Subgraph detection asks whether an $n$-vertex graph, accessed through queries to its adjacency matrix, contains a copy of a fixed graph $H$. We prove the first unconditional superlinear lower bounds on the bounded-error quantum query complexity of this problem, answering a longstanding open question. A copy of $H$ is a certificate of constant size, so the adversary method with nonnegative weights cannot prove superlinear lower bounds. For every fixed $r\ge 4$, detecting the clique $K_r$ requires $n^{λ_r-o(1)}$ queries, where $λ_4=19/18$, the exponents $λ_r$ increase strictly with $r$, and $λ_r\ge 2-4\sqrt{2/r}+O(1/r)$. More generally, we prove superlinear lower bounds for detecting every fixed connected graph $H$ with chromatic number $c\ge 4$. These bounds approach quadratic as $c$ grows: for sufficiently large $c$, detection requires $n^{2-O(\sqrt{\log\log c/c})-o(1)}$ queries. Chromatic number alone does not characterize the quantum query complexity of subgraph detection: we show that detecting the complete bipartite graph $K_{r,r}$ requires $n^{β_r-o(1)}$ queries, where $β_{10}=181/180$ and $β_r\ge 2-O(1/\sqrt{r})$. Our main technical result is a lower bound for finding an all-ones certificate from a known family when the input bits are sampled independently. Its proof combines Zhandry's compressed oracle (CRYPTO 2019) with conditioning on a randomly planted certificate, adapting an argument of Belovs (FOCS 2026). Our hard instances are built from graphs containing many copies of the desired subgraph with limited overlap. For cliques, we use a construction of Gowers and Janzer (CPC 2021); for complete bipartite graphs, we use a random construction. less

Pseudorandom permutations are ubiquitous in theoretical and applied cryptography. PRPs that offer security even against adversaries making quantum queries are of increasing interest, and used in applications ranging from constructing pseudorandom unitaries to separating SZK from BQP. A successful framework for constructing classically-secure PRPs is the key-alternating Even-Mansour approach, which interleaves applications of public permutations with additions of round keys. The single-round construction is already classically secure in the ideal permutation model (IPM), with added rounds offering improved concrete security. However, in the quantum-query setting, the status of this framework is presently unclear. A simple quantum-query attack based on Simon's algorithm breaks the one-round cipher. For two or more rounds, security is only known against non-adaptive adversaries who must prepare all queries in advance. In this work, we show that the two-round Even-Mansour cipher is information theoretically secure in the IPM against adversaries making polynomially-many adaptive forward and inverse quantum queries to all available oracles. Our proof uses compressed permutation oracles and a specially crafted isometry relating the ideal and real experiments. We also show that this construction is minimal, in the sense that essentially any cipher constructed via a single call to a public permutation is quantumly insecure. less

Standard finite quantum de Finetti theorems approximate the $k$-system marginals of permutation-invariant states of $n$-systems by mixtures of independent and identically distributed (iid) states, usually in trace distance. We prove both standard and Renner's exponential de Finetti theorems in the stronger form of operator inequalities, implying bounds in every Schatten norm and for every quantum Rényi divergence satisfying data processing. In the standard case, for fixed local dimension, our $k/n$ error bound in max-relative entropy improves on the previously best known $k^2/n$ scaling, even in the classical setting. The operator-inequality approach is particularly suited to study channel de Finetti representations because operator order between Choi states is equivalent to completely positive (CP) order between the underlying channels. For permutation-covariant channels $N^{(n)}:A^{\otimes n}\to B^{\otimes n}$, where $d_A=\dim A$, we prove that the $k$-system reduced channel is CP-dominated by a mixture of tensor-power channels with error $O(k/\sqrt{n})$ and polynomial dependence on the local dimensions, addressing a question raised by Berta et al. [Math. Program. 194, 781-829 (2022)]. Under the no-signalling condition, we also prove an exponential channel de Finetti theorem where the approximating mixture consists of Choi-almost-iid channels, whose normalized Choi states are almost-iid in the sense of Mazzola-Sutter-Renner. In the case of $r$ defects, the representation error is at most $\mathrm{poly}(n)\bigl(2d_A^4k^3/(nr^2)\bigr)^{(r+1)/2}$ and decays exponentially in $n$ for a suitable choice of parameters $r$ and $k$. less

We present the results of \textbf{MADGRAV}, a deep-learning-based search for high-mass compact binary coalescences, applied to the data collected by the LIGO interferometers during the third observing run and during the first and second part of the fourth observing run. The \textbf{MADGRAV} pipeline consists of a series of sequential convolutional neural networks that perform anomaly detection, glitch classification, coherence testing, and signal ranking. Data from the Hanford and Livingston LIGO detectors are studied (both individually and in coherence) by way of 1 second Q-transform windows. Of the candidates that survive every stage of the pipeline, 48 reach the significance threshold, and we report 47 gravitational wave detections characterised by a false alarm rate below $1\,{\rm yr}^{-1}$ with a probability of astrophysical origin $p_{\rm astro}>0.9$. Of the 47 detections, 44 are shared with the minimally modelled coherent WaveBurst search. The observed total source-frame masses, extracted from official gravitational wave transient catalogues, are in the $14-236 M_{\odot}$ range with a median of $69 M_{\odot}$, and a median SNR of 16. We note that the recovered fraction of confident detections rises with mass: for LIGO detectors network SNR $>10$ the pipeline recovers $8.1\%$ of confident catalog events below $30 M_{\odot}$, $39.8\%$ between $30$ and $100 M_{\odot}$, and $53.3\%$ above $100 M_{\odot}$, corresponding to $33.3\%$, $45.5\%$ and $53.3\%$ of the events detected by coherent WaveBurst in the same bins. These results suggest that anomaly detection pipelines can serve as an independent detection channel complementary to matched filtering in the high-mass high-SNR regime. less

