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Thermodynamic implications of information erasure
Saroosh Shabbir
Quantum Electronics & Quantum OpticsKTH
2014 Future of Wireless Technology Workshop - Huawei
Saroosh Shabbir Information Erasure May 27, 2014 1 / 1
Thermodynamics in computation
Compu�ng devices use energy anddissipate heat.
Is there a fundamental limit to it?
E
Q
W
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Thermodynamics in computation
Compu�ng devices use energy anddissipate heat.
Is there a fundamental limit to it?
E
Q
W
Hea�ng main issue hinderingminiaturiza�on.
Can it be minimised?
ENIAC 1946
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Outline
Classicalinforma�ontheory&physics-Maxwell'sdemonparadox
Implica�ons-Landauer'sprinciple
BeyondLandauer'sprinciple
Quantuminforma�ontheory
SummaryandConclusions
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Information theory
Classical Informa�on : bit
0 1
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Information theory
Classical Informa�on : bit
0 1
Informa�on is physical!
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Maxwell’s Demon
selectgaspar�clesbyopeningdoor
a�achweighttopiston
gasatT
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Maxwell’s Demon
selectgaspar�clesbyopeningdoor
a�achweighttopiston
pressureli�sweightheathasbeenconvertedtowork
gasatT
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Maxwell’s Demon
gasequilibratestoini�altemperature
a�achweighttopiston
pressureli�sweightheathasbeenconvertedtowork
W
Q
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Maxwell’s Demon
extract w
ork from
informati
on!
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Maxwell’s Demon : Experiment
Thermalfluctua�onsleadtojumpsb/wsteps.Onaveragethepar�clefallsdown.
Ablockisplacedbehindthepar�clewhenanupwardjumpisobserved.Par�cleclimbsupthestairswithoutdirectenergyinjec�on.
Toyabietal.NaturePhysics(2010)
extract w
ork from
informati
on!
Saroosh Shabbir Information Erasure May 27, 2014 11 / 1
Maxwell’s Demon : Experiment
Thermalfluctua�onsleadtojumpsb/wsteps.Onaveragethepar�clefallsdown.
Ablockisplacedbehindthepar�clewhenanupwardjumpisobserved.Par�cleclimbsupthestairswithoutdirectenergyinjec�on.
Toyabietal.NaturePhysics(2010)
extract w
ork from
informati
on!
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Maxwell’s Demon Paradox
Cyclicprocessconvertsheatcompletelyintowork!
Violatessecondlawofthermodynamics!
Noprocessispossiblewhosesoleresultistheabsorp�onofheatfromareservoirandtheconversionofthisheatintowork.
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Resolution: Landauer’s Principle
gasequilibratestoini�altemperature
a�achweighttopiston
pressureli�sweightheathasbeenconvertedtowork
W
Q
0100100011110
01001000111100100100011110
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Resolution: Landauer’s Principle
gasequilibratestoini�altemperature
a�achweighttopiston
pressureli�sweightheathasbeenconvertedtowork
W
Q
0100100011110
01001000111100100100011110
To close the the
rmodyn-
amic cycle, the dem
on's
memory needs to be
erased.
Erasure costs wo
rk,
dissipates heat!
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Resolution: Landauer’s Principle
Berutetal.Nature(2012)
To close the the
rmodyn-
amic cycle, the dem
on's
memory needs to be
erased.
Erasure costs wo
rk,
dissipates heat!
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Resolution: Landauer’s Principle
Berut et al. Nature (2012)
2 states with equalprobability 1/2
1 state with probability 1
Shannon Entropy :
To close the the
rmodyn-
amic cycle, the dem
on's
memory needs to be
erased.
Erasure costs wo
rk,
dissipates heat!
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Resolution: Landauer’s Principle
Berut et al. Nature (2012)
2 states with equalprobability 1/2
1 state with probability 1
Shannon Entropy :
at room temperature
To close the the
rmodyn-
amic cycle, the dem
on's
memory needs to be
erased.
Erasure costs wo
rk,
dissipates heat!
Saroosh Shabbir Information Erasure May 27, 2014 18 / 1
Landauer’s Limit
Pop, Nano Research (2010)
Present silicon based digital circuitsfar above the ul�mate Landauer limit.
In 20-30 years, the Landauer limit willbecome important, provided Moore'slaw remains valid.
Saroosh Shabbir Information Erasure May 27, 2014 19 / 1
Landauer’s Limit
Pop, Nano Research (2010)
Present silicon based digital circuitsfar above the ul�mate Landauer limit.
In 20-30 years, the Landauer limit willbecome important, provided Moore'slaw remains valid.
?
