A

Dependability

Perspective

on

Emerging

Technologies

Emerging

technologies

are

set

to

provide

further

provisions

for

computing

in

times

when

the

limits

of

current

technology

of

microelectronics

become

an

ever

closer

presence

A

technology

roadmap

document

lists

biologically-inspired

computing

and

quantum

computing

as

two

emerging

technology

vectors

for

novel

computing

architectures

-LSB-

-RSB-

But

the

potential

benefits

that

will

come

from

entering

the

nanoelectronics

era

and

from

exploring

novel

nanotechnologies

are

foreseen

to

come

at

the

cost

of

increased

sensitivity

to

influences

from

the

surrounding

environment

This

paper

elaborates

on

a

dependability

perspective

over

these

two

emerging

technology

vectors

from

a

designer

's

standpoint

Maintaining

or

increasing

the

dependability

of

unconventional

computational

processes

is

discussed

in

two

different

contexts

one

of

a

bio-inspired

computing

architecture

-LRB-

the

Embryonics

project

-RRB-

and

another

of

a

quantum

computational

architecture

-LRB-

the

QUERIST

project

-RRB-

B.

-LSB-

Performance

and

Reliability

-RSB-

Reliability

Testing

and

Fault-Tolerance

C.

-LSB-

Performance

of

Systems

-RSB-

Fault-Tolerance

Reliability

Availability

and

Serviceability

Design

Reliability

Theory

High-end

computing

has

reached

nearly

every

corner

of

our

present

day

life

in

a

variety

of

forms

taylored

to

accommodate

either

general

purpose

or

specialized

applications

Computers

may

be

considerred

as

fine

exponents

of

the

present

days

technological

wave

if

not

their

finest

they

certainly

do

count

as

solid

indispensable

support

for

the

finest

From

the

very

beginning

of

the

computing

advent

the

main

target

was

squeezing

out

any

additional

performance

The

inception

period

was

not

always

trouble-free

accurate

computation

results

being

required

at

an

ever

faster

pace

on

a

road

that

has

become

manifold

some

applications

do

require

computational

speed

as

a

top

priority

others

are

set

for

the

highest

possible

dependability

while

still

delivering

sufficient

performance

levels

Several

definitions

for

dependability

have

been

proposed

the

ability

of

a

system

to

avoid

service

failures

that

are

more

frequent

or

more

severe

than

is

acceptable

-LSB-

-RSB-

or

the

property

of

a

computer

system

such

that

reliance

can

justifiably

be

placed

on

the

service

it

delivers

-LSB-

-RSB-

-LSB-

-RSB-

Dependability

is

therefore

a

synthetic

term

specifying

a

qualitative

system

descriptor

that

can

generally

be

quantified

through

a

list

of

attributes

including

reliability

fault

tolerance

availability

and

others

In

real

world

a

dependable

system

would

have

to

operate

normally

over

extended

periods

of

time

before

experiencing

any

fail

-LRB-

reliability

availability

-RRB-

and

to

recover

quickly

from

errors

-LRB-

fault

tolerance

self-test

and

self-repair

-RRB-

The

term

acceptable

has

an

essential

meaning

within

the

dependability

's

definition

setting

the

upper

limits

of

the

damages

that

can

be

supported

by

the

system

while

still

remaining

functional

or

computationally

accurate

A

dependability

analysis

should

take

into

consideration

if

not

quantitative

figures

for

the

acceptable

damage

limit

at

least

a

qualitative

parameter

representation

for

its

attributes

Dependable

systems

are

therefore

crucial

for

applications

that

prohibit

or

limit

human

interventions

such

as

long-term

exposure

to

aggressive

-LRB-

or

even

hostile

-RRB-

environments

The

best

examples

are

long

term

operating

machines

as

required

by

managing

deep-underwater/nuclear

activities

and

outer

space

exploration

There

are

three

main

concerns

that

should

be

posed

through

a

system

's

design

in

order

to

achieve

high

dependability

-LSB-

-RSB-

Specifying

the

dependability

requirements

selecting

the

dependability

requirements

that

have

to

be

pursued

in

building

the

computing

system

based

on

known

or

assumed

goals

for

the

part

of

the

world

that

is

directly

affected

by

the

computing

system

Permission

to

make

digital

or

hard

copies

of

all

or

part

of

this

work

for

personal

or

classroom

use

is

granted

without

fee

provided

that

copies

are

not

made

or

distributed

for

profit

or

commercial

advantage

and

that

copies

bear

this

notice

and

the

full

citation

on

the

first

page

To

copy

otherwise

or

republish

to

post

on

servers

or

to

redistribute

to

lists

requires

prior

specific

permission

and/or

a

fee

Designing

and

implementing

the

computing

system

so

as

to

achieve

the

dependability

required

However

this

step

is

hard

to

implement

since

the

system

reliability

can

not

be

satisfied

CF

May

Ischia

Italy

Copyright

ACM

simply

from

careful

design

Some

techniques

can

be

used

to

help

to

achieve

this

goal

such

as

using

fault

injection

to

evaluate

the

design

process

Validating

a

system

gaining

confidence

that

a

certain

dependability

requirement/goal

has

been

attained

This

paper

will

address

these

main

concerns

through

an

attempt

to

provide

an

in-depth

view

over

modern

computing

directions

and

paradigms

which

we

consider

to

be

representative

for

the

efforts

involved

in

improving

overall

dependability

Motivations

We

have

listed

some

of

the

applications

of

dependable

computing

systems

as

linked

to

activities

that

take

place

in

special

environments

such

as

deep

underwater

or

outer

space

At

a

very

first

sight

these

applications

would

appear

specific

enough

to

not

encourage

a

specific

design

for

dependability

approach

in

computing

However

evidence

suggest

this

is

hardly

the

case

on

the

contrary

it

is

difficult

to

imagine

a

domain

left

unconquered

by

computer

systems

during

times

when

industrial

transport

financial

services

and

others

do

rely

heavily

on

accurate

computer

operation

at

any

given

moment

If

computer

innacuracies

could

be

more

easily

overlooked

at

home

professional

environments

can

not

accept

such

missbehaviors

Yet

the

recent

history

of

computing

provides

evidence

that

dependability

is

not

a

sine

qua

non

feature

During

their

life

cycle

electronic

devices

constantly

suffer

a

number

of

influences

that

manifest

predominantly

over

transient

regimes

which

in

turn

introduce

a

variety

of

errors

unified

in

the

literature

under

the

name

