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Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are required to bolster performance guarantees. Here, we introduce an iterative quantum heuristic optimization algorithm with an average worst-case performance, in the presence of depolarizing quantum noise, equivalent to that of a classical greedy algorithm. We implement this algorithm on a programmable superconducting quantum system using up to 72 qubits for solving paradigmatic Sherrington-Kirkpatrick Ising spin glass problems. The quantum-classical algorithm systematically outperforms its classical counterpart, signaling a quantum enhancement with respect to its guaranteed output quality. Moreover, we observe an absolute performance comparable with the guarantees for a state-of-the-art semi-definite programming method. Classical simulations of the algorithm illustrate that a key challenge to reaching quantum advantage remains improving the quantum device characteristics., Comment: 9 pages, 5 figures (+ 9 pages, 7 figures)

Developing quantum computers for real-world applications requires understanding theoretical sources of quantum advantage and applying those insights to design more powerful machines. Toward that end, we introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis (CCPHASE$(\theta)$). We estimate the process fidelity for this scheme via Cycle Benchmarking of $\mathcal{F}=87.1\pm0.8\%$, higher than reference two-qubit gate decompositions. CCPHASE$(\theta)$ is anticipated to have broad experimental implications, and we report a blueprint demonstration for solving a class of binary constraint satisfaction problems whose construction is consistent with a path to quantum advantage., Comment: 12 pages, 10 figures

SRSF1 protein and U1 snRNPs are closely connected splicing factors. They both stimulate exon inclusion, SRSF1 by binding to exonic splicing enhancer sequences (ESEs) and U1 snRNPs by binding to the downstream 5 ' splice site (SS), and both factors affect 5 ' SS selection. The binding of U1 snRNPs initiates spliceosome assembly, but SR proteins such as SRSF1 can in some cases substitute for it. The mechanistic basis of this relationship is poorly understood. We show here by single-molecule methods that a single molecule of SRSF1 can be recruited by a U1 snRNP. This reaction is independent of exon sequences and separate from the U1-independent process of binding to an ESE. Structural analysis and cross-linking data show that SRSF1 contacts U1 snRNA stem-loop 3, which is required for splicing. We suggest that the recruitment of SRSF1 to a U1 snRNP at a 5 ' SS is the basis for exon definition by U1 snRNP and might be one of the principal functions of U1 snRNPs in the core reactions of splicing in mammals., The EMBO Journal, 41 (1), ISSN:0261-4189, ISSN:1460-2075