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Threshold for Life

Threshold for Life. Prof. Isaac Chuang. MIT Media Laboratory. Objective. Question: How Faulty?. Claim: Life can be constructed from faulty components. An Amazing Theorem. Reliable computers can be constructed from faulty components.

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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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