of

transient

faults

soft

errors

or

single

event

upsets

-LRB-

SEUs

-RRB-

The

rate

electronic

devices

are

affected

with

is

known

under

the

term

of

soft

error

rate

or

simply

SER

and

is

measured

in

fails

per

unit

time

Because

it

relies

on

transient

phenomena

due

to

changing

states

and

logical

values

digital

electronics

makes

up

for

a

special

category

that

is

also

affected

by

soft

errors

No

matter

the

name

they

are

referred

under

these

errors

affect

the

computing

processes

and

are

due

to

electromagnetic

noise

and/or

external

radiations

rather

than

design

or

manufacturing

flaws

-LSB-

-RSB-

One

cause

at

the

origin

of

soft

fails

affecting

digital

devices

is

known

to

be

due

to

radioactive

decay

processes

Radioactive

isotopes

widely

used

for

a

range

of

purposes

might

contaminate

semiconductor

materials

leading

to

soft

errors

evidence

is

available

throughout

the

literature

both

by

empirical

observations

and

experimental

results

-LSB-

-RSB-

Consequently

cosmic

rays

containing

a

broad

range

of

energized

atomic/subatomic

particles

may

lead

to

the

appearance

of

soft

fails

Computers

therefore

are

susceptive

to

soft

errors

an

issue

that

will

potentially

become

essential

with

the

advent

of

emerging

technologies

As

acknowledged

by

the

International

Technology

Roadmap

for

Semiconductors

-LRB-

ITRS

-RRB-

issued

at

the

end

of

-LSB-

-RSB-

the

microelectronics

industry

faces

a

challenging

task

in

going

to

and

beyond

scale

in

order

to

address

beyond

CMOS

applications

Scaling

down

the

technology

will

enable

an

extremely

large

number

of

devices

to

be

integrated

onto

the

same

chip

However

the

great

challenge

will

be

to

ensure

the

new

devices

will

be

operational

at

this

scale

-LSB-

-RSB-

since

they

will

exhibit

a

sensitive

behavior

to

soft

fails

In

order

to

address

the

negative

effects

brought

by

technology

scaling

it

is

to

be

expected

that

significant

control

resources

will

need

to

be

implem

ented

-LSB-

-RSB-

Another

challenging

aspect

concerning

emerging

technologies

is

to

match

the

newly

developed

device

technologies

with

new

system

architectures

a

synergistic/collaborative

development

of

the

two

being

seen

as

likely

to

be

very

rewarding

The

potential

of

biologically-inspired

and

quantum

computing

architectures

is

acknowledged

by

the

ITRS

report

on

emerging

technologies

-LSB-

-RSB-

-LRB-

see

Figure

-RRB-

This

paper

will

investigate

the

relevance

of

soft

fails

and

attempt

to

provide

means

of

harnessing

their

negative

effects

on

modern

computing

in

the

context

of

biologically-inspired

and

quantum

computing

architectures

Figure

Bio-inspired

and

quantum

computing

are

acknowledged

as

architectural

technology

vectors

in

emerging

technologies

-LSB-

-RSB-

Paper

Outline

This

paper

is

structured

as

follows

Section

will

address

the

first

main

concern

that

is

specifying

and

selecting

dependability

requirements

that

will

have

to

be

pursued

when

building

a

computational

platform

Parameters

that

describe

and

quantify

dependability

attributes

such

as

reliability

will

be

introduced

with

a

highlight

on

their

accepted

models

and

their

issues

A

particular

consideration

will

be

given

to

the

failure

rate

parameter

which

is

the

basis

of

all

reliability

analyses

Section

will

approach

some

of

the

means

for

design

for

dependability

it

will

therefore

elaborate

upon

two

emerging

technology

vectors

as

seen

by

the

ITRS

report

-LSB-

-RSB-

which

define

two

novel

architectures

namely

biologically-inspired

-LRB-

or

bio-inspired

-RRB-

and

quantum

computing

We

will

introduce

two

projects

and

their

corresponding

architectures

called

Embryonics

-LRB-

as

a

biologically-inspired

computing

platform

-RRB-

and

QUERIST

-LRB-

as

a

quantum

computing

platform

designed

to

allow

and

study

error

injection

-RRB-

These

two

architectures

are

representative

for

the

coming

age

of

nano-computing

where

computational

processes

take

place

as

encoded

at

the

very

inner

core

level

of

matter

be

it

semiconductor

material

-LRB-

for

nanoelectronics

targetted

here

by

the

Embryonics

project

-RRB-

or

atomic

scale

dynamics

-LRB-

for

quantum

computing

targetted

here

by

the

QUERIST

project

-RRB-

This

section

will

then

introduce

dependability

aspects

within

bio-inspired

computing

-LRB-

the

Embryonics

project

being

investigated

in

SubSection

-RRB-

and

within

quantum

computing

-LRB-

the

QUERIST

project

being

investigated

in

SubSection

-RRB-

Finally

Section

will

present

the

conclusions

and

prospects

for

designing

emerging

technology

dependable

computing

systems

as

we

see

them

An

important

dependability

attribute

for

any

given

system

lies

in

its

capacity

to

operate

reliably

for

a

given

time

interval

knowing

that

normal

operation

was

delivered

at

initial

time

-LSB-

-RSB-

Reliability

functions

are

modelled

as

exponential

functions

of

parameter

which

is

the

failure

rate

The

reliability

of

a

system

is

the

consequence

of

the

reliability

of

all

of

its

subsystems

The

heterogeneity

of

the

system

leads

to

a

difficult

quantitative

assessment

of

its

overall

reliability

moreover

estimating

the

reliability

functions

is

further

made

difficult

because

formal

rigour

is

not

commercially

available

this

being

kept

under

military

mandate

-LSB-

-RSB-

The

failure

rate

for

a

given

system

can

be

modelled

as

a

function

of

the

failure

rates

of

its

individual

subsystems

suggestions

being

present

in

the

document

which

is

publicly

available

-LSB-

-RSB-

However

this

document

has

been

strongly

criticized

for

its

failure

rate

estimations

based

on

the

Arrhenius

model

which

relates

the

failure

rate

to

the

operating

temperature

B

E

K

T

Ke

-LRB-

-RRB-

where

K

is

a

constant

K

B

is

Boltzmann

's

constant

T

is

the

absolute

temperature

and

E

is

the

activation

energy

for

the

process

Quantitative

values

for

failure

rates

show

significant

differences

between

those

predicted

using

and

those

from

testing

real

devices

-LRB-

see

-RRB-

There

are

two

conclusions

that

can

be

drawn

from

this

B

-LSB-

-RSB-

Figure

quantitative

estimations

for

failure

rate

values

are

strongly

dependant

on

the

quality

of

information

used

unfortunately

current

reliable

information

about

electronic

devices

