Threshold for Life Prof Isaac Chuang MIT Media
- Slides: 11
Threshold for Life Prof. Isaac Chuang MIT Media Laboratory
Objective • Claim: Life can be constructed from faulty components • Question: How Faulty?
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,
Fault-Tolerant Circuits
Fault-Tolerant Circuits
The Fault-Tolerance Threshold A circuit containing N (error-free) gates can be simulated with probability of error < e, using cd. N faulty gates, which fail with probability p, if p<pth. Proof: Assume 3 -input gates. N=1 easy. e Circuit 2: e Circuit 1: Circuit 3: MAJ p e Fails with probability 3 e+p < 4 e Non-Fault-Tolerant Fails with probability < 3(4 e)2 + p < 49 e 2 If p<e 2 and 49 e 2 < e p<0. 0004 Fault-Tolerant
Efficient Fault Tolerance 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. • Key concept: concatenation (encoding at multiple levels) • Status: pth ¼ 1/6 (Hajek & Weller ’ 91)
Fault-Tolerant Life • Nature does not seem to use such constructions How can life be made fault-tolerant?
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
Von Neumann’s Automaton • Model based on 29 state Cellular Automaton Langton’s 8 -state replicator (not universal) • Universal Turing machine • Universal constructor (simulation from H-H Chou)
Visions of Fault-Tolerant Life • Two interesting questions: What is the fault-tolerance threshold for Life? What would fault-tolerant creatures be like? Rad-hard biology Immortal Biosystems …Reproduction?
