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

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

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 , using N log(N/  ) faulty gates, which fail with probability p, so long as p<p th. 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

6. The Fault-Tolerance Threshold A circuit containing N (error-free) gates can be simulated with probability of error < , using c d N faulty gates, which fail with probability p, if p<p th. Proof: Assume 3-input gates. N=1 easy. Non-Fault-Tolerant Circuit 1:  Circuit 2:  Circuit 3:  p Fails with probability 3  +p < 4  MAJ Fails with probability < 3(4  2 + p < 49  2 If p<  2 and 49  2 <  p<  Fault-Tolerant

7. Efficient Fault Tolerance A circuit containing N (error-free) gates can be simulated with prob. of error < , using O(N log N) faulty gates, which fail with prob. p, if p<p th. Key concept: concatenation (encoding at multiple levels) Status: p th ¼ 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 (simulation from H-H Chou) Langton’s 8-state replicator (not universal) Universal Turing machine Universal constructor

11. 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 biologyImmortal Biosystems…Reproduction?