Search

In this paper, we investigate three schemes for implementing Controlled-NOT (CNOT) gates between individual ytterbium (Yb) rare-earth ions doped into yttrium orthovanadate (YVO$_4$ or YVO). Specifically, we investigate the CNOT gates based on magnetic dipolar interactions between Yb ions, photon scattering off a cavity, and a photon interference-based protocol, with and without an optical cavity. We introduce a theoretical framework for precise computations of gate infidelity, accounting for noise effects. We then compute the gate fidelity of each scheme to evaluate the feasibility of their experimental implementation. Based on these results, we compare the performance of the gate schemes and discuss their respective advantages and disadvantages. We conclude that the probabilistic photon interference-based scheme offers the best fidelity scaling with cooperativity and is superior with the current technology of Yb values, while photon scattering is nearly deterministic but slower with less favourable fidelity scaling as a function of cooperativity. The cavityless magnetic dipolar scheme provides a fast, deterministic gate with high fidelity if close ion localization can be realized., Comment: 18 pages, 11 figures

Measurement-based quantum computing offers a promising route towards scalable, universal photonic quantum computation. This approach relies on the deterministic and efficient generation of photonic graph states in which many photons are mutually entangled with various topologies. Recently, deterministic sources of graph states have been demonstrated with quantum emitters in both the optical and microwave domains. In this work, we demonstrate deterministic and reconfigurable graph state generation with optical solid-state integrated quantum emitters. Specifically, we use a single semiconductor quantum dot in a cavity to generate caterpillar graph states, the most general type of graph state that can be produced with a single emitter. By using fast detuned optical pulses, we achieve full control over the spin state, enabling us to vary the entanglement topology at will. We perform quantum state tomography of two successive photons, measuring Bell state fidelities up to 0.80$\pm$0.04 and concurrences up to 0.69$\pm$0.09, while maintaining high photon indistinguishability. This simple optical scheme, compatible with commercially available quantum dot-based single photon sources, brings us a step closer to fault-tolerant quantum computing with spins and photons.

We study the token swapping problem, in which we are given a graph with an initial assignment of one distinct token to each vertex, and a final desired assignment (again with one token per vertex). The goal is to find the minimum length sequence of swaps of adjacent tokens required to get from the initial to final assignment. The token swapping problem is known to be NP-complete. It is also known to have a polynomial-time 4-approximation algorithm. From the hardness-of-approximation side, it is known to be NP-hard to approximate with ratio better than 1001/1000. Our main result is an improvement of the approximation ratio of the lower bound: We show that it is NP-hard to approximate with ratio better than 14/13. We then turn our attention to the 0/1-weighted version, in which every token has a weight of either 0 or 1, and the cost of a swap is the sum of the weights of the two participating tokens. Unlike standard token swapping, no constant-factor approximation is known for this version, and we provide an explanation. We prove that 0/1-weighted token swapping is NP-hard to approximate with ratio better than $(1-\varepsilon) \ln(n)$ for any constant $\epsilon>0$. Lastly, we prove two barrier results for the standard (unweighted) token swapping problem. We show that one cannot beat the current best known approximation ratio of 4 using a large class of algorithms which includes all known algorithms, nor can one beat it using a common analysis framework., Comment: 23 pages, 3 figures

The frequency or color of photons is an attractive degree of freedom to encode and distribute the quantum information over long distances. However, the generation of frequency-encoded photonic qubits has so far relied on probabilistic non-linear single-photon sources and inefficient gates. Here, we demonstrate the deterministic generation of photonic qubits hyper-encoded in frequency and polarization based on a semiconductor quantum dot in a cavity. We exploit the double dipole structure of a neutral exciton and demonstrate the generation of any quantum superposition in amplitude and phase, controlled by the polarization of the pump laser pulse. The source generates frequency-polarization single-photon qubits at a rate of 4 MHz corresponding to a generation probability at the first lens of 28 $\pm$ 2%, with a photon number purity > 98%. The photons show an indistinguishability > 91% for each dipole and 88% for a balanced quantum superposition of both. The density matrix of the hyper-encoded photonic state is measured by time-resolved polarization tomography, evidencing a fidelity to the target state of 94 $\pm$ 8% and concurrence of 77 $\pm$ 2%, here limited by frequency overlap in our device. Our approach brings the advantages of quantum dot sources to the field of quantum information processing based on frequency encoding.

