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We explore the important task of applying a phase $exp(i f(x))$ to a computational basis state $\left| x \right>$. The closely related task of rotating a target qubit by an angle depending on $f(x)$ is also studied. Such operations are key in many quantum subroutines, and often the function $f$ can be well-approximated by a piecewise linear composition. Examples range from the application of diagonal Hamiltonian terms (such as the Coulomb interaction) in grid-based many-body simulation, to derivative pricing algorithms. Here we exploit a parallelisation of the piecewise approach so that all constituent elementary rotations are performed simultaneously, that is, we achieve a total rotation depth of one. Moreover, we explore the use of recursive catalyst 'towers' to implement these elementary rotations efficiently. Depending on the choice of implementation strategy, we find a depth as low as $O(log n + log S)$ for a register of $n$ qubits and a piecewise approximation of $S$ sections. In the limit of multiple repetitions of the oracle, we find that catalyst tower approaches have an $O(S \cdot n)$ T-count, whereas linear interpolation with QROM has an $O(n^{log_2(3)})$ T-count., Comment: 14 pages, references added, table I updated, code for table I added

In data exploration, users need to analyze large data files quickly, aiming to minimize data-to-analysis time. While recent adaptive indexing approaches address this need, they are cases where demonstrate poor performance. Particularly, during the initial queries, in regions with a high density of objects, and in very large files over commodity hardware. This work introduces an approach for adaptive indexing driven by both query workload and user-defined accuracy constraints to support approximate query answering. The approach is based on partial index adaptation which reduces the costs associated with reading data files and refining indexes. We leverage a hierarchical tile-based indexing scheme and its stored metadata to provide efficient query evaluation, ensuring accuracy within user-specified bounds. Our preliminary evaluation demonstrates improvement on query evaluation time, especially during initial user exploration., Comment: This article appears in 7th International Workshop on Big Data Visual Exploration and Analytics (BigVis 2024)

The $^{246}$Cm(n,$\gamma$) and $^{248}$Cm(n,$\gamma$) cross-sections have been measured at the Experimental Area 2 (EAR2) of the n_TOF facility at CERN with three C$_6$D$_6$ detectors. This measurement is part of a collective effort to improve the capture cross-section data for Minor Actinides (MAs), which are required to estimate the production and transmutation rates of these isotopes in light water reactors and innovative reactor systems. In particular, the neutron capture in $^{246}$Cm and $^{248}$Cm open the path for the formation of other Cm isotopes and heavier elements such as Bk and Cf and the knowledge of (n,$\gamma$) cross-sections of these Cm isotopes plays an important role in the transport, transmutation and storage of the spent nuclear fuel. The reactions $^{246}$Cm(n,$\gamma$) and $^{248}$Cm(n,$\gamma$) have been the two first capture measurements analyzed at n_TOF EAR2. Until this experiment and two recent measurements performed at J-PARC, there was only one set of data of the capture cross-sections of $^{246}$Cm and $^{248}$Cm, that was obtained in 1969 in an underground nuclear explosion experiment. In the measurement at n_TOF a total of 13 resonances of $^{246}$Cm between 4 and 400 eV and 5 of $^{248}$Cm between 7 and 100 eV have been identified and fitted. The radiative kernels obtained for $^{246}$Cm are compatible with JENDL-5, but some of them are not with JENDL-4, which has been adopted by JEFF-3.3 and ENDF/B-VIII.0. The radiative kernels obtained for the first three $^{248}$Cm resonances are compatible with JENDL-5, however, the other two are not compatible with any other evaluation and are 20% and 60% larger than JENDL-5.

