Reliability is a Fungible Resource

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Presentation transcript:

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

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, …

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

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

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

Distributed Voting P1 P2 P3 MAJ Area ~ Failure probability:

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

Recursive Encoding: Area Cost Recursion: Area: Failure probability:

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

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

Only for some functions Effective Region

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