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We present and experimentally demonstrate a novel approach to verification and benchmarking of quantum computing, implementing it on an ion-trap quantum computer. Unlike previous information-theoretically secure verification protocols, which typically require quantum communication between client and server, our approach is implemented entirely on-chip. This eliminates the need for a quantum client and significantly enhances practicality. We perform tomography to justify the additionally required assumption that the noise is independent of the secret used to prepare the Server's single-qubit states. We quantify the soundness error which may be caused by residual secret dependencies. We demonstrate our protocol on the 20-qubit Quantinuum H1-1 ion-trap quantum processing unit, using qubit measurements and resets to construct measurement patterns with up to 52 vertices. To our knowledge, these are the largest verified measurement-based quantum computations performed to date. Our results pave the way for more accessible and efficient verification and benchmarking strategies in near-term quantum devices, enabling robust performance assessment without the added cost of external quantum infrastructure., Comment: 17 pages, 7 figures, comments welcome

Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel $\Phi$ and a known concept class $\mathcal{C}$ of channels, output a quantum channel that approximates $\Phi$ as well as any channel in the concept class $\mathcal{C}$, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by $\mathsf{QAC}^0$ circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one., Comment: 11+52 pages, 2 figures, 1 table

We introduce PointNet-KAN, a neural network for 3D point cloud classification and segmentation tasks, built upon two key components. First, it employs Kolmogorov-Arnold Networks (KANs) instead of traditional Multilayer Perceptrons (MLPs). Second, it retains the core principle of PointNet by using shared KAN layers and applying symmetric functions for global feature extraction, ensuring permutation invariance with respect to the input features. In traditional MLPs, the goal is to train the weights and biases with fixed activation functions; however, in KANs, the goal is to train the activation functions themselves. We use Jacobi polynomials to construct the KAN layers. We extensively evaluate PointNet-KAN across various polynomial degrees and special types such as the Lagrange, Chebyshev, and Gegenbauer polynomials. Our results show that PointNet-KAN achieves competitive performance compared to PointNet with MLPs on benchmark datasets for 3D object classification and segmentation, despite employing a shallower and simpler network architecture. We hope this work serves as a foundation and provides guidance for integrating KANs, as an alternative to MLPs, into more advanced point cloud processing architectures.

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, magic and coherence are arguably of great significance. We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical simulation, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers., Comment: 6 pages, 1 figure, 13 pages of appendix

We propose a new scheme for near-term photonic quantum device that allows to increase the expressive power of the quantum models beyond what linear optics can do. This scheme relies upon state injection, a measurement-based technique that can produce states that are more controllable, and solve learning tasks that are not believed to be tackled classically. We explain how circuits made of linear optical architectures separated by state injections are keen for experimental implementation. In addition, we give theoretical results on the evolution of the purity of the resulting states, and we discuss how it impacts the distinguishability of the circuit outputs. Finally, we study a computational subroutines of learning algorithms named probability estimation, and we show the state injection scheme we propose may offer a potential quantum advantage in a regime that can be more easily achieved that state-of-the-art adaptive techniques. Our analysis offers new possibilities for near-term advantage that require to tackle fewer experimental difficulties.

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.

We present Kolmogorov-Arnold PointNet (KA-PointNet) as a novel supervised deep learning framework for the prediction of incompressible steady-state fluid flow fields in irregular domains, where the predicted fields are a function of the geometry of the domains. In KA-PointNet, we implement shared Kolmogorov-Arnold Networks (KANs) in the segmentation branch of the PointNet architecture. We utilize Jacobi polynomials to construct shared KANs. As a benchmark test case, we consider incompressible laminar steady-state flow over a cylinder, where the geometry of its cross-section varies over the data set. We investigate the performance of Jacobi polynomials with different degrees as well as special cases of Jacobi polynomials such as Legendre polynomials, Chebyshev polynomials of the first and second kinds, and Gegenbauer polynomials, in terms of the computational cost of training and accuracy of prediction of the test set. Additionally, we compare the performance of PointNet with shared KANs (i.e., KA-PointNet) and PointNet with shared Multilayer Perceptrons (MLPs). It is observed that when the number of trainable parameters is approximately equal, PointNet with shared KANs (i.e., KA-PointNet) outperforms PointNet with shared MLPs.

