Quantum algorithms for the subset-sum problem

Abstract. This paper introduces a subset-sum algorithm with heuristic asymptotic cost exponent below 0.25. The new algorithm combines the 2010 Howgrave-Graham–Joux subset-sum algorithm with a new streamlined data structure for quantum walks on Johnson graphs

Noble gases in deepwater oils of the U.S. Gulf of Mexico

Hydrocarbon migration and emplacement processes remain underconstrained despite the vast potential economic value associated with oil and gas. Noble gases provide information about hydrocarbon generation, fluid migration pathways, reservoir conditions, and the relative volumes of oil versus water in the subsurface. Produced gas He‐Ne‐Ar‐Kr‐Xe data from two distinct oil fields in the Gulf of Mexico (Genesis and Hoover‐Diana) are used to calibrate a model that takes into account both water‐oil solubility exchange and subsequent gas cap formation. Reconstructed noble gas signatures in oils reflect simple (two‐phase) oil‐water exchange imparted during migration from the source rock to the trap, which are subsequently modified by gas cap formation at current reservoir conditions. Calculated, oil to water volume ratios ( urn:x-wiley:15252027:media:ggge21714:ggge21714-math-0001) in Tertiary‐sourced oils from the Hoover‐Diana system are 2–3 times greater on average than those in the Jurassic sourced oils from the Genesis reservoirs. Higher urn:x-wiley:15252027:media:ggge21714:ggge21714-math-0002 in Hoover‐Diana versus Genesis can be interpreted in two ways: either (1) the Hoover reservoir interval has 2–3 times more oil than any of the individual Genesis reservoirs, which is consistent with independent estimates of oil in place for the respective reservoirs, or (2) Genesis oils have experienced longer migration pathways than Hoover‐Diana oils and thus have interacted with more water. The ability to determine a robust urn:x-wiley:15252027:media:ggge21714:ggge21714-math-0003, despite gas cap formation and possible gas cap loss, is extremely powerful. For example, when volumetric hydrocarbon ratios are combined with independent estimates of hydrocarbon migration distance and/or formation fluid volumes, this technique has the potential to differentiate between large and small oil accumulations