Papers

Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been thoroughly refined for equilibrium systems, consistently extending it to out-of-equilibrium systems is an active area of research. In this paper, we identify a mutual information-based measure of renormalizability that applies to quantum field theories both in and out of equilibrium. Specifically, we use mutual information to characterize correlations between infinitesimal shells in momentum space and show that the logarithmic derivative of mutual information with mode separation, at large mode separation, is a measure of renormalizability. We first consider Minkowski spacetime, where we introduce dynamics by performing an interaction quench, initializing the field in the free theory vacuum and then turning on the interaction. We show that the late-time mutual information relaxes to that for the interacting vacuum and the logarithmic derivative at large mode separation is negative for super-renormalizable theories, zero for renormalizable (marginal) theories, and positive for non-renormalizable theories. We then consider a conformally-coupled scalar field on the Poincaré patch of de Sitter spacetime, initializing the field in the Bunch-Davies vacuum in the asymptotic past. For different self-interactions and at any finite time, we find that the resulting mutual information has the same qualitative behavior as a function of mode separation, demonstrating that it can be used as a reliable indicator of renormalizability.

We study two-body scattering as an SU(N)-equivariant map acting on tensor-product representation spaces and analyze the entanglement generated by the $S$-matrix. This representation-theoretic perspective separates group structure from dynamics: the decomposition of $R\!\otimes\!R'$ fixes the invariant operator algebra and therefore the qualitative entangling power of the process. For particles in the fundamental representation, $\mathrm{End}_{\mathrm{SU}(N)}(N\!\otimes\!N)=\mathrm{Span}\{\mathbb{I},\mathbb{S}\}$, so only the identity and swap directions preserve separability, whereas generic combinations generate entanglement. Adjoint-adjoint scattering involves a larger invariant algebra involving $d$-tensors and is intrinsically entangling. In Yang-Mills theory one can use color-kinematics duality to show that the color kernel lies on a fixed ray of this operator space, yielding a universal maximum of the outgoing entanglement for scattering at right angles, $E_\star^{(2)}=\tfrac{3}{4}$ for $SU(2)$ and $E_\star^{(3)}\simeq0.91$, independent of kinematics. Dimension-six operators preserve this universality, while dimension-eight deformations populate new color sectors and shift $E_\star^{(N)}$, suggesting that entanglement in color space functions as a tomographic probe of effective operators. In helicity space, requiring maximally entangled inputs to scatter into maximally entangled outputs uniquely selects the Yang-Mills quartic coupling and enforces the color Jacobi identity, restating the on-shell Ward constraints as conditions on entanglement preservation. Our results suggest that the information-theoretic viewpoint unifies algebraic, geometric, and dynamical aspects of scattering.

We analyze a simple and efficient experimental protocol to cool the Sachdev-Ye-Kitaev (SYK) model to low temperatures. The protocol utilizes local couplings between two copies of an SYK model to create a gapped adiabatic path, between a high temperature product state and a low temperature thermofield double state. By smoothly varying the coupling strength between these two limits, one efficiently cools the SYK model. We support these predictions-and demonstrate fast cooling to the low-temperature gravitational regime-via exact numerical solutions to the large-N equations of motion that govern the ground state and dynamical properties of the coupled system. Finally, we present a theoretical framework based upon eigenstate thermalization that provides a microscopic explanation for the efficacy of the cooling protocol; intriguingly, this suggests that the protocol may be applicable for cooling strongly-interacting quantum Hamiltonians more broadly.

I analyze the decoherence of a $\pi$-junction qubit encoded by two co-located Majorana modes. Although not topologically protected, the qubit leverages distinct spatial profiles to couple to two independent environmental baths, realizing the phenomenon of quantum frustration. This mechanism is tested against the threat of quasiparticle poisoning (QP). I show that frustration is effective against Ohmic noise ($s=1$) and has some protection for $0.76<s<1$ sub-Ohmic noise. However, the experimentally prevalent $1/f$ noise ($s\to0$) falls deep within the model's localized phase, where frustration is insufficient. This causes spontaneous symmetry breaking and catastrophic decoherence. The qubit's viability depends on what the effective environment is that these local Majorana wave functions experience.