is

known

to

be

lacking

-LSB-

-RSB-

despite

differences

between

predicted

and

real

values

the

methodology

can

be

useful

for

qualitative

analyses

in

order

to

take

decisions

regarding

sub-system

parts

that

should

benefit

from

improved

designs

Figure

Predicted

vs

real

failure

rates

plotted

against

temperature

-LSB-

-RSB-

So

far

the

failure

rate

of

digital

devices

has

been

considerred

as

due

to

internal

causes

However

this

is

not

always

the

case

soft

fails

being

equally

present

due

to

the

aggressive

influences

of

the

external

environment

which

also

have

to

be

modelled

-LSB-

-RSB-

The

external

envirnment

features

highly

dynamic

changes

in

its

parameters

which

will

eventually

affect

the

normal

operation

of

digital

devices

that

lack

sufficient

protection

or

ability

to

adapt

Ideally

computing

devices

would

behave

in

a

consistent

and

accurate

manner

regardless

of

fluctuations

in

environmental

parameters

This

is

either

a

consequence

of

soft

error

mitigation

techniques

or

due

to

flexible

hardware/software

functionality

that

allow

the

system

as

a

whole

to

adapt

to

environamental

changes

and

tolerate

induced

faults

While

certain

soft

error

mitigation

techniques

are

available

the

technology

scaling

towards

nanoelectronics

affects

their

efficiency

by

integrating

a

larger

number

of

devices

per

chip

-LRB-

which

requires

a

larger

amount

of

redundant/control

logic

or

other

measures

-RRB-

which

feature

at

the

same

time

smaller

dimensions

-LRB-

which

renders

an

electronic

device

much

more

senzitive

to

the

influence

of

stray

energetic

particles

that

reach

it

as

part

of

cosmic

rays

-RRB-

Both

aspects

are

involved

in

the

development

of

the

two

emerging

technology

vectors

mentioned

in

SubSection

although

having

slightly

different

motivations

while

the

nature

of

the

quantum

environment

prohibits

precise

computation

in

the

absence

of

fault

tolerance

techniques

such

techniques

are

targetted

by

bio-inspired

computing

as

means

of

improving

the

dependability

of

a

computing

platform

Bio-Inspired

Computing

If

living

beings

may

be

considered

to

fulfill

computational

tasks

then

Nature

is

the

ultimate

engineer

each

of

the

living

beings

exhibit

solutions

that

were

successfully

tested

and

refined

in

such

ways

human

engineers

will

never

afford

One

reason

is

time

the

testing

period

coinciding

with

the

very

existence

of

life

itself

Another

reason

is

variety

and

complexity

Nature

has

found

and

adapted

a

variety

of

solutions

to

address

complex

survivability

issues

in

a

dynamically

changing

environment

No

matter

how

Nature

approached

the

process

of

evolution

engineering

could

perhaps

benefit

most

from

drawing

inspiration

from

its

mechanisms

rather

from

trying

to

develop

particular

techniques

Bio-inspired

computing

is

not

a

new

idea

John

von

Neumann

was

preoccupied

to

design

a

machine

that

could

replicate

itself

and

was

quite

interested

in

the

study

of

how

the

behavior

of

the

human

brain

could

be

implemented

by

a

computer

-LSB-

-RSB-

-LSB-

-RSB-

He

also

pioneered

the

field

of

dependable

computing

by

studying

the

possibility

of

building

reliable

machines

out

of

unreliable

components

-LSB-

-RSB-

Unfortunately

the

dream

of

implementing

his

self-reproducing

automata

could

not

become

true

until

the

when

massively

programmable

logic

opened

the

new

era

of

reconfigurable

computing

But

when

trying

to

adapt

nature

's

mechanisms

in

digital

devices

it

becomes

most

evident

that

biological

organisms

are

rightfully

the

most

intricate

structures

known

to

man

They

continuously

demonstrate

a

highly

complex

behavior

due

to

massive

parallel

cooperation

between

huge

numbers

of

relatively

simple

elements

the

cells

And

considering

uncountable

variety

of

living

beings

with

a

life

span

up

to

several

hundreds

-LRB-

for

the

animal

regnum

-RRB-

or

even

thousands

-LRB-

for

the

vegetal

regnum

-RRB-

of

years

it

seems

nature

is

the

closest

spring

of

inspiration

for

designing

dependable

fault

tolerant

systems

Investigating

the

particularities

of

natural

systems

a

taxonomy

of

three

categories

of

processes

can

be

identified

-LSB-

-RSB-

Phylogenetic

processes

constitute

the

first

level

of

organization

of

the

living

matter

They

are

concerned

with

the

temporal

evolution

of

the

genetic

heritage

of

all

individuals

therefore

mastering

the

evolution

of

all

species

The

phylogenetic

processes

rely

on

mechanisms

such

as

recombination

and

mutation

which

are

essentially

nondeterministic

the

error

rate

ensures

here

nature

's

diversity

Ontogenetic

processes

represent

the

second

level

of

organization

of

the

living

matter

They

are

also

concerned

with

the

temporal

evolution

of

the

genetic

heritage

of

in

this

case

a

single

multicellular

individual

therefore

mastering

an

individual

's

development

from

the

stage

of

a

single

cell

the

zygote

through

succesive

cellular

division

and

specialization

to

the

adult

stage

These

processes

rely

on

deterministic

mechanisms

any

error

at

this

level

results

in

malformations

Epigenetic

processes

represent

the

third

level

of

organization

of

the

living

matter

They

are

concerned

with

the

integration

of

interactions

with

the

surrounding

environment

therefore

resulting

in

what

we

call

learning

systems

This

taxonomy

is

important

in

that

it

provides

a

model

called

POE

-LRB-

from

Phylogeny

Ontogeny

and

Epigenesis

-RRB-

that

inspires

the

combination

of

processes

in

order

to

create

novel

bio-inspired

hardware

-LRB-

see

Figure

-RRB-

We

believe

this

is

also

important

from

a

dependability

engineering

perspective

for

the

following

reasons

Phylogenetic

processes

were

assimilated

by

modern

computing

as

evolutionary

computation

including

genetic

algorithms

and

genetic

programming

The

essence

of

any

genetic

algorithm

is

the

derivation

of

a

solution

space

based

on

recombination

crossover

and

mutation

processes

that

spawn

a

population

of

individuals

each

encoding

a

possible

solution

One

may

consider

that

each

such

step

with

the

exception

of

discovering

the

solution

is

equivalent

to

a

process

of

error

injection

which

in

turn

leads

to

wandering

from

the

optimal

solution

-LRB-

or

class

of

solutions

-RRB-

However

genetic

algorithms

