Papers

In this paper, we resolve the quantum KKL conjecture of Montanaro and Osborne \cite{MO2010} for quantum Boolean functions on the $n$-qubit hypercube. More precisely, for every self-adjoint unitary $T$, we bound the largest $L_2$-influence from below by a constant multiple of $\mathrm{Var}(T)\log(n)/n$. The proof heavily depends on upper and lower commutator estimates on the Hilbert space.

In thermodynamics it is common to assume that the choice of ensemble (e.g., micro-canonical, canonical, or grand-canonical) should not affect the underlying physics in the thermodynamics limit. We show that this does not necessarily hold for critical exponents. Examining a simplified model of quantum error correction (single step encoding and decoding by a random unitary) and the behavior of both the fidelity and magic at the corresponding threshold, we find different exponents when using generic channels or supposedly equivalent quantum trajectories. Interestingly, the obtained exponents saturate a recently derived information theoretic bound by Feldman et al. (2026), which we extend from the grand-canonical to the canonical case, including intermediate ensembles which we define. Moreover, even the existence of the transition is shown to be ensemble-dependent.

For full-rank density matrices the state space is contractible, the Uhlmann bundle is topologically trivial, and the holonomy admits no quantized invariants; although the Uhlmann phase is genuinely geometric, this topological poverty has kept it from serving as a robust physical diagnostic of mixed-state matter. Mixed states of fixed rank below the Hilbert-space dimension, however, are ubiquitous: reduced states of constrained subsystems, states confined to invariant sectors, and states supported on decoherence-free subspaces can have a support smaller than the Hilbert space, a support that can vary with parameters. Their geometry is far richer: the support carries genuine curvature, non-Abelian holonomy, and Chern topology. We formulate Uhlmann's theory directly on the manifold of rank-$k$ density matrices: minimal purifications make the fixed-rank stratum the base of a principal $U(k)$-bundle whose Uhlmann connection is uniquely determined by a Sylvester equation, and in an eigenframe this connection takes a closed form reducing to the Berry, Wilczek–Zee, and faithful Uhlmann connections at $k=1$, at equal weights, and at $k=N$. The fixed-rank bundle inherits the topology of the Grassmannian, and non-factorizable higher Chern topology requires failure of the global eigenline splitting, which in the present spectral setting requires degeneracy, minimally realized by a rank-2 Yang monopole whose quantized second Chern number links the geometry to the four-dimensional quantum Hall response. Solvable models, from a genuinely non-Abelian holonomy to a dissipatively driven orbit whose Uhlmann holonomy is steered by the reservoir through an elliptic-integral spectral dressing, illustrate the content: the supporting subspace carries the topology, the spectral weights shape the transport, and Uhlmann holonomy provides a direct geometric probe of the resulting mixed-state structures.

We use bosonic tensor networks to connect the lattice sine-Gordon model in the Hamiltonian formulation quantitatively to its continuum theory. Matching the lattice vertex operator to its conformal normalization at the free-boson ultraviolet fixed point yields the exact relation between the bare lattice coupling and the renormalized continuum mass parameter. The soliton mass then approaches Zamolodchikov's exact continuum prediction throughout the studied parameter range, without adjustable parameters. Using uniform matrix product states and a quasiparticle ansatz, we also recover the relativistic soliton dispersion and the two lightest breather masses at the percent level. We simulate real-time collisions of Gaussian soliton-antisoliton wave packets near a reflectionless point and extract the Wigner spatial displacement. We compare this displacement with the exact continuum prediction obtained from the momentum derivative of the transmission phase, recovering its characteristic rapidity dependence. Our bosonic simulations provide a foundation for nonintegrable extensions, offer lessons for renormalization in other Hamiltonian lattice field theories, including gauge theories, and provide benchmarks for continuous-variable quantum simulations.