A recently proposed Boltzmann local equilibrium Wigner function for massive spin-1/2 particles is generalized to the case of Fermi-Dirac statistics. The resulting formula ensures the correct normalization of the mean polarization vector and reproduces the generalized thermodynamic relations with spin that were obtained in earlier studies. Moreover, we show that the macroscopic currents constructed from the Fermi-Dirac Wigner function can be obtained as derivatives of a suitably defined generating function with respect to the Lagrange multipliers (temperature, hydrodynamic flow, and chemical potentials). The identified generating function also indicates that the underlying framework can be classified as a divergence-type theory.

We construct a classical oracle proving that, in a relativized setting, the set of languages decidable by an efficient quantum verifier with a quantum witness (QMA) is strictly bigger than those decidable with access only to a classical witness (QCMA). The separating classical oracle we construct is for a decision problem we coin spectral Forrelation – the oracle describes two subsets of the boolean hypercube, and the computational task is to decide if there exists a quantum state whose standard basis measurement distribution is well supported on one subset while its Fourier basis measurement distribution is well supported on the other subset. This is equivalent to estimating the spectral norm of a "Forrelation" matrix between two sets that are accessible through membership queries. Our lower bound derives from a simple observation that a query algorithm with a classical witness can be run multiple times to generate many samples from a distribution, while a quantum witness is a "use once" object. This observation allows us to reduce proving a QCMA lower bound to proving a sampling hardness result which does not simultaneously prove a QMA lower bound. To prove said sampling hardness result for QCMA, we observe that quantum access to the oracle can be compressed by expressing the problem in terms of bosons – a novel "second quantization" perspective on compressed oracle techniques, which may be of independent interest. Using this compressed perspective on the sampling problem, we prove the sampling hardness result, completing the proof.

A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpreted as higher-order superintegrable perturbations of the 2D spherical (Higgs), hyperbolic, and Euclidean harmonic oscillators. As a new result, the complete polynomial Higgs-type symmetry algebra of the generalized classical system is presented. For the generalized quantum system, the symmetry algebra and the spectra are provided for a representative case.

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications 16, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.

Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations enable quantum technologies, including quantum computing or communication, while revealing the limits of our classical worldview by violating local realism. Given its importance in modern quantum science, we present this tutorial addressing the questions: What is entanglement, how does it differ from classical correlations, and how can it be experimentally verified? Using celebrated examples, such as Schrödinger's cat, we highlight the distinction between classical and quantum correlations and illustrate the definition of entangled and separable states. We review entanglement criteria by discussing Heisenberg-type uncertainty relations for continuous variables and the CHSH inequality for discrete systems. Focusing on concepts of quantum correlations and operational entanglement witnesses, we provide accessible tools and illustrative examples aimed at demystifying entanglement for a broad readership.

Quantum state tomography seeks to reconstruct an unknown state from measurement statistics. A finite measurement (POVM) is pure-state informationally complete (PSI-Complete) if the outcome probabilities determine any pure state up to a global phase. We study rank-one POVMs that are minimally sufficient for this task. We call such a POVM vital if it is PSI-Complete but every proper subcollection is not PSI-Complete. We prove sharp upper bounds on the size of vital rank-one POVMs in dimension \(n\): the size is at most \(\binom{n+1}{2}\) over \(\mathbb{R}\) and at most \(n^{2}\) over \(\mathbb{C}\), and we give constructions that attain these bounds. In the real case, we further exhibit a connection to block designs: whenever \(w \mid n(n-1)\), an \((n,w,w-1)\) design produces a vital rank-one POVM with \(n + n(n-1)/w\) outcomes. We provide explicit constructions for \(w=2,n-1\), and \(n\).

We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e.\ possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a primitive notion of splitting maps within dagger symmetric monoidal categories. Splitting maps give rise to subsystems that admit comparison via a preorder called comprehension, and support an adaptation of the usual categorical trace. We show that the comprehension preorder precisely captures the inclusion partial order between von Neumann algebras, and that the splitting map trace captures the natural notion of von Neumann algebra trace. As a consequence of the development of these diagrammatic tools, we prove that the known equivalence between semi-causality and semi-localisability for factor subsystems extends to all (including non-factor) subsystems.

