Black hole thermodynamics for generic dynamical, non-equilibrium regimes remains a fundamental challenge. We establish dynamical entropy as the Noether charge associated with a generic evolving null surface subject to Dirichlet boundary conditions. We uniquely specify the symmetry generator associated with the dynamical entropy, which is a null vector on the null surface, upon requiring physically motivated geometric conditions that yield a notion of ``dynamical zeroth law.'' We prove that this Noether charge density satisfies the second law of thermodynamics strictly at each instant in time, bypassing the teleological final conditions traditionally required by event horizons. Thus, we extend and generalize the notion of dynamical entropy introduced in \cite{Hollands:2024vbe}, in some different ways: We do not impose background stationarity; our dynamical entropy and the associated second law are local in time and work for generic dynamical gravitational systems. less

We re-examine spontaneous scalarization of black holes within Starobinsky gravity supplemented by the Gauss-Bonnet invariant. A novel feature is uncovered: scalarized solutions split into two smooth branches that connect at a common minimal horizon radius, a multi-branch structure previously unreported for static, spherically symmetric scalarization. Extending the theory with a Maxwell field, we find that this multi-branch structure persists, while a new additional disconnected branch emerges within certain parameter ranges. We thoroughly analyse the transition from a single smooth branch to two disconnected branches. Lastly, we verify, employing the standard Maxwell thermodynamic relations, that all charged hairy solutions obey the first law exactly. less

The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every $α\in[1/2,1)$, yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability. less

A critical limitation of solid-state quantum devices arises from the materials from which they are fabricated: uncontrolled surfaces, interfaces, and structural imperfections introduce numerous sources of loss and decoherence. Despite extensive efforts, linking these decoherence mechanisms to their microscopic material origins -- essential for developing effective mitigation strategies -- remains an outstanding challenge that has slowed coherence improvements. Here, using scanning gate microscopy on live superconducting circuits we identify a previously unrecognised decoherence mechanism originating from Coulomb blockade and microwave-driven charge tunnelling in metallic grains. Such grains are ubiquitous in thin-film devices fabricated by standard lithography processes. By characterising multiple defects across different devices, we find such defects to be as common and as debilitating to device performance as two-level system (TLS) defects, while originating from a fundamentally different physical mechanism. Importantly, conventional characterisation techniques would misattribute this loss to other, microwave power-independent processes. Our observations thus reveal a widespread source of decoherence in superconducting circuits, challenging the prevailing paradigm that coherence lifetimes are primarily limited by TLS defects. Eliminating metallic grains during fabrication provides a clear and practical route to suppress this mechanism, offering a pathway towards improved coherence and reduced noise in microwave-based solid-state quantum devices. less

The Elliptic Curve Discrete Logarithm Problem (ECDLP) is a fundamental problem in cryptography, and reducing the resource requirements of quantum algorithms for solving ECDLP is an important goal. In this work, we present a space-efficient quantum algorithm for solving the ECDLP over prime fields, achieving an implementation with only $3n+6\lfloor \log_2 n \rfloor+O(1)$ logical qubits and $919n^3/\log_2 n+O(n^2)$ Toffoli gates, where $n$ is the bit-length of the prime. For a 256-bit prime-field curve, our construction requires only 835 logical qubits, reducing the previous best estimates of 1098 and 1175 logical qubits by Chevignard et al. [EUROCRYPT 2026] and Babbush et al. [ArXiv Preprint 2026], respectively. The key to our improvement is a new space-efficient reversible modular inversion circuit, which addresses the dominant space bottleneck in affine-coordinate point addition. Starting from the extended Euclidean algorithm (EEA), we refine the register-sharing technique of Proos and Zalka by introducing length registers and location-controlled arithmetic to compactly store and update intermediate variables. We further optimize the reversible update procedures and construct the corresponding controlled arithmetic circuits, resulting in a modular inversion circuit implemented by only $2n+6\lfloor \log_2 n \rfloor+O(1)$ logical qubits and $195n^2+O(n\log_2 n)$ Toffoli gates. This modular inversion circuit together with mid-circuit measurements and classical feed-forward operations provides a space-efficient controlled affine point-addition circuit and a complete implementation of Shor's algorithm for ECDLP. less