Through an uncertainty quantification (UQ) perspective, we show that score-based generative models (SGMs) are provably robust to the multiple sources of error in practical implementation. Our primary tool is the Wasserstein uncertainty propagation (WUP) theorem, a model-form UQ bound that describes how the $L^2$ error from learning the score function propagates to a Wasserstein-1 ($\mathbf{d}_1$) ball around the true data distribution under the evolution of the Fokker-Planck equation. We show how errors due to (a) finite sample approximation, (b) early stopping, (c) score-matching objective choice, (d) score function parametrization expressiveness, and (e) reference distribution choice, impact the quality of the generative model in terms of a $\mathbf{d}_1$ bound of computable quantities. The WUP theorem relies on Bernstein estimates for Hamilton-Jacobi-Bellman partial differential equations (PDE) and the regularizing properties of diffusion processes. Specifically, PDE regularity theory shows that stochasticity is the key mechanism ensuring SGM algorithms are provably robust. The WUP theorem applies to integral probability metrics beyond $\mathbf{d}_1$, such as the total variation distance and the maximum mean discrepancy. Sample complexity and generalization bounds in $\mathbf{d}_1$ follow directly from the WUP theorem. Our approach requires minimal assumptions, is agnostic to the manifold hypothesis and avoids absolute continuity assumptions for the target distribution. Additionally, our results clarify the trade-offs among multiple error sources in SGMs.

We demonstrate that the problem of amplitude estimation, a core subroutine used in many quantum algorithms, can be mapped directly to a problem in signal processing called direction of arrival (DOA) estimation. The DOA task is to determine the direction of arrival of an incoming wave with the fewest possible measurements. The connection between amplitude estimation and DOA allows us to make use of the vast amount of signal processing algorithms to post-process the measurements of the Grover iterator at predefined depths. Using an off-the-shelf DOA algorithm called ESPRIT together with a compressed-sensing based sampling approach, we create a phase-estimation free, parallel quantum amplitude estimation (QAE) algorithm with a total query complexity of $\sim 4.9/\varepsilon$ and a parallel query complexity of $\sim 0.40/\varepsilon$ at 95% confidence. This performance is a factor of $1.1\times$ and $14\times$ improvement over Rall and Fuller [Quantum 7, 937 (2023)], for worst-case complexity, which to our knowledge is the best published result for amplitude estimation. The approach presented here provides a simple, robust, parallel method to performing QAE, with many possible avenues for improvement borrowing ideas from the wealth of literature in classical signal processing., Comment: 12 pages, 6 figures

We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative pricing, and the second based on a novel approach using Quantum Signal Processing (QSP). Previous work in the literature has shown that quantum advantage is possible in the context of individual derivative pricing and that advantage can be leveraged in a straightforward manner in the estimation of the VaR and CVaR. The algorithms we introduce in this work aim to provide an additional advantage by encoding the derivative price over multiple market scenarios in superposition and computing the desired values by applying appropriate transformations to the quantum system. We perform complexity and error analysis of both algorithms, and show that while the two algorithms have the same asymptotic scaling the QSP-based approach requires significantly fewer quantum resources for the same target accuracy. Additionally, by numerically simulating both quantum and classical VaR algorithms, we demonstrate that the quantum algorithm can extract additional advantage from a quantum computer compared to individual derivative pricing. Specifically, we show that under certain conditions VaR estimation can lower the latest published estimates of the logical clock rate required for quantum advantage in derivative pricing by up to $\sim 30$x. In light of these results, we are encouraged that our formulation of derivative pricing in the QSP framework may be further leveraged for quantum advantage in other relevant financial applications, and that quantum computers could be harnessed more efficiently by considering problems in the financial sector at a higher level.