Advancing quantum information processors and building fault-tolerant architectures rely on the ability to accurately characterize the noise sources and suppress their impact on quantum devices. In practice, noise often drifts over time, whereas conventional noise characterization and decoding methods typically assume stationarity or provide only a time-average behavior of the noise. This treatment can result in suboptimal decoding performance. In this work, we present a rigorous analytical framework to capture time-dependent Pauli noise, by exploiting the syndrome statistics of quantum error correction experiments. We propose a sliding-window estimation method which allows us to recover the frequency components of the noise, by using optimal window sizes that we derive analytically. We prove the noise-filtering behavior of sliding windows, linking window size to spectral cutoff frequencies, and provide an iterative algorithm that captures multiple drift frequencies. We further introduce an overlapping window algorithm that enables us to capture rapid multi-frequency noise drifts in a single-pass fashion. Simulations for both phenomenological and circuit-level noise models validate our framework, demonstrating robust tracking of multi-frequency drift. The logical error rate obtained from our estimated models consistently align with the ground-truth logical error rate, and we find suppression of logical errors compared to static error models. Our window-based estimation methods and adaptive decoding offer new insights into noise spectroscopy and decoder optimization under drift using only syndrome data.

Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.

As established in the seminal work by Berry et al.[1], expanding the time evolution operator using truncated Taylor series (up to some order $K$) makes a good candidate for simulating Hamiltonian dynamics. Here, we adapt the method but present an alternative quantum circuit that maintains an equivalent asymptotic elementary gate cost but has an exponentially reduced number of ancilla qubits. This is realized by utilizing mid-circuit measurements (with early abort-and-restart of circuit execution), and transforming a series of multi-controlled$(H^k)$ to a series of singly-controlled$(H^{k'})$, where $H$ is a linear combination of unitaries and $k, k'$ are integers. The proposed circuit utilizes a total of $\lceil \log(K) \rceil + \lceil \log(L) \rceil +n$ qubits, where $L$ is the number of terms in the Hamiltonian and $n$ is the system qubit size. Our shorter width circuit with mid-measurements protocol is implemented and evaluated using the programming language Guppy[2,3].

Coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in fractional Chern insulators. Our approach employs impurities with individually addressable internal states that bind to the anyons, allowing their adiabatic motion and exchange under full spatial control. By combining Ramsey and spin-echo sequences using one and two impurities, the protocol gives independent access to the Aharonov-Bohm and exchange contributions to the total geometric phase, thereby providing an unambiguous probe of anyonic statistics. Our scheme can potentially be implemented in cold-atom quantum simulators as well as in van der Waals heterostructures. Complementary finite-size simulations in non-interacting Chern insulators quantify the system sizes required to faithfully extract geometric phases, highlighting the role of edge effects. Our results establish impurity-based interferometry as a feasible route toward direct anyon braiding experiments in quantum simulators and lay the groundwork for future explorations of non-Abelian braiding and topological quantum control.

Entanglement classification of pure multipartite quantum states is a challenging problem in quantum information theory that can be mathematically stated as orbit classification for some given group action on the ambient Hilbert space. The group action depends on the grained classification one expects, the finer-grained one being the classification up to local unitary transformation (LU). In this article, we show how a variational quantum circuit approach can be used to learn entanglement orbits, and we apply our findings to build a classifier for four-qubit states.

Quantum noise is known to strongly affect quantum computation, thus potentially limiting the performance of currently available quantum processing units. Even learning models based on variational quantum algorithms, which were designed to cope with the limitations of state-of-the art noisy hardware capabilities, are affected by noise-induced barren plateaus, arising when the noise level becomes too strong. However, the generalization performances of such quantum machine learning algorithms can also be positively influenced by a proper level of noise, despite its generally detrimental effects. Here, we propose a pre-training procedure to determine the quantum noise level leading to desirable optimisation landscape properties. We show that an optimized level of quantum noise induces an “equalization” of the directions in the Riemannian manifold, flattening(/enhancing) the initially steep(/shallow) ones by redistributing sensitivity across its principal eigen-directions. We analyse this noise-induced equalization through the lens of the Quantum Fisher Information Matrix, thus providing a recipe that allows to estimate the noise level inducing the strongest equalization. We finally benchmark these conclusions with extensive numerical simulations providing evidence of the beneficial noise effects in the neighborhood of the best equalization, often leading to improved generalization.

