We present a method for accurate determination of atomic transition matrix elements at the 10 −3 level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s-6p matrix elements in rubidium by measuring the light shift around the 421 nm and 423 nm zeros with a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3236(9) ea0 and 0.5230(8) ea0 for the 5s-6p 1/2 and 5s-6p 3/2 elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

We demonstrate universal quantum control over chains of ions in a surface-electrode ion trap, including all the fundamental operations necessary to perform algorithms in a one-dimensional, nearest-neighbor quantum computing architecture. We realize both single-qubit operations and nearest-neighbor entangling gates with Raman laser beams, and we interleave the two gate types. We report average single-qubit gate fidelities as high as 0.970(1) for two-, three-, and four-ion chains, characterized with randomized benchmarking. We generate Bell states between the nearest-neighbor pairs of a three-ion chain, with fidelity up to 0.84(2). We combine one-and two-qubit gates to perform quantum process tomography of a CNOTgate in a two-ion chain, and we report an overall fidelity of 0.76(3). System overviewThe experimental system is shown schematically in figure 1(a). We trap chains of 171 Yb + ions 60 μm above the surface-electrode ion trap described in [19]. This trap features through-chip vias instead of wirebonds. The

We study the Quantum Approximate Optimization Algorithm (QAOA) in the context of the Max-Cut problem. Near-term (noisy) quantum devices are only able to (accurately) execute QAOA at low circuit depths while QAOA requires a relatively high circuit-depth in order to "see" the whole graph [FGG20]. We introduce a classical pre-processing step that initializes QAOA with a biased superposition of all possible cuts in the graph, referred to as a warm-start. In particular, our initialization informs QAOA by a solution to a low-rank semidefinite programming relaxation of the Max-Cut problem. Our experimental results show that this variant of QAOA, called QAOAwarm, is able to outperform standard QAOA on lower circuit depths with less training time (in the optimization stage for QAOA's variational parameters). We provide experimental evidence as well as theoretical intuition on performance of the proposed framework.

Using trapped ion quantum bits in a scalable microfabricated surface trap, we perform the Bernstein-Vazirani algorithm. Our architecture relies upon ion transport and can readily be expanded to larger systems. The algorithm is demonstrated using two-and three-ion chains. For three ions, an improvement is achieved compared to a classical system using the same number of oracle queries. For two ions and one query, we correctly determine an unknown bit string with probability 97.6(8)%. For three ions, we succeed with probability 80.9(3)%.