Threshold for Life

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Threshold for Life
Prof. Isaac Chuang
MIT Media Laboratory
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Objective

• Claim
• Life can be constructed from faulty components

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An Amazing Theorem
von Neumann (1956)
Quantum version Preskill, Shor, Aharonov,
Ben-Or, Gottesman, Chuang,
D. Gottesman and I. Chuang, Nature, vol. 402,
p. 390, 1999
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Fault-Tolerant Circuits
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Fault-Tolerant Circuits
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The Fault-Tolerance Threshold
A circuit containing N (error-free) gates can be
simulated with probability of error lt e, using
cdN faulty gates, which fail with probability p,
if pltpth.
Proof Assume 3-input gates. N1
easy.
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Efficient Fault Tolerance
A circuit containing N (error-free) gates can be
simulated with prob. of error lt e, using O(N log
N) faulty gates, which fail with prob. p, if
pltpth.

• Status pth ¼ 1/6 (Hajek Weller 91)

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Fault-Tolerant Life

• Nature does not seem to use such constructions
• How can life be made fault-tolerant?

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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

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Von Neumanns Automaton

• Model based on 29 state Cellular Automaton

Langtons 8-state replicator (not universal)
(simulation from H-H Chou)

• Universal Turing machine
• Universal constructor

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Visions of Fault-Tolerant Life

• Two interesting questions
• What is the fault-tolerance threshold for Life?

Rad-hard biology
Immortal Biosystems
Reproduction?