Quantum memory plays a critical role in quantum communication, sensing, and computation. However, studies on quantum memory under a unified benchmarking framework remain scarce. In this paper, we propose a weight-based quantifier as a benchmarking method to evaluate the performance advantage of quantum memory in nonlocal exclusion tasks. We establish a general lower bound for the weight-based measure of quantum memory. Moreover, this measure provides fundamental theoretical bounds for transforming a general channel into an ideal quantum memory. Finally, we present explicit calculations of the weight-based quantifier for various channels, including unitary channels, depolarizing channels, maximal replacement channels, stochastic damping channels, and erasure channels.

Multipartite entanglement is regarded as a crucial physical resource in quantum network communication. However, due to the intrinsic complexity of quantum many-body systems, identifying a multipartite entanglement measure that is both efficiently computable and capable of accurately characterizing entanglement remains a challenging problem. To address these issues, we propose a family of two-parameter multipartite entanglement measures for mixed states, termed unified-entropy concentratable entanglements. Many well-known multipartite entanglement measures are recovered as special cases of this family of measures, such as the entanglement of formation and the concentratable entanglements introduced in [Phys. Rev. Lett. 127, 140501 (2021)]. We demonstrate that the unified-entropy concentratable entanglements constitutes a well-defined entanglement monotones, and establish several desirable properties it satisfies, such as subadditivity and continuity. We further investigate the ordering relations of unified-entropy concentratable entanglements and discuss how these quantities can be efficiently estimated on near-term quantum devices. As an application, we demonstrate that the unified-entropy concentratable entanglements can effectively distinguish between multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and W states. The ordering relations of these entanglement measures are further validated using four-partite star quantum network states and four-qubit Dicke states. Moreover, we find that the unified-entropy concentratable entanglements exhibit greater sensitivity than the original concentratable entanglements in detecting certain four-partite star quantum network states.

In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate notions that interpolate between these two properties for linear maps on the space of operators on a Hilbert space, highlighting their natural connections to quantum dynamics and entanglement theory. Finally, we discuss possible constructions that allow one to derive quantum states and evolutions from classical counterparts, and vice versa.

We present an experimental demonstration of boson sampling enhanced by optical feedback lines, a novel approach that introduces temporal correlations among photons to amplify computational complexity. We utilize a 25-mode femtosecond laser-written interferometer with five output channels connected to five input channels to create correlations between consecutive photon arrival events. We have reconstructed the unitary matrix of the chip and have conducted Bayesian analysis to validate the sampler and confirm that the system exhibits behavior distinct from standard boson sampling. We also built a theoretical description of the system based on the transformation of annihilation operators and, using it, delivered the structure of the transmission matrix and the complexity of our boson sampler in terms of a conventional boson sampler. This work advances photonic quantum computing by demonstrating a resource-efficient method to increase sampling complexity, paving the way for scalable demonstration of quantum advantage with single photons.

We investigate a two-qubit SWAP thermal machine – a streamlined analogue of the four-stroke Otto cycle – whose working medium comprises inertially moving Unruh-DeWitt qubit detectors, each coupled to a thermal quantum field bath prepared at a different temperature. In the presence of relative motion between the working medium and the thermal baths, we derive thermodynamic uncertainty relations (TURs) that quantify the trade-off between performance, entropy production, and power fluctuations. Our analysis identifies regimes where relativistic motion leads to stronger violation of classical TURs, previously observed in static quantum setups. In addition, we establish generalized performance bounds for the thermal machine operating as either a heat engine or a refrigerator, and discuss how relativistic motion can enhance their performances beyond the standard Carnot limits defined by rest-frame temperatures.