Quantum superresolution promises to resolve closely spaced sources beyond the diffraction limit, but existing approaches generally rely on idealized source properties or require simultaneous estimation of multiple coupled parameters of realistic sources. Here we introduce a parameter-decoupled measurement that determines the separation of realistic passive sources without estimating their unknown brightness imbalance, mutual coherence, or relative phase. A complete four-parameter quantum Fisher information analysis identifies the separation information that remains accessible in the presence of these nuisance parameters. We then construct a directly measurable log-probability invariant from projection channels whose conditional statistics depend only on the separation. Broad classes of channel pairs satisfy the resulting decoupling condition. For a Gaussian point-spread function, the lowest-order implementation asymptotically attains the four-parameter quantum limit per incident signal in the sub-Rayleigh regime. This approach converts a realistic multiparameter imaging problem into an operationally single-parameter measurement, providing a practical route toward quantum-enhanced resolution of passive spatial, temporal, and spectral signals.

Gradiometry provides a versatile alternative to passive environmental shielding in quasi-static magnetometry, effectively suppressing background noise through differential signal extraction. Nevertheless, traditional implementations rely on multi-sensor architectures restricted to spatial gradients, where subtracting signals from independent detectors involves imperfect suppression of common-mode noise and artifacts, limiting their sensitivity. To overcome these limitations, we introduce a quantum control sequence that enables intrinsic temporal and spatial vectorial gradiometry of magnetic fields using a single quantum sensor. Our method provides direct access to first and higher-order derivatives of the magnetic field and extended applicability via auxiliary nuclear spin memory. We showcase this protocol on an ensemble of nitrogen-vacancy (NV) centers in diamond and combine it with mechanical control to realize high-precision differential sensing. Through detailed numerical simulations, we demonstrate the performance of our scheme in two critical DC magnetometry applications: (i) vector magnetic anomaly detection and (ii) non-invasive gradiometry of neuronal action potentials.

We study macroscopic thermalization in the ferromagnetic Ising model with a weak generic (highly nonlocal and many-body) random quantum perturbation. We prove that a single typical perturbation makes every initial state $|\Phi(0)\rangle$ in a specified energy shell thermalize: a measurement of a large class of macroscopic observables in the time-evolved state $|\Phi(t)\rangle=e^{-i\widetilde H_Lt}|\Phi(0)\rangle$ yields their thermal equilibrium values, within a prescribed precision and with overwhelming probability, at sufficiently large, typical times $t$. The result covers the full finite-temperature range, including the ordered phase, where we use plus boundary conditions. With periodic boundary conditions in the ordered phase, every energy eigenstate in the shell is shown to be an almost balanced macroscopic Schrödinger-cat state. Moreover, every pure initial state becomes such a cat at sufficiently large, typical times, with each branch in the corresponding macroscopic thermal equilibrium. The proof combines the theory of Roos, Sugimoto, Teufel, Tumulka, and Vogel with rigorous Ising large-deviation estimates.

Floquet engineering and cavity quantum electrodynamics represent two complementary descriptions of light-matter interaction, yet their precise connection beyond the small-coupling regime remains subtle. Here, by representing the cavity field in a large-photon-number phase basis, we show that the time-dependent Schrödinger equation of a classically driven system emerges directly from the fully quantized problem, without replacing the field by a classical trajectory or assuming a mean-field decoupling. This establishes a one-to-one correspondence between quasienergies and photon-sector-shifted quantum energies, while providing a direct quantum interpretation of the Floquet mean energy and Anandan phase. Because gauge invariance is exactly preserved at the level of the quantum Hamiltonian, the quantum-to-classical correspondence remains valid beyond perturbative and small-coupling regimes. We further show that light–matter entanglement is encoded in matter–harmonic correlations of the corresponding Floquet mode, thus identifying a semiclassical limit in which Floquet physics emerges without requiring the quantum field itself to approach a coherent classical state.

Feedback-based quantum algorithms recently gained attention by demonstrating how quantum computers can be used to solve optimization problems without resorting to hybrid quantum-classical architectures. Recent progress made with Feedback-based Algorithm for Quantum Optimization (FALQON) variants significantly reduced the depth of the required circuits. In this work, we merge the time-rescaled and second-order FALQON variants into a unified framework. The results show an important improvement over past modifications, reducing circuit depth and allowing a more flexible choice of time-steps, while maintaining stable solutions. This FALQON variant makes it suitable for the NISQ era.