We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, $n_\infty=1,2,3,4$. Compared with the three-family classification of Cook and Lu [Phys. Rev. D 107, 044043 (2023)], our global continuation separates complex conjugation at fixed $m$ from the mirror symmetry connecting the $m$ and $-m$ spectra, yielding a uniform four-family classification without additional symmetry-unrelated roots. The $n_\infty=3$ family approaches the Schwarzschild algebraically special frequency, whereas the $n_\infty=1,2,$ and $4$ families diverge as $ω\propto a^{-4/3}$ along lower-half-plane directions $-150^\circ$, $-90^\circ$, and $-30^\circ$. High-precision data up to $\ell=32$ recover the Cook--Lu small-spin asymptotics and show how the divergent branches are embedded in the global four-family spectrum. The spherical-limit polar labeling and large-$|aω|$ angular ordering are related in a family-dependent manner. For axisymmetric perturbations, we show that the $n_\infty=2$ and $n_\infty=3$ branches coalesce at exceptional points and subsequently evolve toward distinct small-spin limits, rather than exhibiting the overtone-multiplet splitting proposed by Cook and Lu. Finally, we identify a previously unreported anomalous proximity between the $n_\infty=3$ TTM family and the unconventional Kerr quasinormal-mode sequence, with separations reaching order $10^{-8}$ while remaining numerically well resolved. less

It is well-known that every $n$-qubit unitary can be implemented by a $2^{O(n)}$-depth quantum circuit using single- and two-qubit gates. It has been open whether exponential depth is \emph{necessary} for general unitaries, even when allowing for unlimited number of ancilla qubits. We show, perhaps surprisingly, that all unitaries can be approximated to operator norm $ε$ by a circuit of one- and two-qubit gates of depth $\poly(n,\log 1/ε)$ with $2^{O(n)}$ ancilla qubits. In other words, every $n$-qubit unitary can be parallelized to polynomial depth. Moreover, if we allow unbounded fan-out gates, these circuits can be reduced further to \emph{constant} depth. Our construction takes advantage of a novel relationship connecting the unitary synthesis problem of Aaronson and Kuperberg to locally-decodable codes and private information retrieval from complexity theory and cryptography. less

We investigate generalized projective symmetry and its breaking in four-dimensional parity-even metric-affine gravity, considering an action linear in curvature and at most quadratic in torsion and nonmetricity. We derive the action of the generalized projective transformation on the irreducible components of the affine geometry and determine the coupling relations defining the axial, metric-trace, and fully projectively invariant theories. Complete invariance reduces the $12$ gravitational coefficients to a five-parameter family and generates four vectorial Noether identities for the connection equations. Projective invariance makes the connection operator singular, thus we develop a symmetry-adapted method for solving its vacuum field equations. We then analyze couplings to Dirac, electromagnetic, and complex Klein-Gordon fields. Locally exact axial-projective transformations correspond to chiral rotations for massless fermions at the classical level, while a combination of covectors acts as an Abelian connection linking a locally exact vector-projective representative to scalar $U(1)$ symmetry. Standard Maxwell theory is independent of the affine connection, whereas a torsion-dependent Maxwell-like extension can preserve both electromagnetic and projective invariance through compensating Stückelberg fields. Exact gravitational projective invariance makes the corresponding connection directions nondynamical and forces matter currents sourcing them to vanish. Controlled explicit breaking lifts these zero modes and converts them into auxiliary fields. Thus, projective symmetry provides a unified principle for identifying affine gauge modes, constraining matter couplings, and relating symmetry breaking in the gravitational sector to effective matter interactions. less

We show that the space of vacuum initial data sets on a closed manifold often has many non-trivial homotopy groups. The starting point is a result of the second named author, which constructs non-trivial elements in the homotopy groups of the space of initial data sets satisfying the strict dominant energy condition, together with a later result in joint work with Bernd Ammann showing that these elements often persist when the strictness assumption is dropped. In this work, we use a parametrized version of the conformal method to show that these elements may also be represented by maps into the space of vacuum initial data sets. This requires two results that may be of independent interest: metrics admitting conformal Killing vectors can be removed from the space of metrics without changing its weak homotopy type, and over the remaining metrics the York decomposition can be carried out in families, the TT-tensors forming a trivial Hilbert bundle. To our knowledge, this is the first result on the global topology of this space. less

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