View
218
Download
4
Tags:
Embed Size (px)
Citation preview
Threshold for Life
MIT Media Laboratory
Prof. Isaac ChuangProf. Isaac Chuang
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 , using N log(N/) 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
Fault-Tolerant Circuits
Fault-Tolerant Circuits
The Fault-Tolerance Threshold
A circuit containing N (error-free) gates can be simulated with
probability of error < , using cdN faulty gates, which fail with probability p, if p<pth.Proof: Assume 3-input gates. N=1 easy.
Non-Fault-Tolerant
Circuit 1: Circuit 2: Circuit 3:
p
Fails with probability
3+p < 4
Circuit 1: Circuit 2: Circuit 3:
p
Circuit 1: Circuit 2: Circuit 3:
pp
Circuit 1: Circuit 2: Circuit 3:
p
Circuit 1: Circuit 2: Circuit 3:
pp
Circuit 1: Circuit 2: Circuit 3:
p
Circuit 1: Circuit 2: Circuit 3:
pp
MAJ
Fails with probability < 3(42 + p < 492 If p<2 and 492 < p<
Fault-Tolerant
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<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
(simulation from H-H Chou)
Langton’s 8-state replicator (not universal)
• Universal Turing machine• Universal constructor
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?