Secure Delegated Quantum Computation (SDQC) protocols are a vital piece of the future quantum information processing global architecture since they allow end-users to perform their valuable computations on remote quantum servers without fear that a malicious quantum service provider or an eavesdropper might acquire some information about their data or algorithm. They also allow end-users to check that their computation has been performed as they have specified it. However, existing protocols all have drawbacks that limit their usage in the real world. Most require the client to either operate a single-qubit source or perform single-qubit measurements, thus requiring them to still have some quantum technological capabilities albeit restricted, or require the server to perform operations which are hard to implement on real hardware (e.g isolate single photons from laser pulses and polarisation-preserving photon-number quantum non-demolition measurements). Others remove the need for quantum communications entirely but this comes at a cost in terms of security guarantees and memory overhead on the server's side. We present an SDQC protocol which drastically reduces the technological requirements of both the client and the server while providing information-theoretic composable security. More precisely, the client only manipulates an attenuated laser pulse, while the server only handles interacting quantum emitters with a structure capable of generating spin-photon entanglement. The quantum emitter acts as both a converter from coherent laser pulses to polarisation-encoded qubits and an entanglement generator. Such devices have recently been used to demonstrate the largest entangled photonic state to date, thus hinting at the readiness of our protocol for experimental implementations., Comment: 44 pages, 14 figures

$^{180}$Hg is experimentally found to fission asymmetrically. This result was not expected as a naive fragment shell effects study would support the symmetric mode to be the most probable. In the present study we investigate both symmetric and asymmetric $^{180}$Hg fission modes at the mean field level using various multipole moment constraints. Potential energy surfaces are analysed in terms of shell effects that shape their topographies and connections to fragment shell effects are made. The non-occurrence of low energy symmetric fission is interpreted in terms of $^{90}$Zr fragment properties. Throughout this study a comparison with $^{264}$Fm and its symmetric doubly magic $^{132}$Sn fission fragments is done., Comment: 20 pages,7 figures

Given a weighted graph $G$, a $(\beta,\varepsilon)$-hopset $H$ is an edge set such that for any $s,t \in V(G)$, where $s$ can reach $t$ in $G$, there is a path from $s$ to $t$ in $G \cup H$ which uses at most $\beta$ hops whose length is in the range $[dist_G(s,t), (1+\varepsilon)dist_G(s,t)]$. We break away from the traditional question that asks for a hopset that achieves small $|H|$ and instead study its sensitivity, a new quality measure which, informally, is the maximum number of times a vertex (or edge) is bypassed by an edge in $H$. The highlights of our results are: (i) $(\widetilde{O}(\sqrt{n}),0)$-hopsets on undirected graphs with $O(\log n)$ sensitivity, complemented with a lower bound showing that $\widetilde{O}(\sqrt{n})$ is tight up to polylogarithmic factors for any construction with polylogarithmic sensitivity. (ii) $(n^{o(1)},\varepsilon)$-hopsets on undirected graphs with $n^{o(1)}$ sensitivity for any $\varepsilon > 0$ that is at least inverse polylogarithmic, complemented with a lower bound on the tradeoff between $\beta, \varepsilon$, and the sensitivity. (iii) $\widetilde{O}(\sqrt{n})$-shortcut sets on directed graphs with $O(\log n)$ sensitivity, complemented with a lower bound showing that $\beta = \widetilde{\Omega}(n^{1/3})$ for any construction with polylogarithmic sensitivity. We believe hopset sensitivity is a natural measure in and of itself, and could potentially find use in a diverse range of contexts. More concretely, the notion of hopset sensitivity is also directly motivated by the Differentially Private All Sets Range Queries problem. Our result for $O(\log n)$ sensitivity $(\widetilde{O}(\sqrt{n}),0)$-hopsets on undirected graphs immediately improves the current best-known upper bound on utility from $\widetilde{O}(n^{1/3})$ to $\widetilde{O}(n^{1/4})$ in the pure-DP setting, which is tight up to polylogarithmic factors., Comment: Abstract shortened to meet arXiv requirements