The monogamy of quantum entanglement, applied by Almheiri-Marolf-Polchinski-Sully (AMPS) to black holes, obstructs a smooth horizon vacuum after the Page time. We transcribe this argument to Hawking-like phonon radiation from a sonic horizon in the Unruh acoustic metric. An exact purity identity shows that post-Page-time unitarity forces the entanglement between an outgoing phonon and its interior partner to vanish, selecting a non-Hadamard (Boulware-like) phonon state, which we define as an acoustic firewall. Its renormalized stress tensor differs from the smooth state by a constant, negative near-horizon flux, and the thermal-atmosphere energy density it removes, measured by a static calorimeter, grows as $(δr)^{-2}$ in the radial coordinate toward the horizon (singular in the free-fall frame), cut off at the healing length. The construction is kinematic and does not resolve the information paradox; it yields one concrete, falsifiable prediction: a differential phonon-calorimetry signal $\mathcal{R}(δr)=|Δ\mathcal{E}|/\mathcal{E}^{(0)}\to(\ell_κ/δr)^{2}$, present only after the analogue Page time in a Bose-Einstein condensate. less

Dark matter near a black hole and effective extra-dimensional corrections can change the same horizon-scale observables. This creates a simple but important question: if an image differs from Kerr, what caused the difference? We study this problem with DARK-HIDE. The dark-matter branch is described by rotating metrics with radial mass functions, while the hidden-dimensional branch is a rotating braneworld metric with a non-electromagnetic tidal charge. We compare photon regions, critical curves, controlled image morphology, a shadow-size likelihood calibrated to EHT results, and local ZAMO escape cones. A strong negative tidal charge is easy to separate from Kerr and from the two benchmark dark-matter profiles. The difficult case appears after the tidal charge is continuously adjusted to mimic the dark-matter critical curve and image proxy. At $\varepsilon/M=0.025$, the best $P+I$ mimics occur at $q/M^2=-0.01917$ for Einasto and $-0.01117$ for cored cNFW, with small standardized separations of $0.084$ and $0.051$. A ray-bundle caustic test does not pass the required convergence and topology checks, so it is excluded from inference. After marginalizing over spin and isotropic inclination, current EHT shadow-size constraints leave both dark-matter amplitudes prior dominated. They mildly suppress large negative tidal charge, but remain fully compatible with $q=0$. Local escape cones retain a small, smooth, and well-resolved difference between the matched branches. Thus, present shadow size alone cannot break the DARK-HIDE degeneracy, while local photon transport keeps additional strong-field information. less

Reheating after inflation is one of the strongest sources of gravitational waves (GW), producing a stochastic background (SGWB) with a non-thermal spectrum peaked at frequencies of order a few GHz. Detecting it is difficult: experiments based on the inverse Gertsenshtein effect in intense magnetic fields reach the MHz but not the GHz band, where the typical strain is around $10^{-30}$. The same window contains the coalescence of light primordial black hole (PBH) binaries, whose merger frequency $f\simeq4.4\ \mathrm{kHz}\,(M_\odot/M)$ falls in the MHz--GHz range for planetary to sub-planetary masses; since such objects are necessarily sub-solar, their detection would be strong evidence for PBHs as a component of the dark matter. We propose a solid-state detector at GHz frequencies that could integrate over months to years the GW continuously arriving from the Big Bang and search for light PBH binary coalescence. As a concrete realization we consider a modular array of $\sim10^3$ ultra-pure sapphire $(10\ \mathrm{cm})^3$ monocrystals forming a cubic-metre detector read out by cryogenic single-phonon sensors, whose segmentation provides thermal isolation, favourable counting statistics and coincidence-based background rejection. We also compare candidate materials, finding diamond superior per unit volume but limited by the unavailability of large single crystals. Finally, we contrast the two targets. The stationary background is a shot-noise-limited counting problem, best served by a narrow, resonance-enhanced, long-integration search; the loud transient chirp of a nearby merger is better caught by a fast, broad-band search with coincidence tagging. Because the phonon spectrum is continuous, a modular solid-state array can serve both, by staggering resonant cells across the band while running a broad-band subset for chirp tracking. less

Large language models are increasingly assisting with demanding formal theorem-proving tasks, particularly when grounded in machine-checked libraries such as Lean. Agentic systems further amplify this process by searching, reusing, and extending existing formal developments to uncover new discoveries. In quantum computing, Shor's algorithm and its variants present such a demanding case for Lean formalization. In this work, we formalize this algorithm family in Lean through agentic formalization: software agents analyze sources, write Lean code and repair proofs, with human review of the scientific claims and machine checking of the resulting formal proofs. Our formalization develops the mathematical foundations for analyzing quantum attacks in two cryptographic settings: a 2048-bit modulus in the RSA-2048 and the standardized elliptic curve over a 256-bit prime field (P-256). To support these analyses, the formalization ranges from quantum algorithms for order finding to reversible quantum circuits for modular and elliptic-curve arithmetic. Based on [Quantum 5, 433] and [ASIACRYPT 2017, 241--270], we formalize the logical resource estimates for RSA-2048 and P-256, respectively, and provide additional estimates of classical operations. We expect the results pave the way for broader machine-checked quantum cryptanalysis and represent a step toward AI-assisted design and verification of quantum algorithms. less

