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

2. 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, …

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

5. 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

6. 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

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

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

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

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

11. 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

12. Only for some functions
Effective Region

13. 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