prove

to

be

successful

despite

this

error

injection

the

fitness

function

being

responsible

for

the

successful

quantification

of

the

significance

of

the

error

Therefore

genetic

computation

is

intrinsicaly

resilient

to

faults

and

errors

largely

due

to

the

fact

that

they

are

part

of

the

very

process

that

generates

the

solutions

Ontogenetic

processes

have

been

implemented

in

digital

hardware

with

modular

and

uniform

architectures

Such

an

architecture

enables

the

implementation

of

mechanisms

similar

to

the

cellular

division

and

cellular

differentiation

that

take

place

in

living

beings

-LSB-

-RSB-

These

mechanisms

bring

the

advantage

of

distributed

and

hierarchical

fault

tolerance

strategies

the

uniformity

of

the

architecture

also

makes

any

module

to

be

universal

that

is

to

be

able

to

take

over

the

role

of

any

other

damaged

module

Epigenetic

processes

were

assimilated

by

modern

computing

mainly

as

artificial

neural

networks

-LRB-

or

ANNs

-RRB-

as

inspired

by

the

nervous

system

and

much

less

as

inspired

by

the

immune

or

endocrine

systems

from

superior

multicellular

living

beings

ANNs

are

known

to

have

a

generalization

capacity

that

is

to

respond

well

even

if

the

input

patterns

are

not

part

of

the

patterns

used

during

the

learning

phase

This

means

that

ANNs

possess

a

certain

ability

to

tolerante

faults

whether

they

manifest

at

the

inputs

or

inside

their

intenal

architecture

With

the

advent

of

field

programmable

logic

-LRB-

of

which

the

most

salient

representative

are

the

FPGAs

-RRB-

it

is

now

possible

to

change

hardware

functionality

through

software

thus

allowing

information

to

govern

matter

in

digital

electronics

This

is

not

dissimilar

to

what

happens

in

nature

information

coded

in

DNA

affects

the

development

of

an

organism

A

special

kind

of

such

digital

devices

that

change

dynamically

their

behavior

are

known

as

evolvable

or

adaptive

hardware

they

are

bio-inspired

computing

systems

whose

behaviors

may

change

according

to

computational

targets

or

if

harsh

or

unknown

environments

are

to

be

explored

for

the

purpose

of

maximizing

dependability

Figure

The

POE

model

of

bio-inspired

systems

-LSB-

-RSB-

Quantum

Computing

Error

detection

and

correction

techniques

are

vital

in

quantum

computing

due

to

the

destructive

effect

of

the

environment

which

therefore

acts

as

an

omnipresent

error

generator

Error

detection

and

correction

must

provide

a

safe

recovery

process

within

quantum

computing

processes

through

keeping

error

propagation

under

control

Without

such

dependability

techniques

there

could

be

no

realistic

prospect

of

an

operational

quantum

computational

device

-LSB-

-RSB-

There

are

two

main

sources

of

errors

the

first

is

due

to

the

erroneous

behavior

of

the

quantum

gate

producing

the

so-called

processing

errors

the

second

is

due

to

the

macroscopic

environment

that

interacts

with

the

quantum

state

producing

the

storing

and

transmitting

errors

The

consistency

of

any

quantum

computation

process

can

be

destroyed

by

innacuracies

and

errors

if

the

error

probability

in

the

basic

components

-LRB-

qubits

quantum

gates

-RRB-

excedes

an

accuracy

threshold

This

is

a

critical

aspect

since

the

microscopic

quantum

states

are

prone

to

frequent

errors

The

main

error

source

is

the

decoherence

effect

-LSB-

-RSB-

The

environment

is

constantly

attempting

to

measure

the

sensitive

quantum

superposition

state

a

phenomenon

that

can

not

be

avoided

technologically

since

it

is

not

-LRB-

yet

-RRB-

possible

to

isolate

them

perfectly

The

superposition

state

will

decay

through

measuring

and

will

therefore

become

a

projection

of

the

state

vector

onto

a

basis

vector

-LRB-

or

eigenstate

-RRB-

The

most

insidious

error

however

appears

when

decoherence

affects

the

quantum

amplitudes

without

destroying

them

this

is

similar

to

small

analog

errors

Issues

stated

above

are

solved

on

one

hand

through

intrinsic

fault

tolerance

by

technological

implementation

-LRB-

topological

interactions

-LSB-

-RSB-

-RRB-

and

on

the

other

hand

by

error

correcting

techniques

at

the

unitary

-LRB-

gate

network

-RRB-

level

We

will

focus

on

the

error

detecting

and

correcting

techniques

which

are

difficult

to

approach

due

to

quantum

constraints

the

useful

state

can

neither

be

observed

-LRB-

otherwise

it

will

decohere

-RRB-

nor

can

it

be

cloned

Background

As

expressed

in

bra-ket

notation

-LSB-

-RSB-

the

qubit

is

a

normalized

vector

in

some

Hilbert

space

H

-LCB-

-RCB-

being

the

orthonormal

basis

a

a

-LRB-

are

the

so-called

quantum

amplitudes

representing

the

square

root

of

the

associated

measurement

probabilities

for

the

eigenstates

a

a

C

and

respectively

with

a

a

-RRB-

Therefore

the

qubit

can

be

affected

by

types

of

errors

Bit

flip

errors

are

somewhat

similar

to

classical

bit

flip

errors

For

a

single

qubit

things

are

exactly

the

same

as

in

classical

computation

For

or

more

qubits

flip

errors

affecting

the

state

may

modify

it

or

leave

it

unchanged

For

instance

if

we

consider

the

so-called

cat

state

-LRB-

Cat

-RRB-

-LSB-

-RSB-

and

the

first

qubit

is

affected

by

a

bit

flip

error

the

resulting

state

will

be

-LRB-

-RRB-

Cat

But

if

both

qubits

are

affected

by

bit

flips

there

will

be

no

change

in

the

state

-LRB-

-RRB-

Cat

Cat

Phase

errors

affect

the

phase

of

one

of

the

qubit

's

amplitudes

and

is

expressed

as

This

type

of

error

is

very

dangerous

due

to

its

propagation

behavior

but

it

only

makes

sense

when

dealing

with

superposition

states

If

we

consider

an

equally

weighted

qubit

superposition

state

and

inject

a

phase

error

this

results

in

-LRB-

-RRB-

-LRB-

-RRB-

There

is

a

strict

correspondence

between

bit

flip

and

phase

error

types

due

to

the

way

they

map

onto

Hilbert

spaces

with

the

same

dimension

but

different

basis

The

bit

flip

is

an

error

from

the

space

with

basis

H

-LCB-

-RCB-

whereas

the

phase

error

appears

in

the

same

space

with

basis

-LRB-

-RRB-

-LRB-

-RRB-

or

-LCB-

-RCB-

a

The

space

basis

conversion

in

this

case

is

made

by

applying

the

Hadamard

transform

Figure

shows

an

example

of

transforming

a

bit

flip

error

into

a

phase

error

-LRB-

A

and

vice

versa

-LRB-

B.

