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

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

3. Reliable computers can be constructed from faulty components
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
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.
MAJ
Fails with probability < 3(4e)2 + p < 49e2
If p<e2 and 49e2 < e
p<0.0004
Fault-Tolerant
Non-Fault-Tolerant
Circuit 1: e
Circuit 2: e
Circuit 3: e p
Fails with probability
3e+p < 4e

7. 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)

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
Two interesting questions:
What is the fault-tolerance threshold for Life?
What would fault-tolerant creatures be like?
Rad-hard biology
Immortal Biosystems
…Reproduction?