This article introduces an experimental emulation of a novel chunk-based flexible multi-DoF aerial 3D printing framework. The experimental demonstration of the overall autonomy focuses on precise motion planning and task allocation for a UAV, traversing through a series of planned space-filling paths involved in the aerial 3D printing process without physically depositing the overlaying material. The flexible multi-DoF aerial 3D printing is a newly developed framework and has the potential to strategically distribute the envisioned 3D model to be printed into small, manageable chunks suitable for distributed 3D printing. Moreover, by harnessing the dexterous flexibility due to the 6 DoF motion of UAV, the framework enables the provision of integrating the overall autonomy stack, potentially opening up an entirely new frontier in additive manufacturing. However, it's essential to note that the feasibility of this pioneering concept is still in its very early stage of development, which yet needs to be experimentally verified. Towards this direction, experimental emulation serves as the crucial stepping stone, providing a pseudo mockup scenario by virtual material deposition, helping to identify technological gaps from simulation to reality. Experimental emulation results, supported by critical analysis and discussion, lay the foundation for addressing the technological and research challenges to significantly push the boundaries of the state-of-the-art 3D printing mechanism., Comment: This paper has been accepted for publication at IEEE International Conference on Robotics and Automation (ICRA) 2024

We study the convergence problem for mean field control, also known as optimal control of McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the limiting value function $\mathcal{U} :[0,T] \times \mathcal{P}_2(\mathbb{R}^d) \to \mathbb{R}$ is Lipschitz, but may not be differentiable. In this setting, the first and last named authors recently identified an open and dense subset $\mathcal{O}$ of $[0,T] \times \mathcal{P}_2(\mathbb{R}^d)$ on which $\mathcal{U}$ is $\mathcal{C}^1$ and solves the relevant infinite-dimensional Hamilton-Jacobi equation in a classical sense. In the present paper, we use these regularity results, and some non-trivial extensions of them, to derive sharp rates of convergence. In particular, we show that the value functions for the $N$-particle control problems converge towards $\mathcal{U}$ with a rate of $1/N$, uniformly on subsets of $\mathcal{O}$ which are compact in the $p$-Wasserstein space for some $p > 2$. A similar result is also established at the level of the optimal feedback controls. The rate $1/N$ is the optimal rate in this setting even if $\mathcal{U}$ is smooth, while, in general, the optimal global rate of convergence is known to be slower than $1/N$. Thus our results show that the rate of convergence is faster inside of $\mathcal{O}$ than it is outside. As a consequence of the convergence of the optimal feedbacks, we obtain a concentration inequality for optimal trajectories of the $N$-particle problem started from i.i.d. initial conditions.

We present a Mean Field Game approach to obtain the rate function for the empirical measure of interacting particles under McKean-Vlasov dynamics. Although the result is well known, our approach relies on PDE methods and provides another example of the well known connection between Mean Field Games and Large Deviations., Comment: 24 pages

The future of 3D printing utilizing unmanned aerial vehicles (UAVs) presents a promising capability to revolutionize manufacturing and to enable the creation of large-scale structures in remote and hard- to-reach areas e.g. in other planetary systems. Nevertheless, the limited payload capacity of UAVs and the complexity in the 3D printing of large objects pose significant challenges. In this article we propose a novel chunk-based framework for distributed 3D printing using UAVs that sets the basis for a fully collaborative aerial 3D printing of challenging structures. The presented framework, through a novel proposed optimisation process, is able to divide the 3D model to be printed into small, manageable chunks and to assign them to a UAV for partial printing of the assigned chunk, in a fully autonomous approach. Thus, we establish the algorithms for chunk division, allocation, and printing, and we also introduce a novel algorithm that efficiently partitions the mesh into planar chunks, while accounting for the inter-connectivity constraints of the chunks. The efficiency of the proposed framework is demonstrated through multiple physics based simulations in Gazebo, where a CAD construction mesh is printed via multiple UAVs carrying materials whose volume is proportionate to a fraction of the total mesh volume., Comment: This paper has been accepted for publication at 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2023)

Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on Quantum Signal Processing (QSP) to encode financial derivative payoffs directly into quantum amplitudes, alleviating the quantum circuits from the burden of costly quantum arithmetic. Compared to current state-of-the-art approaches in the literature, we find that for derivative contracts of practical interest, the application of QSP significantly reduces the required resources across all metrics considered, most notably the total number of T-gates by $\sim 16$x and the number of logical qubits by $\sim 4$x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of $\sim 5$x. Overall, we find that quantum advantage will require $4.7$k logical qubits, and quantum devices that can execute $10^9$ T-gates at a rate of $45$MHz. While in this work we focus specifically on the payoff component of the derivative pricing process where the method we present is most readily applicable, similar techniques can be employed to further reduce the resources in other applications, such as state preparation.