Transferable hexagonal boron nitride (hBN) hosting negatively charged boron-vacancy (VB$^{-}$) spin defects offers a versatile platform for integrated quantum magnetometry, yet quantitative imaging of magnetic microstructures remains challenging. Here, we integrate a transferred hBN flake with a 4 $\mu$m-diameter permalloy (Py = Ni${81}$Fe${19}$) microdisk and perform spatially resolved optically detected magnetic resonance measurements at room temperature. An applied in-plane magnetic field distorts the vortex-state magnetization, generating edge-localized magnetic surface charges and pronounced stray-field signatures at opposite disk edges. By referencing each pixel to its local zero-field splitting and correcting for a residual out-of-plane bias field, we quantitatively reconstruct the out-of-plane stray-field distribution, revealing peak fields of approximately 11.2 mT. An edge-charge model reproduces the spatial distribution and amplitude of the reconstructed field, linking the ODMR response to the field-driven evolution of the vortex state. These results establish transferred hBN VB$^{-}$ sensors for quantitative magnetometry of magnetic microstructures.

The quantum-thermal escape rate from a metastable well in the absence of dissipation is customarily written as a Boltzmann average of the Hill-Wheeler flux over a continuum of energies. However, this continuum treatment diverges exponentially at low temperature. The divergence originates in a mismatch between a quantum partition function and a classical flux integral; retaining the discrete nature of the quasibound spectrum removes it exactly, and the resulting semiclassical Arrhenius law is obtained in closed form on both sides of the crossover temperature. Evaluating a uniform Kemble transmission probability on Bohr-Sommerfeld levels further recovers the standard WKB decay rate of the lowest resonance at zero temperature. Benchmarked against the resonances of cubic and quintic potentials, obtained by complex scaling, this uniform semiclassical result stays within $9\%$ of the exact rate over eleven orders of magnitude.

In D-Wave quantum annealers, various properties of the ground state have been clarified, whereas the correspondence between theory and experiment for energy relaxation rates in multiqubit excited states remains insufficiently understood. Here, we measured the energy relaxation rates of the first excited states in single-qubit systems and interacting two-qubit systems using a D-Wave quantum annealer. We analyzed the measured relaxation rates using a Gorini-Kossakowski-Sudarshan-Lindblad master equation with independent local $\sigma^{\,\,z}$-type noise channels. The calculated relaxation rates reproduced the overall trends observed experimentally, supporting the model at a qualitative level. We then used the relaxation rates measured for the uncoupled single-qubit systems to calibrate the local relaxation parameters and predict the relaxation rates of the interacting two-qubit systems. The predicted rates remained within a factor of approximately four of the measured rates. These results show that the relaxation measurements on individual qubits can provide a practical estimate of relaxation in small interacting quantum systems and may help clarify relaxation mechanisms in programmable quantum annealers.

We investigate Floquet–spin-orbit compensation in the three-band $\alpha$-$T_3$ system, which interpolates between graphene at $\alpha=0$ and the dice lattice at $\alpha=1$. By tuning the interplay between an off-resonant circularly polarized optical field and intrinsic spin–orbit coupling, we identify three distinct pairwise band-degeneracy conditions in the quasienergy spectrum: (i) valley–spin degeneracy, (ii) spin–band degeneracy, and (iii) flat–dispersive band degeneracy. The flat band is not an artifact of a two-band reduction but rather an exact property of the continuum Hamiltonian at this compensation point, where the complete three-band Hamiltonian supports a momentum-independent dark state. A winding-two low-energy Hamiltonian and a finite-momentum Berry-curvature maximum, whose radius scales as the square root of the detuning, emerge from detuning this contact. We further show that the intrinsic transverse thermoelectric response encodes these spectrum patterns. The flat- and quadratic-band degeneracy can be predicted for $0<\alpha<1/2$ because the two response scales linked to the linear contacts have a monotonic ratio independent of the common spin–orbit energy scale. This allows an inverse determination of $\alpha$ and of the common spectral scale. The analytical results are confirmed by full three-band Kubo calculations, which also define the regime in which this inverse characterization is still observable. These results connect an experimentally accessible, Berry-curvature-sensitive thermoelectric response to tunable Floquet–spin–orbit band geometry.