Small

amplitude

errors

amplitudes

of

the

quantum

bit

can

be

affected

by

small

errors

similar

to

analog

errors

Even

if

such

an

error

does

not

destroy

the

superposition

and

conserves

the

value

of

the

superposed

states

small

amplitude

errors

could

accumulate

over

time

eventually

ruining

the

computation

In

order

to

avoid

this

situation

specific

methodologies

for

digitizing

small

errors

are

used

to

reduce

them

to

a

non-fault

or

a

bit-flip

and

a

-LSB-

-RSB-

Due

to

the

quantum

physics

laws

fault

tolerance

techniques

have

to

comply

with

the

following

computational

constraints

The

observation

destroys

the

state

Since

observation

is

equivalent

to

measurement

this

leads

to

destroying

the

useful

state

superposition

Information

copying

is

impossible

Quantum

physics

renders

the

cloning

of

a

quantum

state

impossible

meaning

that

a

quantum

state

can

not

be

copied

correctly

Therefore

quantum

error

correction

must

address

the

following

problems

Non-destructive

measurement

Despite

the

first

constraint

it

is

necessary

to

find

a

way

to

measure

the

encoded

information

without

destroying

it

Because

the

encoded

state

can

not

be

measured

directly

one

needs

to

properly

prepare

some

scratch

-LRB-

ancilla

-RRB-

qubits

which

can

then

be

measured

Fault-tolerant

recovery

Due

to

the

high

error

rate

in

quantum

computational

devices

it

is

likely

that

the

error

recovery

itself

will

be

affected

by

errors

If

the

recovery

process

is

not

fault-tolerant

then

any

error

coding

becomes

useless

Phase

error

backward

propagation

If

we

consider

the

XOR

gate

from

Figure

-LRB-

A

a

flip

error

affecting

the

target

qubit

-LRB-

b

-RRB-

will

propagate

backwards

and

also

affect

the

source

qubit

This

is

due

to

the

gate

network

equivalence

from

Figure

-LRB-

B

and

the

basis

transformation

described

by

Figure

Figure

Correspondence

between

bit

flip

and

phase

errors

Figure

-LRB-

A

The

backward

propagation

of

a

phase

error

for

the

XOR

gate

-LRB-

B

Gate

network

equivalence

In

order

to

deal

with

the

problems

described

the

next

strategies

have

to

be

followed

Digitizing

small

errors

The

presence

of

small

errors

is

not

a

major

concern

as

they

can

be

digitized

using

a

special

technique

based

on

measuring

auxiliary

-LRB-

ancilla

-RRB-

qubits

-LSB-

-RSB-

Ancilla

usage

Since

qubit

cloning

is

impossible

a

majority

voting

strategy

is

difficult

to

implement

However

by

using

ancilla

qubits

the

eigenstate

information

can

be

duplicated

inside

the

existing

superposition

resulting

in

the

entanglement

of

the

ancilla

with

the

useful

data

Because

any

measurement

performed

on

the

ancilla

could

have

repercussions

on

the

useful

qubits

the

appropriate

strategy

will

employ

special

coding

for

both

data

qubits

and

ancilla

-LRB-

data

errors

only

will

be

copied

onto

the

ancilla

-RRB-

followed

by

the

computation

of

an

error

syndrome

which

has

to

be

obtained

through

measuring

the

ancilla

-LRB-

see

Figure

-RRB-

Avoiding

massive

spreading

of

phase

errors

As

shown

previously

a

phase

error

on

the

target

qubit

will

propagate

on

all

source

qubits

The

solution

is

to

use

more

ancilla

qubits

as

targets

so

that

no

ancilla

qubit

is

used

more

than

once

Figure

Fault-tolerant

procedure

with

ancilla

qubits

Ancilla

and

syndrome

accuracy

Setting

the

ancilla

code

to

some

known

quantum

state

could

be

an

erroneous

process

Computing

the

syndrome

is

also

prone

to

errors

Hence

on

one

hand

one

has

to

make

sure

that

the

ancilla

qubits

are

in

the

right

state

by

verifying

and

recovering

them

if

needed

on

the

other

hand

in

order

to

have

a

reliable

syndrome

it

must

be

computed

repeatedly

Error

recovery

As

the

small

errors

can

be

digitized

-LRB-

therefore

they

are

either

corrected

or

transformed

into

bit

flip

errors

-RRB-

the

recovery

must

deal

only

with

bit

flip

and

phase

errors

A

state

that

needs

to

be

recovered

is

described

by

if

no

error

occurs

for

a

flip

error

for

a

phase

error

for

both

flip

and

phase

errors

error

a

a

a

a

a

a

a

a

a

a

Correcting

a

bit

flip

error

means

applying

the

negation

unitary

transformation

to

the

affected

qubit

To

correct

phase

and

combined

errors

the

following

unitary

operators

will

have

to

be

applied

respectively

N

x

U

Z

Y

N

Z

i

U

U

U

U

i

Quantum

Error

Correcting

Codes

Quantum

error

coding

and

correcting

-LRB-

QECC

-RRB-

is

performed

with

special

coding

techniques

inspired

from

the

classic

Hamming

codes

The

classical

error

coding

is

adapted

so

that

it

becomes

suitable

for

the

quantum

strategy

allowing

only

the

ancilla

qubits

to

be

measured

The

state-of-the-art

in

QECC

is

represented

by

the

stabilizer

encoding

a

particular

case

being

the

Steane

codes

-LRB-

the

Shor

codes

may

also

be

used

-LSB-

-RSB-

-RRB-

Steane

's

code

is

a

single

error

correcting

code

inspired

from

classical

Hamming

coding

and

can

be

adapted

for

ancilla

coding

as

well

Therefore

it

can

not

recover

from

two

identical

qubit

faults

but

it

can

recover

from

a

bit

flip

a

phase

flip

The

Steane

coding

of

and

consists

of

an

equally

weighted

superposition

of

all

the

valid

Hamming

words

with

an

even

and

odd

number

of

respectively

-LRB-

-RRB-

u

u

u

u

c

c

c

S

even

u

u

u

u

c

c

c

-LRB-

-RRB-

u

u

u

u

c

c

c

S

odd

u

u

u

u

c

c

c

-LRB-

-RRB-

Applying

the

Steane

coding

on

an

arbitrary

given

quantum

state

a

a

transforms

it

into

S

S

a

a

S

This

code

was

designed

to

correct

bit-flip

errors

but

by

changing

the

basis

-LRB-

through

a

Hadamard

transform

-RRB-

the

phase

error

transforms

into

a

bit

flip

error

which

can

then

be

corrected

-LRB-

-RRB-

-LRB-

-RRB-

S

S

S

S

S

S

S

H

H

S

-LRB-

-RRB-

Fault

Tolerance

Methodologies

Quantum

error-correcting

codes

exist

for

r

errors

r

r

N

Therefore

a

non-correctable

error

occurs

if

a

number

of

r

errors

occur

simultaneously

before

the

recovery

process

If

the

probability

of

a

quantum

gate

error

or

storage

error

in

the

time

unit

is

of

order

then

the

probability

of

an

error

affecting

the

processed

data

block

becomes

of

order

r

which

is

negligible

if

r

is

sufficiently

large

However

by

increasing

r

the

safe

recovery

also

becomes

more

complex

and

hence

prone

to

errors

it

is

possible

that

r

errors

accumulate

in

the

block

before

the

recovery

is

performed

Considering

the

relationship

between

r

and

the

number

of

computational

steps

required

for

computing

the

syndrome

is

polynomial

of

the

order

p

r

It

was

proven

that

in

order

to

reduce

as

much

as

possible

the

error

probability

r

must

be

chosen

so

that

p

r

e

A

href

html

-LSB-

-RSB-

-LSB-

-RSB-

By

consequence

if

attempting

to

execute

N

cycles

of

error

correction

without

any

r

errors

accumulating

before

the

recovery

ends

then

exp

p

N

Therefore

the

accuracy

degree

will

be

of

the

form

-LRB-

-RRB-

log

p

N

which

is

better

than

the

accuracy

degree

corresponding

to

the

no-coding

case

N

However

there

exists

a

so

that

if

then

non-correctable

error

becomes

likely

which

limits

the

length

of

the

recovery

process

Given

the

extremely

large

number

of

gates

employed

by

a

quantum

algorithm

implementation

also

has

to

be

very

large

for

Shor

's

algorithm

must

be

higher

than

max

N

max

N

N

max

N

max

N

-LSB-

-RSB-

As

shown

in

Figure

the

required

accuracy

degree

approaches

today

's

technological

limits

-LRB-

tipically

for

p

-RRB-

after

N

For

a

fault

tolerant

encoding

solution

for

Shor

algorithm

implementation

this

should

have

happened

after

N

-LSB-

-RSB-

-LSB-

-RSB-

-LRB-

-RRB-

Additional

fault

tolerance

must

be

employed

in

order

to

preserve

reliable

quantum

computation

over

an

arbitrary

number

of

computational

steps

Concatenated

coding

represents

one

such

technique

which

improves

the

reliability

by

shaping

the

size

of

the

code

blocks

and

the

number

of

code

levels

It

is

also

resource

demanding

and

vulnerable

to

correlated

errors

-LSB-

-RSB-

-LSB-

-RSB-

Another

approach

replacing

the

concatenated

codes

is

based

on

Reconfigurable

Quantum

Gate

Arrays

-LRB-

RQGAs

-RRB-

-LSB-

-RSB-

-LSB-

-RSB-

which

are

used

for

configuring

ECC

circuits

based

on

stabilizer

codes

-LSB-

-RSB-

-LSB-

-RSB-

By

using

a

quantum

configuration

register

for

the

RQGA

-LRB-

i.e.

a

superposition

of

classical

configurations

-RRB-

the

reconfigurable

circuit

is

brought

to

a

state

where

it

represents

a

simultaneous

superposition

of

distinct

ECC

circuits

After

measuring

the

configuration

register

only

one

ECC

circuit

is

selected

and

used

if

k

distinct

ECC

circuits

were

superposed

and

the

gate

error

rate

is

then

the

overall

gate

error

probability

becomes

k

-LRB-

s

ee

Figure

-RRB-

As

a

result

the

accuracy

threshold

value

for

the

RQGA

solution

clearly

dominates

the

technological

accuracy

limit

as

s

hown

in

Figure

-LSB-

-RSB-

Figure

Accuracy

plots

p

for

xi

p

for

xi

p

for

xi

xi

for

no-coding

ref

is

the

reference

accuracy

-LRB-

i.e.