The sequential resonant excitation of a 2-level quantum system results in the emission of a state of light showing time-entanglement encoded in the photon-number-basis - notions that can be extended to 3-level quantum systems as discussed in a recent proposal. Here, we report the experimental implementation of a sequential two-photon resonant excitation process of a solid-state 3-level system, constituted by the biexciton-, exciton-, and ground-state of a semiconductor quantum dot. The resulting light state exhibits entanglement in time and energy, encoded in the photon-number basis, which could be used in quantum information applications, e.g., dense information encoding or quantum communication protocols. Performing energy- and time-resolved correlation experiments in combination with extensive theoretical modelling, we are able to partially retrieve the entanglement structure of the generated state., Comment: 14 pages (including 5 figures, 56 citations)

Abstract Meaning Representation (AMR) is a semantic formalism that captures the core meaning of an utterance. There has been substantial work developing AMR corpora in English and more recently across languages, though the limited size of existing datasets and the cost of collecting more annotations are prohibitive. With both engineering and scientific questions in mind, we introduce MASSIVE-AMR, a dataset with more than 84,000 text-to-graph annotations, currently the largest and most diverse of its kind: AMR graphs for 1,685 information-seeking utterances mapped to 50+ typologically diverse languages. We describe how we built our resource and its unique features before reporting on experiments using large language models for multilingual AMR and SPARQL parsing as well as applying AMRs for hallucination detection in the context of knowledge base question answering, with results shedding light on persistent issues using LLMs for structured parsing.

Large Language Models (LLMs) have become capable of generating highly fluent text in certain languages, without modules specially designed to capture grammar or semantic coherence. What does this mean for the future of linguistic expertise in NLP? We highlight several aspects in which NLP (still) relies on linguistics, or where linguistic thinking can illuminate new directions. We argue our case around the acronym RELIES that encapsulates six major facets where linguistics contributes to NLP: Resources, Evaluation, Low-resource settings, Interpretability, Explanation, and the Study of language. This list is not exhaustive, nor is linguistics the main point of reference for every effort under these themes; but at a macro level, these facets highlight the enduring importance of studying machine systems vis-\`a-vis systems of human language.

Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally intractable. A canonical such problem is Tensor PCA, where we observe a tensor $Y$ consisting of a rank-one signal plus Gaussian noise. Multiple lines of work suggest that Tensor PCA becomes computationally hard at a critical value of the signal's magnitude. In particular, below this transition, no low-degree polynomial algorithm can detect the signal with high probability; conversely, various spectral algorithms are known to succeed above this transition. We unify and extend this work by considering tensor networks, orthogonally invariant polynomials where multiple copies of $Y$ are "contracted" to produce scalars, vectors, matrices, or other tensors. We define a new set of objects, tensor cumulants, which provide an explicit, near-orthogonal basis for invariant polynomials of a given degree. This basis lets us unify and strengthen previous results on low-degree hardness, giving a combinatorial explanation of the hardness transition and of a continuum of subexponential-time algorithms that work below it, and proving tight lower bounds against low-degree polynomials for recovering rather than just detecting the signal. It also lets us analyze a new problem of distinguishing between different tensor ensembles, such as Wigner and Wishart tensors, establishing a sharp computational threshold and giving evidence of a new statistical-computational gap in the Central Limit Theorem for random tensors. Finally, we believe these cumulants are valuable mathematical objects in their own right: they generalize the free cumulants of free probability theory from matrices to tensors, and share many of their properties, including additivity under additive free convolution., Comment: 72 pages, 12 figures

We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+\Omega(n^{3/17})$, improving on the previous best lower bound of $\Omega(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the first two steps of a particular three-step research program, introduced in prior work and overviewed here, aimed at producing tight bounds for the problem by aligning aspects of the upper and lower bound constructions. More specifically, we develop techniques that enable the use of inner graphs in the lower bound framework whose technical properties are provably tight with the corresponding assumptions made in the upper bounds. As an additional application of our techniques, we improve the corresponding lower bound for $O(n)$-size additive emulators to $+\Omega(n^{1/14})$., Comment: ICALP 2024