The DeWitt boundary condition can be implemented in the Lorentzian path integral of minisuperspace quantum cosmology by summing only over non-singular paths. In this paper, we present a general definition of the resulting DeWitt kernels, along with specific rules for their construction, and evaluate them rigorously. The lapse integral over the positive half-line yields the Dirichlet Green function of the Wheeler–DeWitt operator, whereas the integral over the whole real line yields the Dirichlet group-averaging kernel; both vanish when either endpoint lies at the singularity. Since the minisuperspace actions are at most quadratic, all lapse integrals are performed in closed form without saddle-point approximations. We obtain the kernels for the closed universe without cosmological constant, for the flat de Sitter universe, and, in terms of Airy functions, for the closed and open de Sitter universes. Throughout, the DeWitt condition is imposed as the boundary condition at the singularity, which selects a self-adjoint constraint operator on the half-line and fixes the kernels uniquely, including their normalization.

Detecting and characterizing quantum correlations are tasks of great relevance in quantum information. More specifically, quantifying the amount of multipartite entanglement is a known difficult task, even for pure states. To this end, several entanglement measures have been proposed, although there is currently no universal manner to do so. In this work, we propose the classical shadows technique to measure the generalized global entanglement introduced in Phys. Rev. A 74, 022314. This particular multipartite entanglement quantifier $E_G^{(n)}$ relies on the linear entropies of all $n$-qubit partitions of a state. As the linear entropy can be written in terms of a complete set of observables of the subsystem, we employ classical shadows to estimate many observables with fewer measurements. We simulate the quantification of $E_G^{(n)}$ for well-known entangled states and for random states, comparing shadow estimations and grouping techniques. Our results show a clear advantage of classical shadows over direct estimation approaches, indicating that it can be a useful tool to quantify entanglement without the need to reconstruct the density operator of the whole system.

Quantum Signal Processing is a powerful quantum framework for generating and approximating univariate polynomials. However, QSP is often limited by circuit-depth bottlenecks and parity constraints on the class of realizable polynomials. In this work, we introduce Weighted Quantum Signal Processing, an extension of QSP in which a weight function is assigned to the central rotation operator. This formulation provides a deeper understanding of QSP, which emerges as the special case of WQSP with unit weights. The choice of weights determines the structure and expressive capabilities of WQSP circuits. When the weights are natural numbers greater than one, WQSP reduces to a pruned version of QSP, revealing parameter redundancies in the standard framework. Through appropriate selection of integer weights, WQSP achieves linear-to-exponential reductions in the number of parameters required to realize arbitrary bounded univariate polynomials while preserving approximation quality. For generic weights, we establish corresponding approximation error bounds and show that, in many cases, the approximation is exact. We analyze WQSP from both a deterministic perspective, where polynomial generation is formulated as the solution of a linear system, and a quantum machine learning perspective, where WQSP serves as a structured and expressive quantum learning model. We further employ this learning framework to parameterize learnable activation functions in Kolmogorov–Arnold Networks for multivariate function approximation. Our results show that WQSP provides a compact, flexible, and theoretically grounded framework for realizing arbitrary univariate polynomials while requiring significantly fewer trainable parameters than conventional QSP. This yields expressive and parameter-efficient neural architectures, highlighting the potential of WQSP as a scalable primitive for quantum-enhanced machine learning.

Coherent perfect absorption, zero transmission and zero reflection are several scattering phenomena governed by interference engineering in Hermitian and non-Hermitian systems. Higher-order coherent perfect absorption can significantly broaden the absorption bandwidth, while existing implementations rely on scattering zero degeneracy induced by exceptional points or additional momentum-dependent phase delays introduced in incident waves. We propose a scheme where a giant atom couples to a one-dimensional coupled-cavity array at two spatially separated sites. The spatially separated coupling configuration of the giant atom generates tunable nonlocal interference phases that dominate the scattering interference process. We further investigate the zero-reflection and zero-transmission behaviors under single-sided incidence. Remarkably, we find that for certain parameter choices, zero transmission can persist over the entire propagating band, rather than being restricted to a single momentum. Our results reveal that the giant-atom interference mechanism enables bandwidth-enhanced coherent perfect absorption and bandwidth-enhanced zero transmission in the absence of exceptional points and incident momentum-dependent phase delays. Our work provides a physical route for coherent wave manipulation in coupled-cavity quantum networks.

