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The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum computing algorithms to address this problem. This study introduces a quantum approach that utilizes Rydberg atoms to tackle the factorization problem. Experimental demonstrations are conducted for the factorization of small composite numbers such as $6 = 2 \times 3$, $15 = 3 \times 5$, and $35 = 5 \times 7$. This approach involves employing Rydberg-atom graphs to algorithmically program binary multiplication tables, yielding many-body ground states that represent superpositions of factoring solutions. Subsequently, these states are probed using quantum adiabatic computing. Limitations of this method are discussed, specifically addressing the scalability of current Rydberg quantum computing for the intricate computational problem., Comment: 12 pages, 5 figures

We report the development of a continuous-wave and pulsed X-band electron spin resonance (ESR) spectrometer for the study of spins on ordered surfaces down to cryogenic temperatures. The spectrometer operates in ultra-high vacuum and utilizes a half-wavelength microstrip line resonator realized using epitaxially grown copper films on single crystal Al$_2$O$_3$ substrates. The one-dimensional microstrip line resonator exhibits a quality factor of more than 200 at room temperature, close to the upper limit determined by radiation losses. The surface characterizations of the copper strip of the resonator by atomic force microscope, low-energy electron diffraction, and scanning tunneling microscope show that the surface is atomically clean, flat, and single crystalline. Measuring the ESR spectrum at 15 K from a few nm thick molecular film of YPc$_2$, we find a continuous-wave ESR sensitivity of $2.6 \cdot 10^{11}~\text{spins}/\text{G} \cdot \text{Hz}^{1/2}$ indicating that a signal-to-noise ratio of $3.9~\text{G} \cdot \text{Hz}^{1/2}$ is expected from a monolayer of YPc$_2$ molecules. Advanced pulsed ESR experimental capabilities including dynamical decoupling and electron-nuclear double resonance are demonstrated using free radicals diluted in a glassy matrix., Comment: 14 pages, 7 figures

Finding the maximum independent set (MIS) of a large-size graph is a nondeterministic polynomial-time (NP)-complete problem not efficiently solvable with classical computations. Here, we present a set of quantum adiabatic computing data of Rydberg-atom experiments performed to solve the MIS problem of up to 141 atoms randomly arranged on the King's lattice. A total of 582,916 events of Rydberg-atom measurements are collected for experimental MIS solutions of 733,853 different graphs. We provide the raw image data along with the entire binary determinations of the measured many-body ground states and the classified graph data, to offer bench-mark testing and advanced data-driven analyses for validation of the performance and system improvements of the Rydberg-atom approach., Comment: 10 pages, 4 figures

Single atoms movable from one place to another would enable a flying quantum memory that can be used for quantum communication and quantum computing at the same time. Guided atoms, e.g., by optical tweezers, provide a partial solution, but the benefit of flying qubits could be lost if they still interact with the guiding means. Here we propose and experimentally demonstrate freely-flying atoms that are not guided but are instead thrown and caught by optical tweezers. In experiments, cold atoms at 40 micro Kelvin temperature are thrown up to a free-flying speed of 0.65 m/s over a travel distance of 12.6 micrometer at a transportation efficiency of 94(3)%, even in the presence of other optical tweezers or atoms en route. This performance is not fundamentally limited but by current settings of optical tweezers with limited potential depth and width. We provide a set of proof-of-principle flying atom demonstrations, which include atom transport through optical tweezers, atom arrangements by flying atoms, and atom scattering off optical tweezers. Our study suggests possible applications of flying atoms, not only in fundamental studies such as single-atom low-energy collisions, but also non-photon quantum communication and flying-qubit-based quantum computing., Comment: 8 pages, 5 figures