In the $k$-Disjoint Shortest Paths ($k$-DSP) problem, we are given a weighted graph $G$ on $n$ nodes and $m$ edges with specified source vertices $s_1, \dots, s_k$, and target vertices $t_1, \dots, t_k$, and are tasked with determining if $G$ contains vertex-disjoint $(s_i,t_i)$-shortest paths. For any constant $k$, it is known that $k$-DSP can be solved in polynomial time over undirected graphs and directed acyclic graphs (DAGs). However, the exact time complexity of $k$-DSP remains mysterious, with large gaps between the fastest known algorithms and best conditional lower bounds. In this paper, we obtain faster algorithms for important cases of $k$-DSP, and present better conditional lower bounds for $k$-DSP and its variants. Previous work solved 2-DSP over weighted undirected graphs in $O(n^7)$ time, and weighted DAGs in $O(mn)$ time. For the main result of this paper, we present linear time algorithms for solving 2-DSP on weighted undirected graphs and DAGs. Our algorithms are algebraic however, and so only solve the detection rather than search version of 2-DSP. For lower bounds, prior work implied that $k$-Clique can be reduced to $2k$-DSP in DAGs and undirected graphs with $O((kn)^2)$ nodes. We improve this reduction, by showing how to reduce from $k$-Clique to $k$-DSP in DAGs and undirected graphs with $O((kn)^2)$ nodes. A variant of $k$-DSP is the $k$-Disjoint Paths ($k$-DP) problem, where the solution paths no longer need to be shortest paths. Previous work reduced from $k$-Clique to $p$-DP in DAGs with $O(kn)$ nodes, for $p= k + k(k-1)/2$. We improve this by showing a reduction from $k$-Clique to $p$-DP, for $p=k + \lfloor k^2/4\rfloor$. Under the $k$-Clique Hypothesis from fine-grained complexity, our results establish better conditional lower bounds for $k$-DSP for all $k\ge 4$, and better conditional lower bounds for $p$-DP for all $p\le 4031$., Comment: Added reference

A novel approach for creating tool paths for continuous carbon fiber-reinforced thermoplastic 3D printing is introduced. The aim is to enable load-bearing connections while avoiding non-manufacturable crossings of paths by generating layer specific patterns. We require a graph representation of the structural design with given desired continuous fiber connections. From this, optimal fiber patterns are obtained for each printing layer by solving linear integer optimization problems. Each layer may have a unique solution based on the history of the previous layers. Additionally, a path planning approach is presented which interprets the obtained layers via curves based on quadratic and cubic B\'ezier splines and their offset curves in constant distance. The single parameter for the construction of the paths is the minimal turning radius of the fibers. The path planning provides a new interpretation for the final geometry of the design to be printed., Comment: 29 pages (single column), 29 figures

Additively manufactured structures often exhibit a correlation between their mechanical properties, such as stiffness, strength, and porosity, and their wall thickness. This correlation stems from the interplay between the manufacturing process and the properties of the filler material. In this study, we investigate the thickness-dependent effect on structural stiffness and propose a nonlocal integral model that introduces surface grading of Young's modulus to capture this phenomenon. We incorporate this model into topology optimization for designing structures with optimized compliance subject to a volume constraint. Notably, elastically degraded surfaces penalize excessively thin features, effectively eliminating them from the optimized design. We showcase the efficacy of our proposed framework by optimizing the design of a two-dimensional cantilever beam and a bridge.

We consider the problem of detecting a planted clique of size $k$ in a random graph on $n$ vertices. When the size of the clique exceeds $\Theta(\sqrt{n})$, polynomial-time algorithms for detection proliferate. We study faster -- namely, sublinear time -- algorithms in the high-signal regime when $k = \Theta(n^{1/2 + \delta})$, for some $\delta > 0$. To this end, we consider algorithms that non-adaptively query a subset $M$ of entries of the adjacency matrix and then compute a low-degree polynomial function of the revealed entries. We prove a computational phase transition for this class of non-adaptive low-degree algorithms: under the scaling $\lvert M \rvert = \Theta(n^{\gamma})$, the clique can be detected when $\gamma > 3(1/2 - \delta)$ but not when $\gamma < 3(1/2 - \delta)$. As a result, the best known runtime for detecting a planted clique, $\widetilde{O}(n^{3(1/2-\delta)})$, cannot be improved without looking beyond the non-adaptive low-degree class. Our proof of the lower bound -- based on bounding the conditional low-degree likelihood ratio -- reveals further structure in non-adaptive detection of a planted clique. Using (a bound on) the conditional low-degree likelihood ratio as a potential function, we show that for every non-adaptive query pattern, there is a highly structured query pattern of the same size that is at least as effective., Comment: 23 pages, 2 figures

