Pierre-Emmanuel Emeriau

Relation entre contextualité quantique et négativité de la fonction de Wigner: La physique quantique a révolutionné notre façon de concevoir la nature et provoque une nouvelle révolution technologique. L'utilisation de l'information quantique dans la technologie promet de supplanter les dispositifs dits classiques utilisés de nos jours. Il est essentiel de comprendre quelles caractéristiques sont intrinsèquement non classiques pour atteindre des performances supérieures à celles des dispositifs actuels. Cette thèse se concentre sur deux comportements non classiques : la contextualité quantique et la négativité de Wigner. Jusqu'à présent, la contextualité a surtout été étudiée dans des scénarios à variables discrètes, où les observables prennent des valeurs dans des ensembles discrets et généralement finis. Il a été démontré que la contextualité est nécessaire et suffisante pour les avantages dans certains cas. D'autre part, la négativité de la fonction de Wigner est une autre caractéristique non classique troublante des états quantiques qui provient de la formulation de l'espace de phase en optique quantique. La négativité de la fonction de Wigner est connue pour être une ressource nécessaire à l'accélération quantique. Nous établissons un cadre robuste pour traiter la contextualité dans les variables continues. Nous quantifions la contextualité dans de tels scénarios en utilisant des outils de la théorie de l'optimisation en dimension infinie. Nous montrons que la négativité de Wigner est équivalente à la contextualité dans les variables continues pour les mesures de Pauli. Nous introduisons ensuite des témoins expérimentaux pour la négativité de Wigner des états quantiques multimodes, basés sur les fidélités avec les états de Fock.

Understanding the energetic efficiency of quantum computers is essential for assessing their scalability and for determining whether quantum technologies can outperform classical computation beyond runtime alone. In this work, we analyze the energy required to solve the Boson Sampling problem, a paradigmatic task for quantum advantage, using a realistic photonic quantum computing architecture. Using the Metric-Noise-Resource methodology, we establish a quantitative connection between experimental control parameters, dominant noise processes, and energetic resources through a performance metric tailored to Boson Sampling. We estimate the energy cost per sample and identify operating regimes that optimize energetic efficiency. By comparing the energy consumption of quantum and state-of-the-art classical implementations, we demonstrate the existence of a quantum energetic advantage -- defined as a lower energy cost per sample compared to the best-known classical implementation -- that emerges before the onset of computational advantage, even in regimes where classical algorithms remain faster. Finally, we propose an experimentally feasible Boson Sampling architecture, including a complete noise and loss budget, that enables a near-term observation of quantum energetic advantage.

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness, and coherence are arguably of great significance. We introduce "path coherence" as a measure of the coherent path 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 estimation of quantum transition amplitudes, 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.

Photonic platforms occupy a central place in quantum technologies. They appear in quantum networks and communication, in near-term quantum advantage schemes, as well as in fault-tolerant quantum computing proposals. In this perspective article, we review the advances and challenges of this technology, and we focus on algorithms and protocols that we call photon-native, i.e. which closely follow the specificities of the hardware.

We present qubit logic on qudits (QLOQ), a compression scheme in which the qubits from a hardware agnostic circuit are divided into groups of various sizes, and each group is mapped to a physical qudit for computation. QLOQ circuits have qubit-logic inputs, outputs, and gates, making them compatible with existing qubit-based algorithms and Hamiltonians. We show that arbitrary qubit-logic unitaries can in principle be implemented with significantly fewer two-level (qubit) physical entangling gates in QLOQ than in qubit encoding. We achieve this advantage in practice for two applications: variational quantum algorithms, and unitary decomposition. The variational quantum eigensolver (VQE) for LiH took 5 hours using QLOQ on one of Quandela's cloud-accessible photonic quantum computers, whereas it would have taken 4.39 years in qubit encoding. We also provide a QLOQ version of the Quantum Shannon Decomposition, which not only outperforms previous qudit-based proposals, but also beats the theoretical lower bound on the CNOT cost of unitary decomposition in qubit encoding.

Reliable randomness is a core ingredient in algorithms and applications ranging from numerical simulations to statistical sampling and cryptography. The outcomes of measurements on entangled quantum states can violate Bell inequalities, thus guaranteeing their intrinsic randomness. This constitutes the basis for certified randomness generation. However, this certification requires spacelike separated devices, making it unfit for a compact apparatus. Here we provide a general method for certified randomness generation on a small-scale application-ready device and perform an integrated photonic demonstration combining a solid-state emitter and a glass chip. In contrast to most existing certification protocols, which in the absence of spacelike separation are vulnerable to loopholes inherent to realistic devices, the protocol we implement accounts for information leakage and is thus compatible with emerging compact scalable devices. We demonstrate a two-qubit photonic device that achieves the highest standard in randomness, yet is cut out for real-world applications. The full 94.5-h-long stabilized process harnesses a bright and stable single-photon quantum-dot-based source, feeding into a reconfigurable photonic chip, with stability in the milliradian range on the implemented phases and consistent indistinguishability of the entangled photons above 93%. Using the contextuality framework, we certify private randomness generation and achieve a rate compatible with randomness expansion secure against quantum adversaries. Published by the American Physical Society 2024