With current advances in gravitational wave (GW) detection made by the worldwide LIGO-Virgo-KAGRA (LVK) network of detectors, ever-more sensitive tests of gravity in the strong-field regime are now possible. This enables one to test gauge theories beyond Einstein-Hilbert action, such as Weyl gauge theories of gravity. The only anomaly-free (quantum) gauge theory of a space-time symmetry beyond Poincaré is based on Weyl gauge group (of dilatations and Poincaré symmetry) with Weyl conformal geometry as its natural underlying geometry. This gauge theory has spontaneous breaking of Weyl gauge symmetry to Einstein-Hilbert and Proca actions, plus a positive cosmological constant. We investigate the GW polarisation modes of Weyl (quadratic) gauge theory of gravity in Weyl geometry and compare our findings to the most recent experimental data. We show how the geodesic deviation equation from Riemannian geometry translates to Weyl geometry, and explain why it is crucial to perform the analysis around de Sitter background, which is the correct low-energy limit of Weyl quadratic gravity, to not alter the GW content, and then compute the polarisation modes. In addition to the two transverse-traceless tensor modes predicted by Einstein-Hilbert action, we find two additional vector modes induced by the transverse fluctuations of the Weyl gauge field. If detected, these vectors modes would be important evidence for Weyl gauge symmetry. less

The ringdown gravitational wave from a binary black hole (BBH) merger is a superposition of quasi-normal modes (QNMs) of the remnant black hole. In general relativity (GR), QNMs are damped harmonic oscillations with frequencies and damping times uniquely determined by the remnant's mass and spin. The measurement of the ringdown modes and performing black hole spectroscopy provides a tool to test the validity of GR. We present a ringdown analysis based on reconstruction of GW signals with coherent WaveBurst (cWB). This method yields tighter constraints on the QNM frequency and damping time than previous measurements. The improved precision results from the noise reduction achieved by the cWB reconstruction and the enhanced ringdown analysis, which probes the remnant properties at earlier times, closer to the merger. We have analyzed publicly available binary black hole (BBH) detections from the third Gravitational-Wave Transient Catalog (GWTC-3). For all events considered, the measured frequency and damping time of the dominant $(l,m)=(2,2)$ mode are found to be consistent with the predictions of GR. A combined analysis further strengthens these constraints, yielding fractional deviations in frequency $δf_{220} = 0.003_{-0.028}^{+0.028}$ and damping time $δτ_{220} = 0.050_{-0.086}^{+0.081}$, consistent with zero within the quoted uncertainties. less

Space-based gravitational-wave (GW) detectors, including LISA and Taiji, offer unprecedented access to regimes where alternative theories of gravity may deviate from General Relativity (GR). Gravitational Quantum Field Theory (GQFT) provides a novel framework in which the Poincaré-type inhomogeneous spin symmetry of Weyl-type fermions in the Standard Model is elevated to a gauge symmetry. Within this construction, the fundamental gravitational field is identified with a gravigauge field which behaves as a Goldstone-type bi-covariant vector field. Unlike GR, GQFT predicts additional polarization states: one transverse scalar (breathing) mode and two vector modes. In this work, we focus on the transverse, isotropic scalar mode and investigate its detectability with Taiji. To isolate this mode, we employ the null-response channel (NRC), a specific interferometric combination designed to suppress contributions from other polarizations. We implement an analytical, dynamic orbital model to realistically simulate a triangular constellation. We compute the response functions and sensitivity curves for various interferometric channels, compare them with the standard Michelson channel, and demonstrate the effectiveness of the NRC approach. Our results show that the NRC provides a reliable, waveform-independent criterion for testing non-GR polarizations, and we anticipate that it will serve as a valuable tool for probing gravitational theories in future space-based GW missions. less

The classical formation of a Schwarzschild black hole from a regular, non-singular configuration has recently been shown to be impossible within general relativity: the geometry inevitably develops a discontinuity at the origin, a phenomenon termed Minkowski breaking by Ovalle, Casadio, and Kamenshchik [PRD 113 (2026), 064042]. This obstruction signals that the transition to the Schwarzschild point mass must be a discrete, quantum event. We uncover the thermodynamic footprint of this transition. Using the explicit family of regular Schwarzschild black holes with a de Sitter core, we show that the inner Killing horizon carries a formal Bekenstein-Hawking entropy $S_{\rm inner} = A_{\rm inner}/4$ that is absent in the singular Schwarzschild state. This entropy is hidden from external observers in equilibrium but, assuming the generalized second law, must be released when the inner horizon disappears. As the collapse parameter $n$ decreases, the inner horizon shrinks and its entropy is gradually released during classical evolution, until the horizon finally vanishes at $n=0$ with the Minkowski breaking. The surface gravity diverges as $n\to0^+$, with the semiclassical description breaking down at $n \sim 1/\ln(h/\ell_P)$; the final disappearance is therefore a deep quantum process. For the $n=3$ regular black hole, the stored entropy is approximately $59\%$ of $A/4$; in the semiclassical limit $n\gg1$, it approaches the full $A/4$. The integer nature of $n$ implies a quantized entropy spectrum, with the Schwarzschild black hole as the ground state within the OCK family. We discuss how the classical mass-inflation instability may be circumvented by the quantum disappearance of the Cauchy horizon, and clarify the continuous vs. discrete nature of the collapse. less