We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth $n \tau$, representing the hidden one-dimensional geometry of vertices, is planted in an ambient random graph on $n$ vertices. For both detection and recovery of the planted dense cycle, we characterize the information-theoretic thresholds in terms of $n$, $\tau$, and an edge-wise signal-to-noise ratio $\lambda$. In particular, the information-theoretic thresholds differ from the computational thresholds established in a recent work for low-degree polynomial algorithms, thereby justifying the existence of statistical-to-computational gaps for this problem., Comment: 31 pages, 1 figure

Quantum emitters such as quantum dots, defects in diamond or in silicon have emerged as efficient single photon sources that are progressively exploited in quantum technologies. In 2019, it was shown that the emitted single photon states often include coherence with the vacuum component. Here we investigate how such photon-number coherence alters quantum interference experiments that are routinely implemented both for characterising or exploiting the generated photons. We show that it strongly modifies intensity correlation measurements in a Hong-Ou-Mandel experiment and leads to errors in indistinguishability estimations. It also results in additional entanglement when performing partial measurements. We illustrate the impact on quantum protocols by evidencing modifications in heralding efficiency and fidelity of two-qubit gates., Comment: 15 pages, 6 figures

The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results regarding the quality of approximation obtained by MP and SA (with polynomially many iterations) for NP-hard optimization problems. We provide rigorous lower bounds for MP and SA with respect to the classical maximum independent set problem when the algorithms are initialized from the empty set. We establish the existence of a family of graphs for which both MP and SA fail to find approximate solutions in polynomial time. More specifically, we show that for any $\varepsilon \in (0,1)$ there are $n$-vertex graphs for which the probability SA (when limited to polynomially many iterations) will approximate the optimal solution within ratio $\Omega\left(\frac{1}{n^{1-\varepsilon}}\right)$ is exponentially small. Our lower bounds extend to graphs of constant average degree $d$, illustrating the failure of MP to achieve an approximation ratio of $\Omega\left(\frac{\log (d)}{d}\right)$ in polynomial time. In some cases, our impossibility results also go beyond Simulated Annealing and apply even when the temperature is chosen adaptively. Finally, we prove time lower bounds when the inputs to these algorithms are bipartite graphs, and even trees, which are known to admit polynomial-time algorithms for the independent set problem., Comment: 44 pages

In this review, we describe the current landscape of emergent quantum materials for quantum photonic applications. We focus on three specific solid-state platforms: single emitters in monolayers of transition metal dichalcogenides, defects in hexagonal boron nitride, and colloidal quantum dots in perovskites. These platforms share a unique technological accessibility, enabling the rapid implementation of testbed quantum applications, all while being on the verge of becoming technologically mature enough for a first generation of real-world quantum applications. The review begins with a comprehensive overview of the current state-of-the-art for relevant single-photon sources in the solid-state, introducing the most important performance criteria and experimental characterization techniques along the way. We then benchmark progress for each of the three novel materials against more established (yet complex) platforms, highlighting performance, material-specific advantages, and giving an outlook on quantum applications. This review will thus provide the reader with a snapshot on latest developments in the fast-paced field of emergent single-photon sources in the solid-state, including all the required concepts and experiments relevant to this technology., Comment: 35 pages, 8 figures, review paper

We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based approaches. A key feature of the architecture is its practicality, grounded in the utilisation of experimentally proven optical components. Our framework enables the execution of any quantum error correcting code, but in particular maintains scalability for low-density parity check codes by exploiting built-in non-local connectivity through distant optical links. To gauge its efficiency, we evaluated the architecture using a physically motivated error model. It exhibits loss tolerance comparable to existing all-photonic architecture but without the need for intricate linear-optical resource-state-generation modules that conventionally rely on resource-intensive multiplexing. The versatility of the architecture also offers uncharted avenues for further advancing performance standards., Comment: 29 pages, 10 figures. Accepted Quantum journal

