Laboratoire de l'Informatique du Parallélisme

Certifying a quantum state in a device-independent (DI) manner, in which no trust is placed on the internal workings of any physical components, is a fundamental task bearing various applications in quantum information theory. The composability of a state-certification protocol is key to its integration as a subroutine within information-theoretic protocols. In this work, we present a composable certification of quantum states in a DI manner under the assumption that a source prepares a finite sequence of independent quantum states that are not necessarily identical. We show that the security relies on the DI analog of the fidelity, called the . We develop methods to compute this quantity under local operations and classical communication in certain Bell scenarios that self-test the singlet state, which may also be of independent interest. Finally, we demonstrate our framework by certifying the singlet state in a composable and DI manner using the Clauser-Horne-Shimony-Holt inequality.

We present a unified framework for multipartite entanglement characterization based on the conditional gradient (CG) method, incorporating both fast heuristic detection and rigorous witness construction with numerical error control. Our method enables entanglement certification in quantum systems of up to ten qubits and applies to arbitrary entanglement structures. We demonstrate its power by closing the gap between entanglement and separability bounds in white noise robustness benchmarks for a class of bound entangled states. Furthermore, the framework extends to entanglement robustness under general quantum noise channels, providing accurate thresholds in cases beyond the reach of previous algorithmic methods. These results position CG methods as a powerful tool for practical and scalable entanglement analysis in realistic experimental settings.

We investigate the performance of algorithms for sparse tensor-sparse tensor multiplication (SpGETT). This operation, also called sparse tensor contraction, is a higher order analogue of the sparse matrix-sparse matrix multiplication (SpGEMM) operation. Therefore, SpGETT can be performed by first converting the input tensors into matrices, then invoking high performance variants of SpGEMM, and finally reconverting the resultant matrix into a tensor. Alternatively, one can carry out the scalar operations underlying SpGETT in the realm of tensors without matrix formulation. We discuss the building blocks in both approaches and formulate a hashing-based method to avoid costly search or redirection operations. We present performance results with the current state-of-the-art SpGEMM-based approaches, existing SpGETT approaches, and a carefully implemented SpGETT approach with a new fine-tuned hashing method, proposed in this paper. We evaluate the methods on real world tensors by contracting a tensor with itself along varying dimensions. Our proposed hashing-based method for SpGETT consistently outperforms the state-of-the-art method, achieving a 25% reduction in sequential execution time on average and a 21% reduction in parallel execution time on average across a variety of input instances.

The analysis of massive scientific data often happens in the form of workflows with interdependent tasks. When such a scientific workflow needs to be scheduled on a parallel or distributed system, one usually represents the workflow as a directed acyclic graph (DAG). The vertices of the DAG represent the tasks, while its edges model the dependencies between the tasks (data to be communicated to successor tasks). When executed, each task requires a certain amount of memory and if it exceeds the available memory, the execution fails. The typical goal is to execute the workflow without failures (satisfying the memory constraints) and with the shortest possible execution time (minimize its makespan). To address this problem, we investigate the memory-aware scheduling of DAG-shaped workflows on heterogeneous platforms, where each processor can have a different speed and a different memory size. We propose a variant of HEFT (Heterogeneous Earliest Finish Time) that accounts for memory and includes eviction strategies for cases when it might be beneficial to remove some data from memory in order to have enough memory to execute other tasks. Furthermore, while HEFT assumes perfect knowledge of the execution time and memory usage of each task, the actual values might differ upon execution. Thus, we propose an adaptive scheduling strategy, where a schedule is recomputed when there has been a significant variation in terms of execution time or memory. The scheduler has been integrated with a runtime system, allowing us to perform a thorough experimental evaluation on real-world workflows. The runtime system warns the scheduler when the task parameters change, so a schedule is recomputed on the fly. The memory-aware strategy allows us to schedule task graphs that would run out of memory with a state-of-the-art scheduler, and the adaptive setting allows us to significantly reduce the makespan.

Autocatalysis is seen as a potential key player in the origin of life, and perhaps more generally in the emergence of Darwinian dynamics. Building on recent formalizations of this phenomenon, we tackle the computational challenge of exhaustively detecting minimal autocatalytic cycles (autocatalytic cores) in reaction networks, and further evaluate the impact of thermodynamic constraints on their realization under mass action kinetics. We first characterize the complexity of the detection problem by proving its NP-completeness. This justifies the use of constraint solvers to list all cores in a given reaction network, and also to group them into compatible sets, composed of cores whose stoichiometric requirements are not contradictory. Crucially, we show that the introduction of thermodynamic realism does constrain the composition of these sets. Compatibility relationships among autocatalytic cores can indeed be disrupted when the reaction kinetics obey thermodynamic consistency throughout the network. On the contrary, these constraints have no impact on the realizability of isolated cores, unless upper or lower bounds are imposed on the concentrations of the reactants. Overall, by better characterizing the conditions of autocatalysis in complex reaction systems, this work brings us a step closer to assessing the contribution of this collective chemical behavior to the emergence of natural selection in the primordial soup.Significance StatementDescribing the processes behind the origin of life requires us to better understand selfamplifying dynamics in complex chemical systems. Detecting autocatalytic cycles is a critical but challenging step in this endeavor. After characterizing the computational complexity of this problem, we investigate the impact of thermodynamic realism on autocatalysis. We demonstrate that individual cycles, regardless of thermodynamic parameters, can always be activated as long as entities may occur at any required concentration. In contrast, two cycles can become mutually incompatible due to thermodynamic constraints, and will thus never run simultaneously. These results clarify the implications of physical realism for the realization of autocatalysis.

Frequent applications of a mixing quantum operation to a quantum system slow down its time evolution and eventually drive it into the invariant subspace of the named operation. We prove this phenomenon, the quantum Zeno effect, and its continuous variant, strong damping, in a unified way for infinite-dimensional open quantum systems, while merely demanding that the respective mixing convergence holds pointwise for all states. Both results are quantitative in the following sense: Given the speed of convergence for the mixing limits, we can derive bounds on the convergence speed for the corresponding quantum Zeno and strong damping limits. We apply our results to prove quantum Zeno and strong damping limits for the photon loss channel with an explicit bound on the convergence speed.

Datasets of labeled network traces are essential for a multitude of machine learning (ML) tasks in networking, yet their availability is hindered by privacy and maintenance concerns, such as data staleness. To overcome this limitation, synthetic network traces can often augment existing datasets. Unfortunately, current synthetic trace generation methods, which typically produce only aggregated flow statistics or a few selected packet attributes, do not always suffice, especially when model training relies on having features that are only available from packet traces. This shortfall manifests in both insufficient statistical resemblance to real traces and suboptimal performance on ML tasks when employed for data augmentation. In this paper, we apply diffusion models to generate high-resolution synthetic network traffic traces. We present NetDiffusion, a tool that uses a finely-tuned, controlled variant of a Stable Diffusion model to generate synthetic network traffic that is high fidelity and conforms to protocol specifications. Our evaluation demonstrates that packet captures generated from NetDiffusion can achieve higher statistical similarity to real data and improved ML model performance than current state-of-the-art approaches (e.g., GAN-based approaches). Furthermore, our synthetic traces are compatible with common network analysis tools and support a myriad of network tasks, suggesting that NetDiffusion can serve a broader spectrum of network analysis and testing tasks, extending beyond ML-centric applications.