Quantum process tomography, the task of learning an unknown quantum channel from black-box access, is a central problem in quantum information. In this setting, protocols with quantum memory can coherently store and jointly process quantum information obtained from multiple channel uses, whereas protocols without quantum memory must measure after each use and retain only a classical transcript of the measurement outcomes. A fundamental open question is whether quantum memory provides a query-complexity advantage even when protocols without quantum memory may adapt their experiments based on all previous outcomes with unbounded classical computational power. In this work, we show that it does. We determine the optimal query complexity of quantum process tomography without quantum memory up to a constant factor to be $Θ(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$, where $d_{\mathrm{in}}$ and $d_{\mathrm{out}}$ are the channel input and output dimensions, respectively, and $\varepsilon$ is the target diamond-norm accuracy. More precisely, we prove that any incoherent protocol for this task, including adaptive protocols, requires $Ω(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$ queries, even when each channel use may be assisted by arbitrary fresh ancilla, and we present a non-adaptive, ancilla-free incoherent protocol achieving the matching upper bound $O(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$. Our results thereby generalize the optimal sample-complexity bounds for single-copy state tomography, recovered as the special case $d_{\mathrm{in}}=1$. By contrast, coherent protocols with quantum memory achieve query complexity $Θ(d_{\mathrm{in}}^2 d_{\mathrm{out}}^2/\varepsilon^2)$. Hence, our results establish a rigorous learning separation between quantum process tomography with and without quantum memory. less

Schrödinger cat states provide a hardware-efficient platform for bosonic quantum error correction by encoding logical information in protected manifolds of harmonic oscillators. While previous work has demonstrated the dissipative stabilization of multi-mode Schrödinger cat states as robust quantum memories, a framework for universal quantum computation has remained unavailable. Here we extend this approach by introducing a universal gate set for dissipatively stabilized multi-mode cat qubits. Using a chain of Kerr non-linear oscillators coupled through engineered non-local dissipation and an effective low-dimensional description, we show how arbitrary single-qubit control can be achieved through arbitrary rotation around the $X$-axis and $π/2$-rotation around the $Z$-axis. We further show how coupling two such stabilized arrays through just one oscillator on each respective array enables coherent entangling operations through implementation of the $XX(π/2)$ gate. Numerical simulations demonstrate high-fidelity gate dynamics and entanglement generation under realistic parameters. Finally, we analyze the effects of induced and intrinsic photon loss, disorder, and the validity regime of the effective low-dimensional theory. Our results establish dissipatively stabilized multi-mode Schrödinger cat states as a potential architecture for universal bosonic quantum computation. less

Hybrid continuous-discrete-variable quantum processors can represent bosonic degrees of freedom directly in oscillator modes, or qumodes, while using qubits for control, readout, and nonlinear operations. Recently proposed trigonometric continuous-variable (CV) gate sets promote periodic functions of oscillator quadratures to elementary operations, making them natural primitives for compact variables, rotor models, lattice gauge theories, and anharmonic dynamics. Here we experimentally demonstrate and benchmark one-qumode cosine gates, and perform a mode-resolved marginal benchmark of two-qumode cosine-gate implementations, on the QSCOUT trapped-ion quantum platform. Our implementation uses collective motional modes of three- and four-ion $^{171}{\rm Yb}^{+}$ chains and realizes finite-step trigonometric-gate circuits through hybrid qubit-qumode operations and conditional phase-space displacements. In contrast to previous theoretical and compilation work, we focus on the gate-level characterization of the trigonometric primitives. We measure Fock-space transition probabilities, study their dependence on gate parameters and Trotter step number, and compare with simulations incorporating thermal initialization and motional dephasing. We also derive ideal gate matrix elements and phase-space diagnostics, connecting the measurements to the non-Gaussian structure generated by these gates. These results establish trigonometric CV gates as reusable building blocks for bosonic Hamiltonian simulations and hybrid quantum algorithms requiring intrinsically non-polynomial operations. less