We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional settings. In the classical spiked Wigner model (with a general i.i.d. spike prior) we show that an existing test based on linear spectral statistics achieves the best possible tradeoff curve between type I and type II error rates among all computationally efficient tests, even though there are exponential-time tests that do better. This result is conditional on an appropriate complexity-theoretic conjecture, namely a natural strengthening of the well-established low-degree conjecture. Our result shows that the spectrum is a sufficient statistic for computationally bounded tests (but not for all tests). To our knowledge, our approach gives the first tool for reasoning about the precise asymptotic testing error achievable with efficient computation. The main ingredients required for our hardness result are a sharp bound on the norm of the low-degree likelihood ratio along with (counterintuitively) a positive result on achievability of testing. This strategy appears to be new even in the setting of unbounded computation, in which case it gives an alternate way to analyze the fundamental statistical limits of testing., Comment: 30 pages, 1 figure

The aspect ratio of a (positively) weighted graph $G$ is the ratio of its maximum edge weight to its minimum edge weight. Aspect ratio commonly arises as a complexity measure in graph algorithms, especially related to the computation of shortest paths. Popular paradigms are to interpolate between the settings of weighted and unweighted input graphs by incurring a dependence on aspect ratio, or by simply restricting attention to input graphs of low aspect ratio. This paper studies the effects of these paradigms, investigating whether graphs of low aspect ratio have more structured shortest paths than graphs in general. In particular, we raise the question of whether one can generally take a graph of large aspect ratio and reweight its edges, to obtain a graph with bounded aspect ratio while preserving the structure of its shortest paths. Our findings are: - Every weighted DAG on $n$ nodes has a shortest-paths preserving graph of aspect ratio $O(n)$. A simple lower bound shows that this is tight. - The previous result does not extend to general directed or undirected graphs; in fact, the answer turns out to be exponential in these settings. In particular, we construct directed and undirected $n$-node graphs for which any shortest-paths preserving graph has aspect ratio $2^{\Omega(n)}$. We also consider the approximate version of this problem, where the goal is for shortest paths in $H$ to correspond to approximate shortest paths in $G$. We show that our exponential lower bounds extend even to this setting. We also show that in a closely related model, where approximate shortest paths in $H$ must also correspond to approximate shortest paths in $G$, even DAGs require exponential aspect ratio., Comment: ITCS 2024

Many applications of quantum optics demand delicate quantum properties of light carefully tailored to accomplish a specific task. To this end, numerical simulations of quantum light sources are vital for designing, characterizing, and optimizing quantum photonic technology. Here, I show that exploiting information hidden in zero-photon measurement outcomes provides an exponential speedup for time-integrated photon counting simulations, realizing eight orders of magnitude reduction in the time to compute six-photon detection probabilities while achieving ten orders of magnitude higher precision compared to the state of the art. This enables simulations of large photonic experiments with an unprecedented level of physical detail. It can accelerate the design of sources to generate photonic resource states for quantum sensing and measurement-based quantum computing while capturing realistic imperfections. It also establishes a general theoretical framework to study dynamic interactions between stationary qubits mediated by measurements of flying qubits, which can be used to model distributed quantum computing and quantum communication., Comment: 9 pages, 3 figures

Multimodal image registration is a challenging but essential step for numerous image-guided procedures. Most registration algorithms rely on the computation of complex, frequently non-differentiable similarity metrics to deal with the appearance discrepancy of anatomical structures between imaging modalities. Recent Machine Learning based approaches are limited to specific anatomy-modality combinations and do not generalize to new settings. We propose a generic framework for creating expressive cross-modal descriptors that enable fast deformable global registration. We achieve this by approximating existing metrics with a dot-product in the feature space of a small convolutional neural network (CNN) which is inherently differentiable can be trained without registered data. Our method is several orders of magnitude faster than local patch-based metrics and can be directly applied in clinical settings by replacing the similarity measure with the proposed one. Experiments on three different datasets demonstrate that our approach generalizes well beyond the training data, yielding a broad capture range even on unseen anatomies and modality pairs, without the need for specialized retraining. We make our training code and data publicly available., Comment: This preprint was submitted to MICCAI 2023. The Version of Record of this contribution will be published in Springer LNCS