Local operations assisted by classical communication (LOCC) play a fundamental role in the resource-theoretic formulation of entanglement theory inducing an operationally meaningful ordering in the set of entangled states. The particular class within LOCC of local unitary (LU) transformations is obviously closed under inversion. Thus, LU-equivalent states are interconvertible by LOCC and have therefore the same entanglement. For this reason LU-equivalence has been thoroughly studied in the context of entanglement theory. However, as I note here with a simple example, the converse is not true: there exist entangled states that are interconvertible by LOCC but which are not LU-equivalent. This motivates studying under which conditions LOCC interconvertibility is characterized by LU-equivalence. I provide a sufficient condition for this to hold. When one considers multipartite states with full entanglement dimensionality (as quantified by the Schmidt number vector) LOCC interconvertibility can only hold under LU-equivalence.

We propose a framework for incorporating quantum-computing-based electronic-structure calculations into universal machine-learning interatomic potentials (uMLIPs). Rather than constructing an interatomic potential from scratch, we refine a pretrained DFT-based uMLIP using a small set of accurate reference energies obtained from quantum computing. We demonstrate the approach for three chemically distinct applications: the Menshutkin reaction, water adsorption in the metal-organic framework HKUST-1, and CO hopping on a high-entropy-alloy nanoparticle. For the Menshutkin reaction, fine-tuning on gas-phase configurations improves the transition-state energy inside a carbon nanotube but not the product energy. For water adsorption in HKUST-1, fine-tuning with only 14 reference configurations brings adsorption thermodynamics obtained from millions of configurations sampled by Widom insertion into closer agreement with reference values. For CO hopping on an IrPdPtRhRu nanoparticle, the preference for on-top over bridge adsorption is recovered in the finite-temperature free-energy profile obtained from enhanced-sampling molecular dynamics, even though the reference data contain only energies. These results demonstrate that the proposed framework provides a practical route for incorporating quantum-computing calculations into realistic atomistic simulations and that quantum-computing reference data can improve pretrained uMLIPs.

Metallic nanogaps concentrate terahertz (THz) fields into deep subwavelength volumes and support field-driven electron tunneling when the insulating barrier becomes sufficiently narrow. Here, we demonstrate mechanical control of tunneling-mediated nonlinear THz transmission in a flexible nanogap metasurface. The metasurface consists of Au/PMMA/Au nanogaps fabricated on a polyethylene terephthalate substrate, enabling continuous tuning of the gap geometry through macroscopic bending. In the flat state, the resonant transmission exhibits only a weak dependence on the incident THz field strength. Upon bending, increasing the incident field strength induces pronounced resonance suppression accompanied by saturation of the voltage developed across the nanogaps. This nonlinear response is consistent with the opening of a field-dependent tunneling conduction channel through the mechanically narrowed PMMA barriers. Simmons-model calculations illustrate the strong increase in tunneling current density and the associated dissipative gap response as the local gap width approaches the few-nanometer regime. These results establish mechanical deformation as a macroscopic means of controlling tunneling-mediated THz nonlinearities in flexible metasurfaces.