Background: The $^{14}$N(n,p)$^{14}$C reaction is of interest in neutron capture therapy, where nitrogen-related dose is the main component due to low-energy neutrons, and in astrophysics, where 14N acts as a neutron poison in the s-process. Several discrepancies remain between the existing data obtained in partial energy ranges: thermal energy, keV region and resonance region. Purpose: Measuring the 14N(n,p)14C cross section from thermal to the resonance region in a single measurement for the first time, including characterization of the first resonances, and providing calculations of Maxwellian averaged cross sections (MACS). Method: Time-of-flight technique. Experimental Area 2 (EAR-2) of the neutron time-of-flight (n_TOF) facility at CERN. $^{10}$B(n,${\alpha}$)$^7$Li and $^{235}$U(n,f) reactions as references. Two detection systems running simultaneously, one on-beam and another off-beam. Description of the resonances with the R-matrix code sammy. Results: The cross section has been measured from sub-thermal energy to 800 keV resolving the two first resonances (at 492.7 and 644 keV). A thermal cross-section (1.809$\pm$0.045 b) lower than the two most recent measurements by slightly more than one standard deviation, but in line with the ENDF/B-VIII.0 and JEFF-3.3 evaluations has been obtained. A 1/v energy dependence of the cross section has been confirmed up to tens of keV neutron energy. The low energy tail of the first resonance at 492.7 keV is lower than suggested by evaluated values, while the overall resonance strength agrees with evaluations. Conclusions: Our measurement has allowed to determine the $^{14}$N(n,p) cross-section over a wide energy range for the first time. We have obtained cross-sections with high accuracy (2.5 %) from sub-thermal energy to 800 keV and used these data to calculate the MACS for kT = 5 to kT = 100 keV., Comment: 18 pages, 15 figures, 4 tables

We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant pre-factors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage., Comment: 40 pages, 15 figures. v2: minor corrections and updates to match journal version

Rapid and sustained condensate droplet departure from a surface is key towards achieving high heat transfer rates in condensation, a physical process critical to a broad range of industrial and societal applications. Despite progress in enhancing condensation heat transfer through inducing its dropwise mode with hydrophobic materials, sophisticated surface engineering methods that can lead to further enhancement of heat transfer are still highly desirable. Here, by employing a three-dimensional, multiphase computational approach, we present an effective out-of-plane biphilic surface topography, that reveals an unexplored capillarity-driven departure mechanism of condensate droplets. This texture consists of biphilic diverging micro-cavities wherein a matrix of small hydrophilic spots is placed at their bottom, that is, amongst the pyramid-shaped, superhydrophobic micro-textures forming the cavities. We show that an optimal combination of the hydrophilic spots and the angles of the pyramidal structures can achieve high deformational stretching of the droplets, eventually realizing an impressive slingshot-like droplet ejection process from the texture. Such a droplet departure mechanism has the potential to reduce the droplet ejection volume and thus enhance the overall condensation efficiency, compared to coalescence-initiated droplet jumping from other state-of-the-art surfaces. Simulations have shown that optimal pyramid-shaped biphilic micro-structures can provoke droplet self-ejection at low volumes, up to 56% lower compared to superhydrophobic straight pillars, revealing a promising new surface micro-texture design strategy towards enhancing condensation heat transfer efficiency and water harvesting capabilities.