Quantum computing aims at exploiting quantum phenomena to efficiently perform computations that are unfeasible even for the most powerful classical supercomputers. Among the promising technological approaches, photonic quantum computing offers the advantages of low decoherence, information processing with modest cryogenic requirements, and native integration with classical and quantum networks. To date, quantum computing demonstrations with light have implemented specific tasks with specialized hardware, notably Gaussian Boson Sampling which permitted quantum computational advantage to be reached. Here we report a first user-ready general-purpose quantum computing prototype based on single photons. The device comprises a high-efficiency quantum-dot single-photon source feeding a universal linear optical network on a reconfigurable chip for which hardware errors are compensated by a machine-learned transpilation process. Our full software stack allows remote control of the device to perform computations via logic gates or direct photonic operations. For gate-based computation we benchmark one-, two- and three-qubit gates with state-of-the art fidelities of $99.6\pm0.1 \%$, $93.8\pm0.6 \%$ and $86\pm1.2 \%$ respectively. We also implement a variational quantum eigensolver, which we use to calculate the energy levels of the hydrogen molecule with high accuracy. For photon native computation, we implement a classifier algorithm using a $3$-photon-based quantum neural network and report a first $6$-photon Boson Sampling demonstration on a universal reconfigurable integrated circuit. Finally, we report on a first heralded 3-photon entanglement generation, a key milestone toward measurement-based quantum computing.

The task of natural language inference (NLI) asks whether a given premise (expressed in NL) entails a given NL hypothesis. NLI benchmarks contain human ratings of entailment, but the meaning relationships driving these ratings are not formalized. Can the underlying sentence pair relationships be made more explicit in an interpretable yet robust fashion? We compare semantic structures to represent premise and hypothesis, including sets of contextualized embeddings and semantic graphs (Abstract Meaning Representations), and measure whether the hypothesis is a semantic substructure of the premise, utilizing interpretable metrics. Our evaluation on three English benchmarks finds value in both contextualized embeddings and semantic graphs; moreover, they provide complementary signals, and can be leveraged together in a hybrid model., Comment: International Conference on Computational Semantics (IWCS 2023); v2 fixes an imprecise sentence below Eq. 5

Translated texts bear several hallmarks distinct from texts originating in the language. Though individual translated texts are often fluent and preserve meaning, at a large scale, translated texts have statistical tendencies which distinguish them from text originally written in the language ("translationese") and can affect model performance. We frame the novel task of translationese reduction and hypothesize that Abstract Meaning Representation (AMR), a graph-based semantic representation which abstracts away from the surface form, can be used as an interlingua to reduce the amount of translationese in translated texts. By parsing English translations into an AMR and then generating text from that AMR, the result more closely resembles originally English text across three quantitative macro-level measures, without severely compromising fluency or adequacy. We compare our AMR-based approach against three other techniques based on machine translation or paraphrase generation. This work makes strides towards reducing translationese in text and highlights the utility of AMR as an interlingua., Comment: EACL 2024 Camera-ready

Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem that has been extensively studied in recent years. We study a hypergraph version of the problem. Let $G^r(n,p)$ denote the $r$-uniform Erd\H{o}s-R\'enyi hypergraph model with $n$ vertices and edge density $p$. We consider detecting the presence of a planted $G^r(n^\gamma, n^{-\alpha})$ subhypergraph in a $G^r(n, n^{-\beta})$ hypergraph, where $0< \alpha < \beta < r-1$ and $0 < \gamma < 1$. Focusing on tests that are degree-$n^{o(1)}$ polynomials of the entries of the adjacency tensor, we determine the threshold between the easy and hard regimes for the detection problem. More precisely, for $0 < \gamma < 1/2$, the threshold is given by $\alpha = \beta \gamma$, and for $1/2 \le \gamma < 1$, the threshold is given by $\alpha = \beta/2 + r(\gamma - 1/2)$. Our results are already new in the graph case $r=2$, as we consider the subtle log-density regime where hardness based on average-case reductions is not known. Our proof of low-degree hardness is based on a conditional variant of the standard low-degree likelihood calculation., Comment: 31 pages