The exploitation of certification tools by end users represents a fundamental aspect of the development of quantum technologies as the hardware scales up beyond the regime of classical simulatability. Certifying quantum networks becomes even more crucial when the privacy of their users is exposed to malicious quantum nodes or servers as in the case of multi-client distributed blind quantum computing, where several clients delegate a joint private computation to remote quantum servers, such as federated quantum machine learning. In such protocols, security must be provided not only by keeping data hidden but also by verifying that the server is correctly performing the requested computation while minimizing the hardware assumptions on the employed devices. Notably, standard verification techniques fail in scenarios where the clients receive quantum states from untrusted sources such as, for example, in a recently demonstrated linear quantum network performing multi-client blind quantum computation. However, recent theoretical results provide techniques to verify blind quantum computations even in the case of untrusted state preparation. Equipped with such theoretical tools, in this work, we provide the first experimental implementation of a two-client verifiable blind quantum computing protocol in a distributed architecture. The obtained results represent novel perspectives for the verification of multi-tenant distributed quantum computation in large-scale networks., Comment: Minor changes in the description of the experimental setup

Anomaly detection involves identifying instances within a dataset that deviate from the norm and occur infrequently. Current benchmarks tend to favor methods biased towards low diversity in normal data, which does not align with real-world scenarios. Despite advancements in these benchmarks, contemporary anomaly detection methods often struggle with out-of-distribution generalization, particularly in classifying samples with subtle transformations during testing. These methods typically assume that normal samples during test time have distributions very similar to those in the training set, while anomalies are distributed much further away. However, real-world test samples often exhibit various levels of distribution shift while maintaining semantic consistency. Therefore, effectively generalizing to samples that have undergone semantic-preserving transformations, while accurately detecting normal samples whose semantic meaning has changed after transformation as anomalies, is crucial for the trustworthiness and reliability of a model. For example, although it is clear that rotation shifts the meaning for a car in the context of anomaly detection but preserves the meaning for a bird, current methods are likely to detect both as abnormal. This complexity underscores the necessity for dynamic learning procedures rooted in the intrinsic concept of outliers. To address this issue, we propose new testing protocols and a novel method called Knowledge Exposure (KE), which integrates external knowledge to comprehend concept dynamics and differentiate transformations that induce semantic shifts. This approach enhances generalization by utilizing insights from a pre-trained CLIP model to evaluate the significance of anomalies for each concept. Evaluation on CIFAR-10, CIFAR-100, and SVHN with the new protocols demonstrates superior performance compared to previous methods.

In this technical report, we extensively investigate the accuracy of outputs from well-known generative artificial intelligence (AI) applications in response to prompts describing common fluid motion phenomena familiar to the fluid mechanics community. We examine a range of applications, including Midjourney, Dall-E, Runway ML, Microsoft Designer, Gemini, Meta AI, and Leonardo AI, introduced by prominent companies such as Google, OpenAI, Meta, and Microsoft. Our text prompts for generating images or videos include examples such as "Von Karman vortex street", "flow past an airfoil", "Kelvin-Helmholtz instability", "shock waves on a sharp-nosed supersonic body", etc. We compare the images generated by these applications with real images from laboratory experiments and numerical software. Our findings indicate that these generative AI models are not adequately trained in fluid dynamics imagery, leading to potentially misleading outputs. Beyond text-to-image/video generation, we further explore the transition from image/video to text generation using these AI tools, aiming to investigate the accuracy of their descriptions of fluid motion phenomena. This report serves as a cautionary note for educators in academic institutions, highlighting the potential for these tools to mislead students. It also aims to inform researchers at these renowned companies, encouraging them to address this issue. We conjecture that a primary reason for this shortcoming is the limited access to copyright-protected fluid motion images from scientific journals.

The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates for each random operation. We introduce a version of the RB protocol that creates Haar-randomness using a directly accessible universal gate set of equal sequence length rather than relying upon a t-design or even an approximate one. This makes our protocol highly resource efficient and practical for small qubit numbers. We exemplify our protocol for creating Haar-randomness in the case of single and two qubits. Benchmarking our result with the standard RB protocol, allows us to calculate the overestimation of the average gate fidelity as compared to the standard technique. We augment our findings with a noise analysis which demonstrates that our method could be an effective tool for building accurate models of experimental noise., Comment: 13 pages, 11 figures

The relevance of shallow-depth quantum circuits has recently increased, mainly due to their applicability to near-term devices. In this context, one of the main goals of quantum circuit complexity is to find problems that can be solved by quantum shallow circuits but require more computational resources classically. Our first contribution in this work is to prove new separations between classical and quantum constant-depth circuits. Firstly, we show a separation between constant-depth quantum circuits with quantum advice $\mathsf{QNC}^0/\mathsf{qpoly}$, and $\mathsf{AC}^0[p]$, which is the class of classical constant-depth circuits with unbounded-fan in and $\pmod{p}$ gates. In addition, we show a separation between $\mathsf{QAC}^0$, which additionally has Toffoli gates with unbounded control, and $\mathsf{AC}^0[p]$. This establishes the first such separation for a shallow-depth quantum class that does not involve quantum fan-out gates. Secondly, we consider $\mathsf{QNC}^0$ circuits with infinite-size gate sets. We show that these circuits, along with (classical or quantum) prime modular gates, can implement threshold gates, showing that $\mathsf{QNC}^0[p]=\mathsf{QTC}^0$. Finally, we also show that in the infinite-size gateset case, these quantum circuit classes for higher-dimensional Hilbert spaces do not offer any advantage to standard qubit implementations.