We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense $N\times N$ matrix of classical data to precision $\epsilon$; the minimal-depth method achieves a $T$-depth of $\mathcal{O}{(\log (N/\epsilon))},$ while the minimal-count method achieves a $T$-count of $\mathcal{O}{(N\log(1/\epsilon))}$. We examine resource tradeoffs between the different approaches, and we explore implementations of two separate models of quantum random access memory (QRAM). As part of this analysis, we provide a novel state preparation routine with $T$-depth $\mathcal{O}{(\log (N/\epsilon))}$, improving on previous constructions with scaling $\mathcal{O}{(\log^2 (N/\epsilon))}$. Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.

We study the regularity and long time behavior of the one-dimensional, local, first-order mean field games system and the planning problem, assuming a Hamiltonian of superlinear growth, with a non-separated, strictly monotone dependence on the density. We improve upon the existing literature by obtaining two regularity results. The first is the existence of classical solutions without the need to assume blow-up of the cost function near small densities. The second result is the interior smoothness of weak solutions without the need to assume neither blow-up of the cost function nor that the initial density be bounded away from zero. We also characterize the long time behavior of the solutions, proving that they satisfy the turnpike property with an exponential rate of convergence, and that they converge to the solution of the infinite horizon system. Our approach relies on the elliptic structure of the system and displacement convexity estimates. In particular, we apply displacement convexity methods to obtain both global and local a priori lower bounds on the density., Comment: v3: The material on the long time behavior is new. Updated title and abstract

In this work, we explore the problem of correctly and efficiently answering complex SPJ queries issued directly on top of dirty data. We introduce QueryER, a framework that seamlessly integrates Entity Resolution into Query Processing. QueryER executes analysis-aware deduplication by weaving ER operators into the query plan. The experimental evaluation of our approach exhibits that it adapts to the workload and scales on both real and synthetic datasets.

The 235U(n,f) cross section was measured in a wide energy range (25 meV - 170 keV) at the n_TOF facility at CERN, relative to 6Li(n,t) and 10B(n,alpha) standard reactions, with high resolution and accuracy, with a setup based on a stack of six samples and six silicon detectors placed in the neutron beam. In this paper we report on the results in the region between thermal and 10 keV neutron energy. A resonance analysis has been performed up to 200 eV, with the code SAMMY. The resulting fission kernels are compared with the ones extracted on the basis of the resonance parameters of the most recent major evaluated data libraries. A comparison of the n_TOF data with the evaluated cross sections is also performed from thermal to 10 keV neutron energy for the energy-averaged cross section in energy groups of suitably chosen width. A good agreement is found in average between the new results and the latest evaluated data files ENDF-B/VIII and JEFF-3.3, as well as with respect to the IAEA reference files. However, some discrepancies are still present in some specific energy regions. The new dataset here presented, characterized by unprecedented resolution and accuracy, can help improving the evaluations in the Resolved Resonance Region and up to 10 keV, and reduce the uncertainties that affect this region.

We introduce a quantum algorithm to compute the market risk of financial derivatives. Previous work has shown that quantum amplitude estimation can accelerate derivative pricing quadratically in the target error and we extend this to a quadratic error scaling advantage in market risk computation. We show that employing quantum gradient estimation algorithms can deliver a further quadratic advantage in the number of the associated market sensitivities, usually called greeks. By numerically simulating the quantum gradient estimation algorithms on financial derivatives of practical interest, we demonstrate that not only can we successfully estimate the greeks in the examples studied, but that the resource requirements can be significantly lower in practice than what is expected by theoretical complexity bounds. This additional advantage in the computation of financial market risk lowers the estimated logical clock rate required for financial quantum advantage from Chakrabarti et al. [Quantum 5, 463 (2021)] by a factor of ~7, from 50MHz to 7MHz, even for a modest number of greeks by industry standards (four). Moreover, we show that if we have access to enough resources, the quantum algorithm can be parallelized across 60 QPUs, in which case the logical clock rate of each device required to achieve the same overall runtime as the serial execution would be ~100kHz. Throughout this work, we summarize and compare several different combinations of quantum and classical approaches that could be used for computing the market risk of financial derivatives.