the

accuracy

allowed

by

today

's

state

of

the

art

technology

-RRB-

Figure

A

quantum

configuration

register

acts

as

a

superposition

of

k

distinct

circuits

sharing

the

same

input

state

and

the

same

output

qubits

In

order

to

model

the

erroneous

behavior

of

a

device

of

system

it

is

necessary

to

understand

the

causality

of

phenomena

concerned

A

defect

affecting

a

device

from

a

physical

point

of

view

is

called

a

fault

or

a

fail

Faults

may

be

put

in

evidence

through

logical

misbehavior

in

which

case

they

transform

into

errors

Finally

errors

accumulating

can

lead

to

system

failure

-LSB-

-RSB-

The

fault-error

failure

causal

chain

is

essential

to

developping

techniques

that

reduce

the

risk

of

error

occurrence

even

in

the

presence

of

faults

in

order

to

minimize

the

probability

of

a

system

failure

and

can

be

architecture

specific

We

will

elaborate

next

on

techniques

used

by

a

bio-inspired

and

by

a

quantum

computing

platform

Figure

Evolution

of

accuracy

threshold

value

for

RQHW

stabilizer

codes

-LRB-

xir

-RRB-

the

technological

accuracy

limit

-LRB-

lim

-RRB-

is

also

provided

for

a

relevant

comparison

The

Embryonics

Approach

Several

years

before

his

untimely

death

John

von

Neumann

began

developping

a

theory

of

automata

which

was

to

contain

a

systematic

theory

of

mixed

mathematical

and

logical

forms

aimed

to

a

better

understanding

of

both

natural

systems

and

computers

-LSB-

-RSB-

The

essence

of

von

Neumann

's

message

appears

to

entail

the

formula

genotype

ribotype

phenotype

He

provided

the

foundations

of

a

self-replicating

machine

-LRB-

the

phenotype

-RRB-

consisting

of

its

complete

description

-LRB-

the

genotype

-RRB-

which

is

interpreted

by

a

ribosome

-LRB-

the

ribotype

-RRB-

Embryonics

-LRB-

a

contraction

for

embryonic

electronics

-RRB-

is

a

long

term

research

project

launched

by

the

Logic

Systems

Laboratory

at

the

Swiss

Federal

Institute

of

Technology

Lausanne

Switzerland

Its

aim

is

to

explore

the

potential

of

biologically-inspired

mechanisms

by

borrowing

and

adapting

them

from

nature

into

digital

devices

for

the

purpose

of

endowing

them

with

the

remarkable

robustness

present

in

biological

entities

-LSB-

-RSB-

Though

perhaps

fuzzy

at

a

first

glance

analogies

between

biology

and

electronics

are

pres

ented

in

Table

-LSB-

-RSB-

-LSB-

-RSB-

But

if

we

consider

that

the

function

of

a

living

cell

is

determined

by

the

genome

and

that

a

computer

's

functionality

is

determined

by

the

operating

program

then

the

two

worlds

may

be

regarded

as

sharing

a

certain

degree

of

similarity

Three

fundamental

features

shared

by

living

entities

are

required

to

be

targetted

by

Embryonics

in

order

to

embody

the

formula

genotype

ribotype

phenotype

into

digital

hardware

multicellular

organisms

are

made

of

a

finite

number

of

cells

which

in

turn

are

made

of

a

finite

number

of

chemically

bonded

molecules

each

cell

-LRB-

beginning

with

the

original

cell

the

zygote

-RRB-

may

generate

one

or

several

daughter

cell

-LRB-

s

-RRB-

through

a

process

called

cellular

division

both

the

parent

and

the

daughter

cell

-LRB-

s

-RRB-

share

the

same

genetic

information

called

the

genome

different

types

of

cells

may

exist

due

to

cellular

differentiation

a

process

through

which

only

a

part

of

the

genome

is

executed

These

fundamental

features

led

the

Embryonics

project

to

settle

for

an

architectural

hierarchy

of

four

levels

-LRB-

see

Figure

-RRB-

We

will

not

delve

very

deep

inside

the

Embryonics

phylosophy

as

such

details

were

broadly

covered

by

literature

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

we

will

however

introduce

each

of

the

four

levels

in

order

to

be

able

to

see

how

this

bio-inspired

platform

fits

modern

design

for

dependability

efforts

Table

Analogies

present

in

Embryonics

-LSB-

-RSB-

Biology

Electronics

Multicellular

organism

Parallel

computer

systems

Cell

Processor

Molecule

FPGA

Element

Figure

Structural

hierarchy

in

Embryonics

-LSB-

-RSB-

The

upmost

level

in

Embryonics

bearing

a

certain

similarity

to

what

is

found

in

nature

is

the

population

level

composed

of

a

number

of

organisms

One

level

down

the

hierarchy

constitutes

the

organismic

level

and

corresponds

to

individual

entities

in

a

variety

of

functionalities

and

sizes

Each

of

the

organisms

may

be

further

decomposed

into

smaller

simpler

parts

called

cells

which

in

turn

may

be

decomposed

in

molecules

According

to

Embryonics

a

biological

organism

corresponds

in

the

world

of

digital

systems

to

a

complete

computer

a

biological

cell

is

equivalent

to

a

processor

and

the

smallest

part

in

biology

the

molecule

may

be

seen

as

the

smallest

programmable

element

in

digital

electronics

-LRB-

s

ee

Table

-RRB-

An

extremely

valuable

consequence

of

the

Embryonics

architecture

is

that

each

cell

is

universal

containing

a

copy

of

the

whole

of

the

organism

's

genetic

material

the

genome

This

enables

very

flexible

redundancy

strategies

the

living

organisms

being

capable

of

self-repair

-LRB-

healing

-RRB-

or

self-replication

-LRB-

cloning

-RRB-

-LSB-

-RSB-

Self-replication

may

be

of

great

interest

in

the

nanoelectronics

era

where

extremely

large

areas

of

programmable

logic

will

probably

render

any

centralized

control

very

inefficient

Instead

the

self-replication

mechanism

implemented

in

Embryonics

will

allow

the

initial

colonization

of

the

entire

programmable

array

in

a

decentralized

and

distributed

manner

Figure

presents

an

example

of

such

colonization

At

initial

time

the

configuration

bitstream

-LRB-

containing

the

genome

-RRB-

enters

the

bottom

left

corner

of

a

programmable

array

and

at

each

clock

cycle

the

genome

is

pushed

through

and

partitions

the

programmable

space

accordingly

From

a

dependability

standpoint

the

Embryonics

hierarchical

architecture

offers

incentives

for

an

also

hierarchical

self-repair

strategy

Because

the

target

applications

are

those

in

which

the

failure

frequency

must

be

very

low

to

be

acceptable

two

levels

of

self-repair

are

offered

at

the

molecular

level

-LRB-

programmable

logic

is

susceptible

to

soft

fail

occurrences

-RRB-

and

at

the

cellular

level

-LRB-

soft

fails

manifest

at

this

level

as

soft

errors

-RRB-

Let

us

consider

an

example

of

a

simple

cell

made

of

lines

and

columns

of

molecules

of

which

one

column

contains

spare

molecules

If

a

fault

occurs

inside

an

active

cell

it

can

be

repaired

through

transferring

its

functionality

toward

the

appropriate

spare

molecule

which

will

become

active

-LRB-

see

Figure

-RRB-

Figure

Space

colonization

in

Embryonics

-LSB-

-RSB-

Figure

Self-repair

at

the

molecular

level

faulty

molecule

E

is

replaced

by

spare

molecule

H

which

becomes

active

-LSB-

-RSB-

The

self-repair

process

at

molecular

level

ensures

the

fault

recovery

as

long

as

there

are

spare

molecules

left

for

repair

However

it

is

possible

for

a

cell

to

experience

a

multiple

error

in

which

case

the

self-repair

mechanism

at

the

molecular

level

can

no

longer

reconfigure

the

inside

of

the

cell

successfully

If

such

a

situation

arises

then

a

second

self-repair

strategy

is

trigerred

at

a

higher

level

The

cell

will

die

therefore

trigerring

the

self-repair

at

the

cellular

level

the

entire

column

containing

the

faulty

cell

-LRB-

cell

C

in

this

example

-RRB-

being

deactivated

its

role

being

taken

by

the

nearest

spare

column

to

the

right

-LRB-

see

Figure

-RRB-

A

critique

that

could

be

addressed

to

the

current

Embryonics

design

would

be

its

strategy

of

self-repair

at

the

higher

cellular

level

in

case

of

a

faulty

cell

an

entire

column

containing

that

cell

will

be

deactivated

its

role

being

transferred

to

the

first

available

column

of

spares

to

the

right

-LRB-

s

ee

Figure

-RRB-

There

are

two

points

in

which

this

strategy

could

benefit

Instead

of

deactivating

a

whole

column

of

cells

it

would

be

more

efficient

to

only

deactivate

the

faulty

cell

only

-LRB-

see

Figure

-RRB-

The

resources

affected

by

the

role

transfer

would

be

greatly

reduced

-LRB-

one

cell

versus

an

entire

column

-RRB-

coupled

with

the

fact

that

particle

flux

generating

soft

fails

is

unlikely

to

be

homogeneous

and

isotrope

This

means

regions

assimilable

more

likely

to

cells

rather

than

entire

column

of

cells

would

be

more

affected

by

soft

fails

not

to

mention

that

during

genetic

data

transfer

-LRB-

required

by

taking

over

the

role

of

the

faulty

cell

-RRB-

there

is

a

greater

risk

of

enduring

a

new

soft

fail

-LRB-

moving

data

is

much

more

sensitive

to

soft

fails

than

static

data

-RRB-

-LSB-

-RSB-

-LSB-

-RSB-

Such

a

strategy

would

be

consistent

with

that

used

for

the

self-repair

at