In this paper, we introduce a new approach to quantum benchmarking inspired by quantum verification motivating new paradigms of quantum benchmarking. Our proposed benchmark not only serves as a robust indicator of computational capability but also offers scalability, customizability, and universality. By providing formal statements regarding the quality of quantum devices while assuming device consistency, we eliminate the reliance on heuristics. We establish a deep connection between quantum verification and quantum benchmarking. For practical application, we present a concrete benchmarking protocol derived from a quantum verification protocol, and prove it to match our redefined standards for quantum benchmarking., Comment: 19 pages

Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. This will be an essential building block for near- and middle-term quantum ecosystems before the availability of full fault tolerance, where one may want to suppress errors not only in expectation values but also in quantum states. We propose an effective state purification gadget with a moderate quantum overhead by projecting $M$ noisy quantum inputs to their symmetric subspace defined by a set of projectors forming a symmetric subgroup with order $M$. Our method, applied in every short evolution over $M$ redundant copies of noisy states, can suppress both coherent and stochastic errors by a factor of $1/M$, respectively. This reduces the circuit implementation cost $M$ times smaller than the state projection to the full symmetric subspace proposed by Barenco et al. more than two decades ago. We also show that our gadget purifies the depolarised inputs with probability $p$ to asymptotically $O\left(p^{2}\right)$ with an optimal choice of $M$ when $p$ is small. The sampling cost scales $O\left(p^{-1}\right)$ for small $p$, which is also shown to be asymptotically optimal. Our method provides flexible choices of state purification depending on the hardware restrictions before fully fault-tolerant computation is available., Comment: 32 pages, 14 figures

With the advent of delegated quantum computing as a service, verifying quantum computations is becoming a question of great importance. Existing information theoretically Secure Delegated Quantum Computing (SDQC) protocols require the client to possess the ability to perform either trusted state preparations or measurements. Whether it is possible to verify universal quantum computations with information-theoretic security without trusted preparations or measurements was an open question so far. In this paper, we settle this question in the affirmative by presenting a modular, composable, and efficient way to turn known verification schemes into protocols that rely only on trusted gates. Our first contribution is an extremely lightweight reduction of the problem of quantum verification for BQP to the trusted application of single-qubit rotations around the Z axis and bit flips. The second construction presented in this work shows that it is generally possible to information-theoretically verify arbitrary quantum computations with quantum output without trusted preparations or measurements. However, this second protocol requires the verifier to perform multi-qubit gates on a register whose size is independent of the size of the delegated computation., Comment: 15+12 pages, 4 figures

In this work, we highlight an unforeseen behavior of the expressivity of Parameterized Quantum Circuits (PQC) for machine learning. A large class of these models, seen as Fourier Series which frequencies are derived from the encoding gates, were thought to have their Fourier coefficients mostly determined by the trainable gates. Here, we demonstrate a new correlation between the Fourier coefficients of the quantum model and its encoding gates. In addition, we display a phenomenon of vanishing expressivity in certain settings, where some Fourier coefficients vanish exponentially when the number of qubits grows. These two behaviors imply novel forms of constraints which limit the expressivity of PQCs, and therefore imply a new inductive bias for Quantum models. The key concept in this work is the notion of a frequency redundancy in the Fourier series spectrum, which determines its importance. Those theoretical behaviours are observed in numerical simulations.

Fourier neural operators (FNOs) are invariant with respect to the size of input images, and thus images with any size can be fed into FNO-based frameworks without any modification of network architectures, in contrast to traditional convolutional neural networks (CNNs). Leveraging the advantage of FNOs, we propose a novel deep-learning framework for classifying images with varying sizes. Particularly, we simultaneously train the proposed network on multi-sized images. As a practical application, we consider the problem of predicting the label (e.g., permeability) of three-dimensional digital porous media. To construct the framework, an intuitive approach is to connect FNO layers to a classifier using adaptive max pooling. First, we show that this approach is only effective for porous media with fixed sizes, whereas it fails for porous media of varying sizes. To overcome this limitation, we introduce our approach: instead of using adaptive max pooling, we use static max pooling with the size of channel width of FNO layers. Since the channel width of the FNO layers is independent of input image size, the introduced framework can handle multi-sized images during training. We show the effectiveness of the introduced framework and compare its performance with the intuitive approach through the example of the classification of three-dimensional digital porous media of varying sizes.