Stimulus-responsive hydrogels convert temperature changes into magnetic-field shifts detectable by nitrogen-vacancy (NV) centers, enabling nanoscale thermometry in soft and biological environments. Existing hydrogel-nanodiamond demonstrations rely on NV ensembles, whose high photon throughput is accompanied by gradient-induced inhomogeneous broadening, while idealized single-NV projections assume high-fluence fluorescence/ODMR readout. Here we study a pulsed single-NV route for the same class of sensors and ask whether decoherence-aware coherent control can improve thermometric performance over optimized Ramsey interrogation at equal detected-photon budget. Using a sigmoidal volume-phase-transition model, dipolar magnetic transduction, and Lindblad master-equation simulations, we find a reproducible 25-27% per-shot sensitivity gain over optimized Ramsey, i.e., a 57-60% gain in Fisher information (1.57-1.60). The same gain carries over to the photon-normalized Fisher information. The rate gain is governed by the measurement duty cycle, the fraction of the experimental cycle spent accumulating signal rather than initializing, reading out or waiting, and becomes largest when the overhead or optical-dose constraint dominates the cycle time. The optimized trajectories reveal a response-shaping mechanism in which phase accumulation is concentrated near the end of the sequence, and a closed-form depth-two solution reproduces the numerical optimum and exhibits that mechanism analytically. The advantage is most pronounced when the dephasing time is short compared with the measurement overhead or dose-limited waiting time, which is the operating regime targeted by hydrogel-transduced single-spin biosensing.

We report on the mapping of classical microwave transmission line theory onto the quantum scattering matrix description. By means of a generalized flux formalism a la Devoret, we derive a charge-current vector living on the confining electrodes, to which a Hodge-like decomposition is applied. The presented theory holds equally well for all types of waves traveling within Cartesian and cylindrical guide geometries (the usual Transverse Electric Magnetic, but also Transverse Magnetic and Transverse Electric ones). We then demonstrate how a generic load decomposes into a series of complex coefficients $Z_{load}(\alpha)$, for each mode $\alpha$ propagating along the line. This decomposition leads to a particular classification of traveling waves: gradient-type and curl-type charge-currents. This distinction shines a new light on a broken gauge symmetry exhibited by a class of Transverse Electric modes. Our results provide a universal theoretical framework, which finds a direct usage in microwave-based quantum information transfer.

We introduce a new model for a system of interacting bosons placed in an array of sites. At its core is a nonlinear, nonlocal evolution equation, which we have dubbed the Schrödinger-Dirichlet equation. The construction is closely related to the Bose-Hubbard model and to a specific type of generalized bosons. In contrast to conventional mean-field closures, the resulting nonlinear dynamics need not preserve product structure and can generate entanglement from initially separable states. The relevant methods of analysis are based on harmonic analysis for the multiplicative group of positive rationals.

We propose a Bell-measurement node for quantum repeaters based on a planar semiconductor microcavity operating in the strong-coupling regime. Cavity photons hybridize with quantum-well excitons to form polaritons combining properties of photons and matter quasiparticles. A control photon loaded into one polariton mode changes the polarization response seen by a subsequently incident target photon. This conditional rotation is governed by the interplay of self-induced Larmor precession triggered by spin-dependent exciton-exciton interactions and the polarization beats caused by the splitting of transverse-electric and transverse-magnetic cavity modes. We identify conditions of the experiment that enable implementation of a controlled-Z gate and allow to distinguish all four Bell states in the ideal limit. The one-sided scattering scheme provides a lower interaction threshold than a scalar Kerr reference under the same assumptions. At a selected operating point, the bandwidth-induced identification error scales as the fourth power of the pulse bandwidth in the narrow-band limit. An additional fixed input rotation reduces this error even further. We describe the entanglement swapping between remote memories and determine the minimum quality of the elementary links needed to obtain an entangled output.

We determine the ultimate information rate of a relaxing multilevel quantum sensor under unrestricted adaptive control and construct an explicit strategy that attains it. We consider sensing a weak field that couples the ground state to several excited states that decay back to the ground state, a setting that reduces to amplitude-damping sensing for a single excited state. We show that the ultimate information rate is exactly the mean population lifetime of the bright state coupled to the ground state by the signal. Although the sensing dynamics generally involve several decay modes, an explicit rank-one protocol that monitors the ground–bright coherence using fresh meters and classical feedback attains this rate while keeping its finite-time information deficit bounded by a constant. For independently relaxing identical sensors, independent local monitoring attains the sum of their individual optimal rates, so intersensor entanglement and joint quantum error correction cannot increase the asymptotic rate. Consequently, the free population-decay curve provides an operational measure of the optimal sensing performance under arbitrary adaptive control.