the

molecular

level

which

would

simplify

a

thorough

reliability

analysis

Concatenated

coding

would

also

seem

easier

to

be

implemented

and

the

strategy

consistency

would

mean

that

concatenated

coding

would

not

be

limited

to

a

two-level

hierarchy

-LSB-

-RSB-

-LSB-

-RSB-

Figure

Molecular

self-repair

failure

the

cell

dies

-LRB-

bottom

-RRB-

triggering

the

cellular

self-repair

-LRB-

top

-RRB-

-LSB-

-RSB-

We

consider

a

cell

of

M

lines

and

N

columns

being

composed

of

modules

of

M

lines

and

n

s

columns

-LRB-

for

instance

the

cell

presented

in

Figure

consists

of

a

single

such

module

of

two

active

columns

and

one

spare

column

-RRB-

of

which

s

are

spares

In

order

to

meet

certain

reliability

criteria

it

is

necessary

to

know

what

is

the

number

s

of

spare

columns

of

molecules

that

correspond

to

n

columns

of

active

molecules

that

is

the

horizontal

dimensions

for

such

a

module

We

will

not

provide

a

thorough

reliability

analysis

as

this

has

been

done

previously

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

instead

we

will

analyze

the

influences

of

the

proposed

consistent

self-repair

strategy

at

both

molecular

and

cellular

levels

through

the

use

of

logic

molecules

Therefore

Equation

-LRB-

-RRB-

holds

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

k

ModRow

i

R

t

Prob

no

fails

t

Prob

i

fails

t

N

k

n

s

-LRB-

-RRB-

where

-LRB-

-RRB-

ModRow

R

t

represents

the

reliability

function

for

a

row

within

a

module

Then

considering

the

failure

rate

for

one

molecule

the

probability

of

all

molecules

-LRB-

both

active

and

spare

-RRB-

to

operate

normally

in

a

module

's

row

becomes

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

n

s

t

Prob

no

fails

t

e

-LRB-

-RRB-

The

probability

of

a

row

enduring

i

fails

in

the

active

molecules

part

is

the

conditional

probability

of

having

n-i

active

molecules

operating

normally

while

a

number

of

s-i

spare

molecules

are

ready

to

activate

-LRB-

that

is

they

are

not

affected

by

errors

themselves

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

Prob

i

fails

t

Prob

i

fails

active

t

Prob

i

spares

ok

t

-RRB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

n

i

t

n

i

t

n

Prob

i

fails

active

t

e

e

i

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

it

k

i

t

k

Prob

i

spares

ok

t

e

e

i

-LRB-

-RRB-

Then

the

reliability

function

for

an

entire

cell

is

the

cummulated

reliability

functions

for

the

total

number

of

modules

-LRB-

-RRB-

-LRB-

-RRB-

MN

n

s

Cell

ModRow

R

t

R

t

-LRB-

-RRB-

Figure

Proposed

reconfiguration

strategy

at

the

cellular

level

A

self-repair

strategy

that

conserves

the

consistency

between

the

molecular

and

the

cellular

level

would

allow

for

a

more

straightforward

reliability

analysis

Basically

it

would

be

sufficient

to

substitute

dimension

parameters

in

Equations

-LRB-

-RRB-

-LRB-

-RRB-

with

those

approapriate

to

the

analysis

of

an

organism

instead

of

a

cell

To

illustrate

this

we

will

consider

an

organism

of

M

lines

and

N

columns

being

composed

of

modules

of

M

lines

and

n

s

columns

of

which

s

are

spares

we

will

also

use

the

organism

partitioning

into

modules

similar

to

the

partitioning

of

cells

used

before

Therefore

Equation

-LRB-

-RRB-

transforms

into

Equation

-LRB-

-RRB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

k

CellMR

i

R

t

Prob

no

fails

t

Prob

i

fails

t

N

k

n

s

-LRB-

-RRB-

where

-LRB-

-RRB-

CellMR

R

t

represents

the

reliability

function

for

a

row

of

cells

within

an

organism

module

In

this

case

the

significance

of

the

terms

will

be

as

follows

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

n

s

Cell

Prob

no

fails

t

R

t

-LRB-

-RRB-

While

Equation

-LRB-

-RRB-

continues

to

hold

under

the

form

of

Equation

-LRB-

-RRB-

the

significance

of

its

terms

will

change

according

to

the

dimensions

at

the

cellular

level

-LCB-

-RCB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

Prob

i

fails

t

Prob

i

fails

active

t

Prob

i

spares

ok

t

-RRB-

i

k

i

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

n

i

Cell

Cell

n

Prob

i

fails

active

t

R

t

R

t

i

-LRB-

-RRB-

-LCB-

-RCB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

i

Cell

Cell

k

Prob

i

spares

ok

t

R

t

R

t

i

-LRB-

-RRB-

Finally

similar

to

Equation

-LRB-

-RRB-

the

reliability

function

for

an

entire

organism

is

the

cummulated

reliability

functions

for

the

total

number

of

its

modules

-LRB-

-RRB-

-LRB-

-RRB-

M

N

n

s

Org

CellMR

R

t

R

t

-LRB-

-RRB-

Equations

-LRB-

-RRB-

to

-LRB-

-RRB-

provide

the

basics

for

a

thorough

reliability

analysis

for

the

proposed

uniform

strategy

of

hierarchical

reconfiguration

as

opposed

to

the

analysis

provided

by

-LSB-

-RSB-

which

specifically

targetted

the

current

Embryonics

architecture

Despite

having

settled

the

reliability

model

both

analyses

are

incomplete

in

that

the

failure

rate

parameter

is

missing

which

makes

a

precise

quantitative

dependability

target

difficult

to

meet

However

a

reliability

analysis

is

still

valuable

from

a

qualitative

point

of

view

allowing

a

direct

comparison

of

different

systems

The

QUERIST

Approach

In

order

to

deal

with

errors

induced

by

the

constant

influence

of

the

external

environment

upon

computational

processes

the

following

assumptions

were

made

errors

appear

randomly

are

uncorrelated

-LRB-

neither

in

space

nor

in

time

-RRB-

there

are

no

storage

errors

and

there

are

no

leakage

phenomena

involved

-LSB-

-RSB-

Classical

HDL-based

fault

injection

methodologies

can

be

mapped

to

simulating

quantum

circuits

without

intervention

provided

that

the

new

error

and

fault

models

are

taken

into

account

-LSB-

-RSB-

Of

course

efficiency

criteria

require

that

they

be

adapted

to

one

of

the

available

efficient

simulation

frameworks

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

QUERIST

-LRB-

from

QUantum

ERror

Injection

Simulation

Tool

-RRB-

is

the

name

of

such

a

project

fostering

simulated

fault

injection

techniques

in

quantum

circuits

-LSB-

-RSB-

Similar

to

classical

computation

simulated

fault

injection

is

used

in

order

to

evaluate

the

employed

FTAMS

-LRB-

Fault

Tolerance

Algorithms

and

Methodologies

-RRB-

-LSB-

-RSB-

-LSB-

-RSB-

An

overview

of

the

QUERIST

project

is

presented

in

Figure

The

three

cycles

of

initialization

simulation

and

data

computation

are

common

to

both

classical

and

quantum

approaches

The

first

cycle

takes

the

quantum

circuit

HDL

description

as

an

input

Two

abstract

inputs

are

considered

the

HDL

model

and

the

assumed

error

model

the

first

influences

how

the

HDL

description

is

presented

while

the

second

one

dictates

the

test

scenario

by

defining

the

start/stop

simulation

states

-LRB-

since

qubits

are

equally

prone

to

error

all

the

signals

must

be

observed

-RRB-

HDL

modeling

of

quantum

circuits

in

order

to

attain

efficient

simulation

is

discussed

in

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

The

outputs

of

the

first

cycle

which

are

also

inputs

for

the

simulation

cycle

consist

of

a

test

scenario

and

an

executable

HDL

model

with

the

corresponding

entanglement

analysis

dictated

by

the

bubble-bit

encoded

quantum

states

-LSB-

-RSB-

-LSB-

-RSB-

The

output

of

the

second

cycle

consists

of

time

diagrams

for

all

qubits

from

the

start

to

the

stop

states

Useful

information

extracted

from

the

raw

bubble-bit-represented

qubit

traces

are

compared

to

correct

qubit

values

the

result

being

the

probabilistic

accuracy

threshold

value

in

the

third

cycle

The

initialization

and

simulation

cycles

depend

on

specific

aspects

of

quantum

circuit

simulation

-LSB-

-RSB-

The

data

processing

cycle

is

independent

from

the

specific

simulation

framework

and

is

aimed

at

determining

the

accuracy

threshold

as

the

main

reliability

measure

that

also

defines

the

feasibility

of

the

quantum

circuit

implementations

Suppose

that

at

simulation

time

t

we

observe

signals

-LCB-

-RCB-

n

s

s

s

In

our

analysis

s

i

is

the

state

observed

during

non-faulty

simulation

so

for

the

same

state

in

a

faulty

environment

we

will

have

the

state

i

s

For

validation

of

the

quantum

FTAMs

we

need

to

compare

i

s

with

i

s

This

can

be

done

by

using

operator

-LRB-

-RRB-

i

i

dif

s

s

This

means

that

the

total

number

of

overall

state

errors

at

simulation

time

t

is

The

error

rate

on

the

overall

observed

states

at

moments

-LRB-

t

n

i

i

i

e

dif

s

s

-RRB-

m

t

t

t

will

be

given

by

m

sim

j

j

t

e

m

The

used

FTAMs

are

only

valid

if

the

relationship

between

the

experimental

sim

and

the

assumed

singular

error

rate

is

of

the

order

sim

-LSB-

-RSB-

This

paper

presented

arguments

in

favor

of

two

novel

computing

architectures

for

the

purpose

of

addressing

the