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties compared to parts where only coarse features are included. One of these improvements is better global buckling resistance of the component. However, thin features are prone to local buckling. Normally, analyses with high computational effort are conducted on high-resolution finite element meshes to optimize parts with good global and local stability. Until recently, works focused only on either global or local buckling behavior. We use two-scale optimization based on asymptotic homogenization of elastic properties and local buckling behavior to reduce the effort of full-scale analyses. For this, we present an approach for concurrent local and global buckling optimization of parameterized graded lattice structures. It is based on a worst-case model for the homogenized buckling load factor, which acts as a safeguard against pure local buckling. Cross-modes residing on both scales are not detected. We support our theory with numerical examples and validations on dehomogenized designs, which show the capabilities of our method, and discuss the advantages and limitations of the worst-case model., Comment: submitted to Structural and Multidisciplinary Optimization

We study the computational complexity of two related problems: recovering a planted $q$-coloring in $G(n,1/2)$, and finding efficiently verifiable witnesses of non-$q$-colorability (a.k.a. refutations) in $G(n,1/2)$. Our main results show hardness for both these problems in a restricted-but-powerful class of algorithms based on computing low-degree polynomials in the inputs. The problem of recovering a planted $q$-coloring is equivalent to recovering $q$ disjoint planted cliques that cover all the vertices -- a potentially easier variant of the well-studied planted clique problem. Our first result shows that this variant is as hard as the original planted clique problem in the low-degree polynomial model of computation: each clique needs to have size $k \gg \sqrt{n}$ for efficient recovery to be possible. For the related variant where the cliques cover a $(1-\epsilon)$-fraction of the vertices, we also show hardness by reduction from planted clique. Our second result shows that refuting $q$-colorability of $G(n,1/2)$ is hard in the low-degree polynomial model when $q \gg n^{2/3}$ but easy when $q \lesssim n^{1/2}$, and we leave closing this gap for future work. Our proof is more subtle than similar results for planted clique and involves constructing a non-standard distribution over $q$-colorable graphs. We note that while related to several prior works, this is the first work that explicitly formulates refutation problems in the low-degree polynomial model. The proofs of our main results involve showing low-degree hardness of hypothesis testing between an appropriately constructed pair of distributions. For refutation, we show completeness of this approach: in the low-degree model, the refutation task is precisely as hard as the hardest associated testing problem, i.e., proving hardness of refutation amounts to finding a "hard" distribution., Comment: 23 pages

Planted dense cycles are a type of latent structure that appears in many applications, such as small-world networks in social sciences and sequence assembly in computational biology. We consider a model where a dense cycle with expected bandwidth $n \tau$ and edge density $p$ is planted in an Erd\H{o}s-R\'enyi graph $G(n,q)$. We characterize the computational thresholds for the associated detection and recovery problems for the class of low-degree polynomial algorithms. In particular, a gap exists between the two thresholds in a certain regime of parameters. For example, if $n^{-3/4} \ll \tau \ll n^{-1/2}$ and $p = C q = \Theta(1)$ for a constant $C>1$, the detection problem is computationally easy while the recovery problem is hard for low-degree algorithms., Comment: 41 pages, 1 figure

Random graph models with community structure have been studied extensively in the literature. For both the problems of detecting and recovering community structure, an interesting landscape of statistical and computational phase transitions has emerged. A natural unanswered question is: might it be possible to infer properties of the community structure (for instance, the number and sizes of communities) even in situations where actually finding those communities is believed to be computationally hard? We show the answer is no. In particular, we consider certain hypothesis testing problems between models with different community structures, and we show (in the low-degree polynomial framework) that testing between two options is as hard as finding the communities. In addition, our methods give the first computational lower bounds for testing between two different `planted' distributions, whereas previous results have considered testing between a planted distribution and an i.i.d. `null' distribution., Comment: Accepted to Innovations in Theoretical Computer Science (ITCS) 2023