-fermion and conformal limits, our results reduce to the difference between the current cumulants carried by right- and left-moving excitations, recovering previously known expressions. In interacting integrable models, where a decomposition into independent right and left movers is no longer meaningful at the operator level, a similar structure survives at the level of the entanglement spectrum, yielding a unified description of entanglement Hamiltonian fluctuations across free, conformal, and interacting integrable systems.

We study a returning quantum change interval in which a source emits $\lvert\psi\rangle$ over one interval and $\lvert0\rangle$ elsewhere. A collective measurement on the full sequence identifies both endpoints with minimum error. We analyze the Gram matrix using Toeplitz comparison and Følner transfer, together with an exact decomposition by excitation number and interval hull. The resulting bounds establish asymptotic Bayes optimality of the square root measurement (SRM). Let $c=\lvert\langle0\vert\psi\rangle\rvert$ and $p_1(x)=4(1-x^2)K^2(x^2)/\pi^2$, where $K$ is the complete elliptic integral of the first kind. For a known interval length $i$, the SRM success probability and the Bayes optimum converge to the same Toeplitz symbol integral as the number $N$ of translations grows. For fixed $i$ and $0<c<1$, their gap is $P_{\mathrm{opt}}(G_{N,i})-P_{\mathrm{SRM}}(G_{N,i})=O_{i,c}(N^{-1/2})$. If $i$ and $N$ both diverge, their common limit is $p_1(c^2)$, with no constraint on their relative growth. For unknown length, the uniform prior over all $M_n=n(n+1)/2$ nonempty intervals gives the common limit $p_1(c)^2$ at fixed overlap. For a varying overlap $c_n$, set $\tau_n=n(1-c_n)(\log n)^2$. Uniformly for $0\leq\tau_n\leq T$, we obtain $M_nP_X=(1+2\sqrt{\tau_n}/\pi+\sqrt{2}\tau_n/\pi^2)^2+O_T(\log\log n/\log n)$, where $X\in\{\mathrm{tr},\mathrm{SRM},\mathrm{opt}\}$. More generally, if $c_n$ approaches one from below and $n p_1(c_n)\to\infty$, the same three quantities satisfy $P_X\sim p_1(c_n)^2$. These asymptotic laws also extend to joint detection and exact localization in the presence of a no change prior.

We prove the first quantum-classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $\alpha=e^{\beta\Delta}$, where $\Delta = \max E-\min E$, every classical algorithm querying the value, gradient, or any higher-order derivatives of the log-density requires $\Omega(\alpha)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrt{\alpha}\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{\Omega(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.