Key-length extension (KLE) techniques provide a general approach to enhancing the security of block ciphers by using longer keys. There are mainly two classes of KLE techniques, cascade encryption and XOR-cascade encryption. This paper presents several quantum meet-in-the-middle (MITM) attacks against two specific KLE constructions. For the two-key triple encryption (2kTE), we propose two quantum MITM attacks under the Q2 model. The first attack, leveraging the quantum claw-finding (QCF) algorithm, achieves a time complexity of $O(2^{2\kappa/3})$ with $O(2^{2\kappa/3})$ quantum random access memory (QRAM). The second attack, based on Grover's algorithm, achieves a time complexity of $O(2^{\kappa/2})$ with $O(2^\kappa)$ QRAM. The latter complexity is nearly identical to Grover-based brute-force attack on the underlying block cipher, indicating that 2kTE does not enhance security under the Q2 model when sufficient QRAM resources are available. For the 3XOR-cascade encryption (3XCE), we propose a quantum MITM attack applicable to the Q1 model. This attack requires no QRAM and has a time complexity of $O(2^{(\kappa+n)/2})$ ($\kappa$ and $n$ are the key length and block length of the underlying block cipher, respectively.), achieving a quadratic speedup over classical MITM attack. Furthermore, we extend the quantum MITM attack to quantum sieve-in-the-middle (SITM) attack, which is applicable for more constructions. We present a general quantum SITM framework for the construction $ELE=E^2\circ L\circ E^1$ and provide specific attack schemes for three different forms of the middle layer $L$. The quantum SITM attack technique can be further applied to a broader range of quantum cryptanalysis scenarios.

The conversion of the modulation signal from the coupling light to the probe light and the conversion of the additional phase noise from the coupling light to the amplitude noise of the probe light in the electromagnetically induced transparency (EIT) spectrum of the cesium atomic ladder type three level system were investigated by detecting the probe light output noise spectrum. It was demonstrated that frequency stabilization via external modulation can effectively avoid the transfer of modulation noise. In the experiment, two frequency stabilization methods external modulation transfer spectroscopy and internal modulation transfer spectroscopy were employed to achieve the frequency stabilization of the coupling light. The probe light noise spectra at the frequency stabilized output terminal and the detection output terminal were measured under both methods.

We describe the generation of correlated photon pairs by means of spontaneous parametric down-conversion of an optical pump in the form of a finite energy Airy beam. The optical system function, which contributes to the propagation of the down-converted beam before being registered by the detectors, is computed. The spectral function is utilized to calculate the biphoton amplitude for finding the coincidence count of the inbound Airy photons in both far-field and near-field configurations. We report the reconstruction of the finite energy Airy beam in the spatial correlation of the down-converted beams in near field scenario. In far field, the coincidence counts resembles the probability density of the biphoton in momentum space, revealing a direct mapping of the anti-correlation of the biphoton momentum. By examining the spatial Schmidt modes, we also demonstrate that longer crystals have tighter real-space correlations, but higher-dimensional angular correlations, whereas shorter crystals have fewer modes in momentum space and broader multimode correlations in position space.

Simulating molecular systems on quantum computers requires efficient mappings from Fermionic operators to qubit operators. Traditional mappings such as Jordan-Wigner or Bravyi-Kitaev often produce high-weight Pauli terms, increasing circuit depth and measurement complexity. Although several local qubit mappings have been proposed to address this challenge, most are specialized for structured models like the Hubbard Hamiltonian and perform poorly for realistic chemical systems with dense two-body interactions. In this work, we utilize a suite of techniques to construct compact and noise-resilient Fermion-to-qubit mappings suitable for general molecular Hamiltonians. Building on the Generalized Superfast Encoding (GSE) and other similar works, we demonstrate that it outperforms prior encodings in both accuracy and hardware efficiency for molecular simulations. Our improvements include path optimization within the Hamiltonian's interaction graph to minimize operator weight, introduction of multi-edge graph structures for enhanced error detection without added circuit depth, and a stabilizer measurement framework that directly maps logical terms and stabilizers to the Z-basis using Clifford simulation. Applying these methods to simulations of $(H_2)_2$ and $(H_2)_3$ systems yields significantly improved absolute and correlation energy estimates under realistic hardware noise, with further accuracy gains achieved by increasing code distance. We also propose a [[2N, N, 2]] variant of GSE compatible with square-lattice and (quasi-)linear hardware topologies, demonstrating a twofold reduction in RMSE for orbital rotations on IBM Kingston hardware. These results establish GSE as a very attractive mapping for molecular quantum simulations.

