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A scalable photonic computer solving the subset sum problem.

ABSTRACT: The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)-complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network through a femtosecond laser direct writing technique. We show that the photons sufficiently dissipate into the networks and search for solutions in parallel. In the case of successive primes, our approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize computations intractable for conventional computers, and suggest the SSP as a good benchmarking platform for the race between photonic and conventional computers on the way toward "photonic supremacy."

SUBMITTER: Xu XY

PROVIDER: S-EPMC6994215 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature

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A scalable photonic computer solving the subset sum problem.

Xu Xiao-Yun XY Huang Xuan-Lun XL Li Zhan-Ming ZM Gao Jun J Jiao Zhi-Qiang ZQ Wang Yao Y Ren Ruo-Jing RJ Zhang H P HP Jin Xian-Min XM

Science advances 20200131 5

The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)-complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network thro ...[more]

PMID: 32064352

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Project description:In this paper we argue that a synthesis of findings across the various sub-areas of research in complex problem solving and consequently progress in theory building is hampered by an insufficient differentiation of complexity and difficulty. In the proposed framework of person, task, and situation (PTS), complexity is conceptualized as a quality that is determined by the cognitive demands that the characteristics of the task and the situation impose. Difficulty represents the quantifiable level of a person's success in dealing with such demands. We use the well-documented "semantic effect" as an exemplar for testing some of the conceptual assumptions derived from the PTS framework. We demonstrate how a differentiation between complexity and difficulty can help take beyond a potentially too narrowly defined psychometric perspective and subsequently gain a better understanding of the cognitive mechanisms behind this effect. In an empirical study a total of 240 university students were randomly allocated to one of four conditions. The four conditions resulted from contrasting the semanticity level of the variable labels used in the CPS system (high vs. low) and two instruction conditions for how to explore the CPS system's causal structure (starting with the assumption that all relationships between variables existed vs. starting with the assumption that none of the relationships existed). The variation in the instruction aimed at inducing knowledge acquisition processes of either (1) systematic elimination of presumptions, or (2) systematic compilation of a mental representation of the causal structure underpinning the system. Results indicate that (a) it is more complex to adopt a "blank slate" perspective under high semanticity as it requires processes of inhibiting prior assumptions, and (b) it seems more difficult to employ a systematic heuristic when testing against presumptions. In combination, situational characteristics, such as the semanticity of variable labels, have the potential to trigger qualitatively different tasks. Failing to differentiate between 'task' and 'situation' as independent sources of complexity and treating complexity and difficulty synonymously threaten the validity of performance scores obtained in CPS research.

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A scalable photonic computer solving the subset sum problem.

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A scalable photonic computer solving the subset sum problem.

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