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Threshold for Life

This article delves into the groundbreaking theorem that life can be constructed from faulty components, inspired by the work of Prof. Isaac Chuang at MIT Media Laboratory. It examines the fault-tolerance threshold for circuits and extends the discussion to biological systems, questioning how life can achieve reliability through self-repair, reproduction, and evolution. By comparing quantum circuits and von Neumann's self-reproducing automata, we explore theoretical frameworks that could lead to fault-tolerant life forms and their characteristics.

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Threshold for Life

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  1. Threshold for Life Prof. Isaac Chuang MIT Media Laboratory

  2. Objective • Question: • How Faulty? • Claim: • Life can be constructed from faulty components

  3. An Amazing Theorem Reliable computers can be constructed from faulty components • A circuit containing N (error-free) gates can be simulated with probability of error at most e, using N log(N/e) faulty gates, which fail with probability p, so long as p<pth. von Neumann (1956) Quantum version: Preskill, Shor, Aharonov, Ben-Or, Gottesman, Chuang*,… * D. Gottesman and I. Chuang, Nature, vol. 402, p. 390, 1999

  4. Fault-Tolerant Circuits

  5. Fault-Tolerant Circuits

  6. The Fault-Tolerance Threshold Circuit 1: e Circuit 2: e p MAJ Circuit 3: e Fails with probability 3e+p < 4e Fails with probability < 3(4e)2 + p < 49e2 If p<e2 and49e2 <e p<0.0004 Non-Fault-Tolerant Fault-Tolerant A circuit containing N (error-free) gates can be simulated with probability of error < e, using cdN faulty gates, which fail with probability p, if p<pth. Proof: Assume 3-input gates. N=1 easy.

  7. Efficient Fault Tolerance • Key concept: concatenation (encoding at multiple levels) A circuit containing N (error-free) gates can be simulated with prob. of error < e, using O(N log N) faulty gates, which fail with prob. p, if p<pth. • Status: pth¼ 1/6 (Hajek & Weller ’91)

  8. Fault-Tolerant Life • Nature does not seem to use such constructions • How can life be made fault-tolerant?

  9. What is Life? • Desirable characteristics: • Self repair • Self reproduction • Growth • Evolution Schrodinger • von Neumann (1966) Theory of Self-Reproducing Automata: elementary machine capable of reproduction and universal computation

  10. Von Neumann’s Automaton • Model based on 29 state Cellular Automaton Langton’s 8-state replicator (not universal) (simulation from H-H Chou) • Universal Turing machine • Universal constructor

  11. Visions of Fault-Tolerant Life • What would fault-tolerant creatures be like? • Two interesting questions: • What is the fault-tolerance threshold for Life? Rad-hard biology Immortal Biosystems …Reproduction?

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