Fast optimization algorithms and the cosmological constant

Bao, Ning; Bousso, Raphael; Jordan, Stephen; Lackey, Brad

doi:10.1103/PhysRevD.96.103512

Fast optimization algorithms and the cosmological constant

Journal Article · Mon Nov 13 00:00:00 EST 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.96.103512· OSTI ID:1420107

Bao, Ning ^[1]; Bousso, Raphael ^[2]; Jordan, Stephen ^[3]; Lackey, Brad ^[4]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Inst. for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics
Univ. of California, Berkeley, CA (United States). Center for Theoretical Physics and Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States)
Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Mathematics

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here in this paper, we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10^-120 in a randomly generated 10⁹ -dimensional Arkani-Hamed–Dimopoulos–Kachru landscape.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1420107

Alternate ID(s):: OSTI ID: 1408566

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 10 Vol. 96; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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