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Reliability is a Fungible Resource

Reliability is a Fungible Resource. Isaac Chuang. MIT EECS & Department of Physics. 2006. An Amazing Theorem. Reliable computers can be constructed from faulty components.

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Reliability is a Fungible Resource

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  1. Reliability is a Fungible Resource Isaac Chuang MIT EECS & Department of Physics 2006

  2. 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, …

  3. Reliability and Area (I) s • Suppose failure depends on area: Pfail(A) • Example: MOSFET Probability Vth Voltage 0 1

  4. Pfail$ Area Fungibility e Ae • What tradeoffs are possible? • Larger area, more reliable • Generic behavior! • Molecular, Quantum, … Pfail(A) Is this the best possible? Area

  5. Reliability and Area (II) Circuit 1: e Circuit: e Circuit 2: e Vote Circuit 3: e Area: ~3A Pfail: ~3e2 • Consider a circuit which fails with probability e Area: A Pfail: e

  6. Distributed Voting P1 MAJ MAJ P2 MAJ P3 • Area ~ • Failure probability:

  7. Double Encoding P1 Dist. MAJ P2 P3 Area: P1 Dist. MAJ Dist. MAJ P2 Failure probability: P3 P1 Dist. MAJ P2 P3

  8. Recursive Encoding: Area Cost • Recursion: • Area: • Failure probability:

  9. Pfail$ Area Fungibility P1 MAJ P2 MAJ P3 MAJ • What tradeoffs are possible? Pfail(A) • Area • Pfail e’ e Ae A’e Area

  10. Example: erfc(A1/4) Reliability $ Area Fungible Region ~10-12 10 Fault Tolerant 10-9 8 10-7 Normal Pfail -log(Pfail) 6 4 2 Area 0 100 200 300

  11. Only for some functions Function Effective Region

  12. Conclusions Reliability $ Space, Time, Energy Fault Tolerance can save resources Sarpeshkar-Mead Model • CMOS? • Neurons, Energy, Rad. Hardening • Side-results from quantum : vN can be useful • Avagadro scale engineering

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