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Sill Torres – QCA
Evaluating the Impact of Interconnections in Quantum-dot Cellular Automata (QCA)
Frank Sill Torres1,2, Robert Wille1,3, Marcel Walter2, Philipp Niemann1,2, Daniel Große1,2, Rolf Drechsler1,2
1DFKI GmbH (Germany), 2University of Bremen (Germany)3JKU Linz (Austria)
2Sill Torres – QCA
Outline
Motivation
Design Automation
Analysis Environment
Results
Conclusions
3Sill Torres – QCA
MotivationQuantum-dot Cellular Automata (QCA)
Promising nanotechnology based on quantum dots
Remarkable low energy dissipation
Several (experimental) physical realizations based on different concepts (Metal islands, nanomagnets, dangling bonds, …)
Metal islands
Nanomagnets
Dangling bonds
4Sill Torres – QCA
Challenging routing in QCA
– QCA is (nearly) planar technology
Current state: 1 layer for logic & routing, 1 layer for crossings
Outlook: low amount of layers
– Data flow must follow clocking constraint (clock 1 → clock 2 → clock 3 → … )
– Only orthogonal routing
Simple example:
MotivationInterconnections
b
af
1 2 3
4 2
3 4 1b
a
f3
Routing overhead
5Sill Torres – QCA
More complex design
Interconnections with notable impact on Area, Delay, Energyincrease
Question: What is the actual impact?
MotivationInterconnections cont’d
1 2 3
4 3 2
3 4 1
4
1
2
42 1 3
1
4
3
2
1 2 3 4 1
co4 3 2 1 4
b
a
s
6Sill Torres – QCA
Design AutomationComparison
CMOS Process QCA Process
Transistors andconnections
MOS layers
QCA cells andits positions
Layers of specific material
No Differences
Some Differences
7Sill Torres – QCA
Design AutomationPrincipal Flow
g2
g3
s
a
b
f
1 2 3
2 3 4 1
4
HDL Description
Netlist
Tile (clock zone) grid
Layout
1 2 3
2 3 4
s
a
fb1
4
8Sill Torres – QCA
Design AutomationGate Library
Routing Elements Simple Gates Complex Gates
Wire
Bent wire
Fanout
Inverter
Majority
OR
NOR
XOR
9Sill Torres – QCA
Components of energy dissipation of QCA:
Dissipated energy: Eenv = Eclk + Ein – Eout
QCADesigner-E - Physics simulator including determination of energy dissipation of QCA (https://github.com/FSillT/QCADesigner-E)
Design AutomationEnergy Model
-
-
Eclk - Energy from clock
Eenv - Energy to environment
Eout - Energy to neighboring cell(s)
Ein - Energy from neighboring cell(s)
( )tanh '2env thE dtλ η= Γ ⋅ + Γ∫
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Design AutomationCharacterized Gate library
Area [µm²]
Delay[tiles]
Energy Disspation [meV]Regl. Mode (25 GHz) Fast mode (100 GHz)
000 ... 111 000 ... 111
Rou
ting
Elem
ents Wire 0.01 1 0.09 ... - 0.82 ... -
Bent-wire 0.01 1 0.10 ... - 0.84 ... -Fanout 0.01 1 0.12 ... - 1.15 ... -
Logi
c G
ates
Inverter 0.01 1 0.13 ... - 1.19 ... -Majority 0.01 1 0.15 ... 0.15 1.41 ... 1.41OR 0.01 1 0.18 ... - 1.30 ... -NOR 0.02 2 0.31 ... - 2.49 ... -... ... ... ... ... ... ... ... ...
11Sill Torres – QCA
Analysis Environment
1. Diagonal arrangement of clocking
2. Levelizing of netlist graph
3. Diagonal placement of each level
4. Routing
P&R Algorithm
2 3
3 4 1
42 3
1
o1
o2
o3
o4
o6
L1 L2 L3
2 3
3 4 1
42 3
1
o2
o1
o3
2 3
3 4 1
42 3
1
o2
o1
o3
12Sill Torres – QCA
Synthesis:
– Synthesis library (*.lib) for QCA gate library
– Synopsys Design Compiler
– ABC (AIG, BDD)
EFPL Benchmarks
Analysis EnvironmentFlow
Benchmark name Inputs Outputs AND nodesAdder (adder) 256 129 1020Barrel shifter (barrel) 135 128 3336Max (max) 512 130 2865Sine (sin) 24 25 5416
... … … …
13Sill Torres – QCA
0
2000
4000
6000
8000
10000
0 1000 2000 3000 4000 5000 6000
Inte
rcon
nect
ion
Ove
rhea
d
AND nodes of initial benchmarks
Area
AIG BDD Comm
ResultsArea
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0
10
20
30
40
50
60
0 1000 2000 3000 4000 5000 6000
Inte
rcon
nect
ion
Ove
rhea
d
AND nodes of initial benchmarks
Delay
AIG BDD Comm
ResultsDelay
15Sill Torres – QCA
ResultsEnergy Dissipation
0
100
200
300
400
500
600
700
0 1000 2000 3000 4000 5000 6000
Inte
rcon
nect
ion
Ove
rhea
d
AND nodes of initial benchmarks
Energy (Regular)
AIG BDD Comm
16Sill Torres – QCA
QCA is a promising nanotechnology for low energy applications
Specific characteristics of QCA design require notable amount of interconnections
Here: Evaluation of this impact
Results indicate high impact of Interconnections with consequenceson area, delay, energy
Requirements for future research:
– Comprehensive synthesis cost model for interconnections
– New synthesis strategies with emphasis on reduction of interconnections
– Exploration of new concepts (systolic arrays, logic duplication, …)
Conclusions
Sill Torres – QCA
Evaluating the Impact of Interconnections in Quantum-dot Cellular Automata (QCA)
Frank Sill Torres1,2, Robert Wille1,3, Marcel Walter2, Philipp Niemann1,2, Daniel Große1,2, Rolf Drechsler1,2
1DFKI GmbH (Germany), 2University of Bremen (Germany)3JKU Linz (Austria)
