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Reliability is a Fungible Resource

Explore the concept that reliable computers can be built from faulty components, examining tradeoffs between area and reliability in circuit design, with insights into fault tolerance and effective resource utilization.

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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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