Efficient networks for quantum factoring

We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A K-bit number can be factored in time of order K3 using a machine capable of storing 5K+1 qubits. Evaluation of the modular exponential function (the bottleneck of Shor’s algorithm) could be achieved with about 72K3 elementary quantum gates; implementation using a linear ion trap would require about 396K3 laser pulses. A proof-of-principle demonstration of quantum factoring (factorization of 15) could be performed with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be a useful computer, it will be a powerful device for exploring experimentally the properties of entangled quantum states

Rates of Relative Sea Level Rise Along the United States East Coast

Recent studies have indicated that some coastal areas, including the East Coast of the United States, are experiencing higher rates of sea level rise than the global average. Rates of relative sea level rise are affected by changes in ocean dynamics, as well as by surface elevation fluctuations due to local land subsidence or uplift. In this study, we derived long-term trends in annual mean relative sea level using tide gauge data obtained from the Permanent Service for Mean Sea Level for stations along the United States East Coast. Stations were grouped by location into the Northeast, Mid-Atlantic, and Southeast regions of the United States East Coast, with the intent of investigating relative sea level rise variability between the three regions. Trends for each region were calculated using stations with a minimum record length of at least 30 years; the longest record began in 1856. Records that were less than 70 percent complete were rejected. For the three-year moving averages, Northeast trends were calculated to be 2.79 mm/yr, Mid-Atlantic trends were calculated to be 4.02 mm/yr, and Southeast trends were calculated to be 2.92 mm/yr. For the five-year moving averages, Northeast trends were calculated to be 2.81 mm/yr, Mid-Atlantic trends were calculated to be 4.04 mm/yr, and Southeast trends were calculated to be 2.91 mm/yr. The Mid-Atlantic region of the United States East Coast was determined to be experiencing significantly higher rates of relative sea level rise than the other regions