challenges

raised

by

the

forthcoming

nanoelectronics

era

Distributed

self-testing

and

self-repairing

will

probably

become

a

must

in

the

next

years

as

centralized

control

logic

is

expected

to

become

unable

to

harness

the

extremely

large

number

of

devices

all

equally

prone

to

errors

that

will

be

integrated

onto

the

same

chip

Bio-inspired

computing

brings

valuable

techniques

that

explore

the

potential

of

massively

parallel

distributed

computation

and

fault-tolerance

that

will

likely

provide

an

essential

help

to

jumpstart

new

nanoelectronic

architectures

As

one

of

the

representatives

of

bio-inspired

computing

the

Embryonics

project

presents

a

hierarchical

architecture

that

achieves

fault

tolerance

through

implementing

an

also

hierarchical

reconfiguration

A

similar

approach

for

maximizing

fault

tolerance

is

present

in

quantum

computing

the

QUERIST

project

even

if

bio-inspired

and

quantum

computing

may

seem

dissimilar

at

a

first

glance

they

both

achieve

fault

tolerance

by

adapting

the

same

techniques

from

classical

computing

and

using

essentially

the

same

error

model

Nanoelectronics

will

potentially

change

the

way

computing

systems

are

designed

not

only

because

of

the

sheer

number

of

devices

that

will

coexist

onto

the

same

chip

but

also

because

of

the

sensitivity

of

these

devices

Figure

An

overview

of

the

QUERIST

project

Therefore

if

nanoelectronics

is

to

be

employed

to

build

dependable

computing

machines

-LRB-

a

certain

contradiction

notwithstanding

-RRB-

valuable

expertise

in

design

can

be

drawn

from

natural

sciences

While

biology

provides

countless

examples

of

successfully

implemented

fault

tolerance

strategies

physics

offers

theoretical

foundations

both

of

which

were

found

to

share

common

ground

It

is

perhaps

a

coincidence

worth

exploring

in

digital

computing

-LSB-

-RSB-

Aharonov

D.

Ben-Or

M.

Fault

Tolerant

Quantum

Computation

with

Constant

Error

Proc

ACM

Ann

Symposium

on

Theory

of

Computing

El

Paso

Texas

May

pp.

-LSB-

-RSB-

Avizienis

A.

Laprie

J.C.

Randell

B.

Landwehr

C.

Basic

Concepts

and

Taxonomy

of

Dependable

and

Secure

Computing

IEEE

Transactions

on

Dependable

and

Secure

Computing

-LRB-

Jan-Mar

-RRB-

-LSB-

-RSB-

Butts

M.

DeHon

A.

Golstein

S.C.

Molecular

Electronics

Devices

Systems

and

Tools

for

Gigagate

Gigabit

Chips

Proc

Intl.

Conference

on

CAD

-LRB-

ICCAD

-RRB-

pp.

-LSB-

-RSB-

Canham

R.

Tyrrell

A

An

Embryonic

Array

with

Improved

Efficiency

and

Fault

Tolerance

Proc

IEEE

NASA/DoD

Conference

on

Evolvable

Hardware

Chicago

Il

-LSB-

-RSB-

Gaisler

J.

Evaluation

of

a

Microprocessor

with

Built-In

Concurrent

Error

Detection

Proc

Annual

Intl.

Symposium

on

Fault-Tolerant

Computing

-LRB-

-RRB-

pp.

-LSB-

-RSB-

Goldstein

S.C.

The

Challenges

and

Opportunities

of

Nanoelectronics

Proc

Government

Microcircuit

Applications

and

Critical

Technology

Conference

-LRB-

GOMAC

Tech

-RRB-

Monterey

CA

March

-LSB-

-RSB-

Gottesman

D.

Class

of

quantum

error-correcting

codes

saturating

the

quantum

Hamming

bound

Phys

Rev.

A

pp.

-LSB-

-RSB-

Johnson

B.W.

Design

and

Analysis

of

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Digital

Systems

Addison-Wesley

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J.-C

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-RRB-

Dependability

Basic

Concepts

and

Terminology

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Computing

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Fault-Tolerant

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Springer-Verlag

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-RSB-

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P.

Dahlgren

P.

Johansson

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Karlsson

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Particle

Induced

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Combinational

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Sipper

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Proc

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the

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M.

eds

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Computing

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Universitaires

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-LSB-

-RSB-

Von

Neumann

J

The

Computer

and

the

Brain

-LRB-

nd

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-RRB-

Physical

Science

-LSB-

-RSB-

Von

Neumann

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The

Theory

of

Self-Reproducing

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A.

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Burks

ed

University

of

Illinois

Press

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IL

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-RSB-

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Neumann

J.

Probabilistic

Logic

and

the

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Reliable

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from

Unreliable

Components

In

C.E.

Shannon

J.

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-LRB-

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Studies

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Mathematical

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Press

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-RSB-

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M.A.

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Quantum

Computation

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Quantum

Information

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Press

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-RSB-

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C.

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Reliability

Analysis

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Self-Repairing

Embryonic

Systems

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Workshop

on

Evolvable

Hardware

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-RSB-

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P.D.T.

Practical

Reliability

Engineering

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Wiley

Sons

th

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-RSB-

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J.

Fault

Tolerant

Quantum

Computation

In

H.K.

Lo

S.

Popescu

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Spiller

eds

Introduction

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Self-Repairing

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Arrays

Inspired

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Biological

Processes

Ph.D.

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Politehnica

University

of

Timisoara

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L.

Udrescu

M.

Vladutiu

M.

Survivability

Analysis

in

Embryonics

A

New

Perspective

Proc

IEEE

NASA/DoD

Conference

on

Evolvable

Hardware

Washington

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Udrescu

M.

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Self-Repairing

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Proc

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Tempesti

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Embryonics

Electronic

Stem

Cells

Proc

Artificial

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The

MIT

Press

Cambridge

MA

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Tempesti

G.

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D.

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Embryonics

Artificial

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Driven

by

Artificial

DNA

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International

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-LRB-

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Tempesti

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Biology

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Markov

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High-performance

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of

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France

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B.W.

A

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on

the

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of

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on

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Injection

Techniques

Technical

Report

University

of

Virginia

May

-LSB-

-RSB-

ITRS

International

Technology

Roadmap

for

Semiconductors

Emerging

Research

Devices

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-RSB-

Society

of

Reliability

Engineers

pubs

-LSB-

-RSB-

error detection
fault tolerance
evolvable hardware
computer system
reliability
querist
dependable system
dependability
digital devices
failure rate
computing architecture
soft errors
nanoelectronics
embryonics
correction techniques
quantum computing
environment
emerging technologies
computing system

computing technology
self repair
system design
bio-inspired computing
self replication
nano computing
bio-inspired digital design
bio-computing
fault-tolerance assessment