2020/07/05 by Hannah Earley, Earley, Hannah
Computer Science · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Nanocluster Synthesis and Applications #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2007.03605
openalex publication_date 2020/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse the maximum achievable rate of sustained computation for a given\nconvex region of three dimensional space subject to geometric constraints on\npower delivery and heat dissipation. We find a universal upper bound across\nboth quantum and classical systems, scaling as \√(AV) where V is the\nregion volume and A its area. Attaining this bound requires the use of\nreversible computation, else it falls to scaling as A. By specialising our\nanalysis to the case of Brownian classical systems, we also give a\nsemi-constructive proof suggestive of an implementation attaining these bounds\nby means of molecular computers. For regions of astronomical size, general\nrelativistic effects become significant and more restrictive bounds\nproportional to \√(AR) and R are found to apply, where R is its\nradius. It is also shown that inhomogeneity in computational structure is\ngenerally to be avoided. These results are depicted graphically in Figure 1.\n