Environmental noise is a major source of decoherence and errors in quantum systems. In a non-Markovian environment, the noise has a finite correlation time, and the system can retain information about its previous interactions with the environment. Here, we investigate how such environmental memory can be observed through a finite-duration coherent quantum operation. Coherent control dynamically reshapes the stochastic coupling operator and thereby changes how two-time noise correlations affect the quantum process. For Ornstein-Uhlenbeck noise, we show analytically that two different limits reduce the information on the correlation time. In the short-memory limit, the leading dynamics depend on the integrated-noise combination {\sigma}/{\tau}c, where {\sigma} is the noise variance and {\tau}c is the correlation time, making these parameters locally degenerate. In the long-memory limit, the stochastic field becomes quasi-static during the operation, and sensitivity to the correlation time is suppressed. Exact stochastic simulations for a driven single-qubit X{\pi} rotation and a two-qubit exchange gate show that independent correlation-time information becomes largest between these limits, when the environmental and control timescales are comparable. Noncommuting controls enhance this information, whereas commuting controls do not. Simulations at different gate durations tg further show that the information window approximately follows the dimensionless correlation ratio {\tau}c/tg. These results provide a timescale-matching principle for probing finite-correlation non-Markovian noise with coherent quantum control.

We consider the 4.8.8 color code in a brickwork layout on the square lattice with nearest-neighbor gates. We identify periodic superdense circuits with twelve CNOT layers that appear to preserve the full distance of these codes. Including ancillas, the family uses $q=(2d^2+5d-5)/2$ physical qubits for distance $d$: asymptotically $2/3$ as many as the triangular 6.6.6 color code and $1/2$ as many as the rotated surface code at the same code distance. Circuit-level simulations targeting superconducting architectures demonstrate favorable scaling of 4.8.8 color codes at plausible physical noise rates, including both for planar codes and their toroidal cousins under periodic boundary conditions.

Polarization qubits offer a direct route to fiber-based quantum communication, yet the fiber that carries them also scrambles their reference frame through uncontrolled birefringence. Active compensation commonly relies on monitoring and feedback, raising a natural question: can the link itself suppress coherent polarization drift before it reaches the receiver? We show that it can within a regime of sufficiently correlated unitary drift. Our central idea is to embed a fixed cyclic sequence of Pauli rotations along the fiber, turning propagation distance into a spatial toggling frame. Rather than estimating and inverting the unknown transformation, the sequence repeatedly reverses its leading action. We establish exact refocusing for constant generators compatible with a two-segment echo, show that a four-frame Pauli cell cancels the leading contribution of any traceless quasi-static generator, and bound the residual error for smoothly varying birefringence. We then connect these guarantees to operational BB84 quantities, including measured QBERs, the resulting secret fraction, and insertion loss. In simulations of a 50 km fiber with spatially correlated birefringence, a representative design reduces the mean QBER from 6.11% to 0.224% at a device spacing of 1.25 km. With an assumed per-device transmission of t = 0.997, this raises the asymptotic key rate per launched pulse by a factor of approximately 2.5. For this parameter set, the best design in the tested scan is not the densest one: error suppression and optical loss create a finite operating window. These results provide a loss-aware design principle for passive polarization stabilization and suggest a low-overhead complement to active tracking in polarization-encoded QKD networks.

Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.

We examine the geometric interpretation of the quantum geometric tensor proposed in [Phys. Rev. B 110, 035404 (2024)] for mixed quantum states, focusing on its imaginary part, which is proportional to a weighted sum of the Berry curvatures of the eigenstates of the density operator. While the real part naturally decomposes into Fisher–Rao and weighted Fubini–Study contributions, we show that the imaginary part does not, in general, coincide with the curvature of a connection on a globally defined U(1) line bundle whose holonomy yields a mixed-state geometric phase. Using a two-level system as an explicit example, we demonstrate that its surface integral depends on the choice of surface bounded by the same closed path, with ambiguities that are not integer multiples of $2\pi$.