This study systematically benchmarks classical optimization strategies for the Quantum Approximate Optimization Algorithm when applied to Generalized Mean-Variance Problems under near-term Noisy Intermediate-Scale Quantum conditions. We evaluate Dual Annealing, Constrained Optimization by Linear Approximation, and the Powell Method across noiseless, sampling noise, and two thermal noise models. Our Cost Function Landscape Analysis revealed that the Quantum Approximate Optimization Algorithm angle parameters $\gamma$ were largely inactive in the noiseless regime. This insight motivated a parameter-filtered optimization approach, in which we focused the search space exclusively on the active $\beta$ parameters. This filtering substantially improved parameter efficiency for fast optimizers like Constrained Optimization by Linear Approximation (reducing evaluations from 21 to 12 in the noiseless case) and enhanced robustness, demonstrating that leveraging structural insights is an effective architecture-aware noise mitigation strategy for Variational Quantum Algorithms.

Building on the infinite-component Chern–Simons theory of three-dimensional fracton phases by Ma et al. [Phys. Rev. B 105, 195124 (2022)] and the Toeplitz braiding of anyons by Li et al.~[Phys. Rev B 110, 205108 (2024)], we show that stacking $(3+1)$D $BF$ topological field theories, which serve as low-energy effective descriptions of a class of three-dimensional topological orders, along a fourth spatial direction gives rise to an exotic class of four-dimensional fracton phases. Their low-energy physics is governed by a new field-theoretic framework, namely \textit{infinite-component $BF$} (i$BF$) theories, characterized by asymmetric integer Toeplitz $K$ matrices. Under open boundary conditions along the stacking direction, i$BF$ theories with properly chosen $K$ matrices exhibit a striking phenomenon termed Toeplitz particle–loop braiding, where a particle and a loop placed on opposite three-dimensional boundaries acquire a strongly oscillating yet robustly nonvanishing braiding phase even at infinite separation. This nonlocal braiding admits a geometric interpretation: adiabatically transporting the particle induces a winding boundary trajectory on the opposite boundary that encircles the loop. We show that this robustness originates from boundary zero singular modes (ZSMs) of Toeplitz $K$ matrices revealed by singular value decomposition, rather than from boundary zero eigenmodes responsible for previously known Toeplitz braiding of anyons, and that the same ZSM mechanism also underlies directional amplification in the rapidly developing field of non-Hermitian physics. We analytically and numerically study representative i$BF$ theories with Hatano–Nelson–type and non-Hermitian Su–Schrieffer–Heeger–type $K$ matrices, establishing a universal correspondence between ZSMs and Toeplitz particle–loop braiding.

The generation of quantum entanglement is important for a wide range of quantum technology protocols. In nanophotonics, a promising platform for quantum technologies, entanglement generation via plasmon-mediated coupling in quantum dot qubits is often modeled within the dipole limit, where only dipolar plasmons of the mediating nanoparticle are considered, and the local response approximation, where nonlocal corrections are ignored. However, multipolar effects manifest strongly at coupling distances less than the nanoparticle size, while nonlocal optical effects stem from a size-induced dielectric response. We investigated these two important effects in the generation of two-qubit entanglement mediated by plasmonic coupling. A cavity quantum electrodynamic approach is employed, where the induced plasmonic effects lead to modified transition rates in the dynamics of the coupled quantum dot qubits. We find that multipolar modes and size-dependent damping lead to entanglement decay at small coupling distances and limit mediated entanglement with certain particle sizes. We discuss potential implications of multipolar modes in entanglement-based quantum sensing.

We study the transversality of the Toffoli gate in a hybrid-code system that employs two quantum error correction codes with special structure. We find that a system using a triorthogonal code with its paired code supports a fully transversal implementation of the Toffoli gate. Through circuit-level analysis, we prove the transversality of the Toffoli operation in this system. Based on this hybrid-code framework, we propose a Toffoli state distillation protocol that does not rely on pre-distilled $\mathbf{T}$-gate magic states. In our approach, the Toffoli state is directly distilled layer by layer within the hybrid-code system using only transversal operations. Numerical simulations demonstrate that our method uses approximately 50% fewer qubit resources than previously reported protocols.