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Landauer’s Limit
Pop, Nano Research (2010)
Present silicon based digital circuitsfar above the ul�mate Landauer limit.
In 20-30 years, the Landauer limit willbecome important, provided Moore'slaw remains valid.
?Further scaling down degrades perfo-rmance. Need complimen�ng interc-onnect technologies.
Saroosh Shabbir Information Erasure May 27, 2014 21 / 1
Landauer’s Limit
Pop, Nano Research (2010)
Present silicon based digital circuitsfar above the ul�mate Landauer limit.
In 20-30 years, the Landauer limit willbecome important, provided Moore'slaw remains valid.
?Further scaling down degrades perfo-rmance. Need complimen�ng interc-onnect technologies.
Silicon photonics instead of electronics.
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Beyond Landauer’s Principle
Anyirreversiblelogicaltransforma�onofclassicalinforma�onproducesatleastkTln2heatperbit.
Landauer1961
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Beyond Landauer’s Principle
Theonlycomputeropera�onsthatmustbethermodynamicallyirreversiblearethelogicallyirreversibleones.
Landauer1961
Examples:AND,NAND,OR,XOR,ERASE
Anyirreversiblelogicaltransforma�onofclassicalinforma�onproducesatleastkTln2heatperbit.
Landauer1961
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Beyond Landauer’s Principle
The only computer opera�ons that must be thermodynamically
irreversible are the logically irreversible ones.Landauer 1961
Erasure of informa�on is the only inherently irreversible
computer opera�on.Benne� 1982
Examples : AND, NAND, OR, XOR, ERASE
Examples: NOT, Toffoli
Any irreversible logical transforma�on of classical
informa�on produces at least kT ln2 heat per bit.Landauer 1961
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Classical vs Quantum information
Classical Informa�on : bit
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Classical vs Quantum information
Classical Informa�on : bit Quantum Informa�on : qubit
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Classical vs Quantum information
Classical Informa�on : bit Quantum Informa�on : qubit
"superpositions"
increased information
processing capac
ity
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Classical vs Quantum information
Classical Informa�on : bit Quantum Informa�on : qubit
"superpositions"
increased information
processing capac
ity
Different states
Encode differentinforma�on
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Quantum correlation - Entanglement
..... spooky ac�on at a distance ..... Einstein 1935
50% chance
Bob's coin
is heads
50% chance
Alice's coin
is tails
Alice Bob
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Quantum correlation - Entanglement
Alice Bob
..... spooky ac�on at a distance ..... Einstein 1935
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Quantum correlation - Entanglement
Alice Bob
Alice Bob
100% chance
Bob's coin is
heads
100% chance
Alice's coin is
tails
..... spooky ac�on at a distance ..... Einstein 1935
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Quantum correlation - Entanglement
Alice
Alice Bob
100% chance
Bob's coin is
tails
100% chance
Alice's coin is
heads
Entanglement gives 100% accurate predic�ve power
Correla�ons are non local
..... spooky ac�on at a distance ..... Einstein 1935
Bob
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Quantum correlation - Entanglement
Alice
Alice Bob
100% chance
Bob's coin is
heads
100% chance
Alice's coin is
tails
Entanglement gives 100% accurate predic�ve power
Correla�ons are non local
Quantum cryptography : secure communica�on
Commercially available - id Quan�que Switzerland
Bob
..... spooky ac�on at a distance ..... Einstein 1935
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Quantum thermodynamics
bit
Eraseinforma�onanddissipateheat
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Quantum thermodynamics
Eraseinforma�onandcooltheenvironment
bit ebit
delRioetal.,Nature(2011)
Eraseinforma�onanddissipateheat
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Quantum thermodynamics
Eraseinforma�onandcooltheenvironment
Entanglementhasathermodynamiccostaswell.Hiltetal.,PRE(2011)
Doesnotallowustoviolatethesecondlaw.
bit ebit
delRioetal.,Nature(2011)
Eraseinforma�onanddissipateheat
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Summary
Informa�on is physical!
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Summary
Informa�on is physical! Irreversible processes suchas erasure have a thermo-dynamic cost.
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Summary
Informa�onisphysical! Irreversibleprocessessuchaserasurehaveathermo-dynamiccost.
Quantumcorrela�onsdonotbreakthesecondlawofthermodynamics.
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Summary
Informa�on is physical! Irreversible processes suchas erasure have a thermo-dynamic cost.
Quantum correla�onsdo not break the secondlaw of thermodynamics.
Thank you!
Dr Janet Anders - University of Exeter
Dr Eric Lutz - Freie Universität Berlin
Prof. Gunnar Björk - KTH
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