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Quantum-Cellular-Automata QC withEndohedral Fullerenes
Seminar in Quantum Information Processing
Yossi Weinstein
Physics Department, Technion – Israel Institute of Technology
Make TEX not Word
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.1/23
oOutline
o Cellular automata and quantum cellularautomata.
o 1-qubit and 2-qubit gates.o Fullerenes – a nobel prize discovery.o Endohedral-fullerene based quantum
computers.o physical-implementation requirements for
quantum computing.o Verifying that all the requirements are met.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.2/23
oOutline
o Cellular automata and quantum cellularautomata.
o 1-qubit and 2-qubit gates.
o Fullerenes – a nobel prize discovery.o Endohedral-fullerene based quantum
computers.o physical-implementation requirements for
quantum computing.o Verifying that all the requirements are met.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.2/23
oOutline
o Cellular automata and quantum cellularautomata.
o 1-qubit and 2-qubit gates.o Fullerenes – a nobel prize discovery.
o Endohedral-fullerene based quantumcomputers.
o physical-implementation requirements forquantum computing.
o Verifying that all the requirements are met.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.2/23
oOutline
o Cellular automata and quantum cellularautomata.
o 1-qubit and 2-qubit gates.o Fullerenes – a nobel prize discovery.o Endohedral-fullerene based quantum
computers.
o physical-implementation requirements forquantum computing.
o Verifying that all the requirements are met.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.2/23
oOutline
o Cellular automata and quantum cellularautomata.
o 1-qubit and 2-qubit gates.o Fullerenes – a nobel prize discovery.o Endohedral-fullerene based quantum
computers.o physical-implementation requirements for
quantum computing.
o Verifying that all the requirements are met.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.2/23
oOutline
o Cellular automata and quantum cellularautomata.
o 1-qubit and 2-qubit gates.o Fullerenes – a nobel prize discovery.o Endohedral-fullerene based quantum
computers.o physical-implementation requirements for
quantum computing.o Verifying that all the requirements are met.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.2/23
oCellular Automata1D Cellular automaton
ti ti+1
· · · � � � · · · =⇒ · · · � � � · · ·
2D Cellular automatonti ti+1
. . . ... ... ... . .. . . . ... ... ... . ..
· · · � � � · · · · · · � � � · · ·
· · · � � � · · · =⇒ · · · � � � · · ·
· · · � � � · · · · · · � � � · · ·
. .. ... ... ... . . . . .. ... ... ... . . .Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.3/23
oMotivation - scalable addressabilityLocal addressing requires a large overhead.E.g. In NMR, a large computer requires acrowded frequency set→NMRQC limited to ∼ 30
qubits. [Jones, Fort. der Physik 48, 909 (2000).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.4/23
oQuantum Cellular Automata
[S. Lloyd, Science 261, 1569 (1993).]
ABCABCABC
Non-identical neighbors→ directionality.
[S. C. Benjamin, PRA 61, 020301 (2000).]
ABABAB
No need for asymmetric neighborhood
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.5/23
oLocal Gates Scheme
CU
q3
CU CU CU
q2
CU CU CU
q1
CU CU
CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU CU CU
q2
CU CU CU
q1
CU
CU
CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU CU CU
q2
CU CU CU
q1
CU
CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU CU CU
q2
CU CU
CUq1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU CU CU
q2
CU
CU
CU
q1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU CU CU
q2
CU
CU CU
q1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU CU
CUq2
CU CU CU
q1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU
CU
CU
q2
CU CU CU
q1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CU
q3
CU
CU CU
q2
CU CU CU
q1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oLocal Gates Scheme
CUq3
CU CU CU
q2
CU CU CU
q1
CU CU CU
o The logical qubits are evenly separated.o A control unit (CU) can be moved with
respect to the qubits.o The global operations are desined to affect
“all” the qubits that are in contact with thecontrol unit.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.6/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q
∗
1
CUCU CUCU
CU
CU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q
∗
1
CUCU
CU
CU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q
∗
1
CU
CU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CUCU CUCU
CU
CUCUCU
q
∗
1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CUCU CUCU CU
CU
CUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CUCU
CU
CU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU CUCU
q2
CU
CU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU CUCU
CU
CU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′CUCU
CU
CU CUCU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3
′
CU
CU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CU
CU
q3
′CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CU
CU
q3′
CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CU
CU
CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CU
CU
CUCU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CU
CU
q2
CUCU CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CU
CU
CUCU CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CUCU CU
CU
CUCUCUCU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CUCU CUCU CUCU
CU
CU
q∗1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CUCU CUCU CUCUCU
CU
q
∗
1
CUCU CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q
∗
1
CU
CU
CUCU CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q
∗
1
CUCU CU
CU
CUCU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oControlled Gates
CUCU
q3′
CUCU CUCU CUCU
q2
CUCU CUCU CUCUCUCU
q
∗
1
CUCU CUCU CU
CU
o When the CU reaches the Control bit, aglobal operation SWAPs the values of thecontrol and the CU.
o When the CU reaches the Target, a globaloperation performs some gate U iff the valueof the CU is |1〉.
o The CU returns to reclaim its initial value fromthe control.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.7/23
oGlobal Operations
AUf , BU
f , f ∈
{
0, 1, 2 non edge qubit0, 1 edge qubit
ANOT1 BNOT
1 ANOT1 BNOT
1
B−A1
−
B1
−
A0
1−
B0
1−
A−
01
B−
01
A−
0
B−
0
A− Logical |0〉
B−A0
−
B0
−
A1
0−
B1
0−
A−
10
B−
10
A−
1
B−
1
A− Logical |1〉
Using a slightly differentstructure, we can haveA−B−
1
A−
1
B−
10
A−
10
B1
01
A1
01
B0
1−
A0
1−
B1
−
A1
−
B− Control unit
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.8/23
oGlobal Operations
AUf , BU
f , f ∈
{
0, 1, 2 non edge qubit0, 1 edge qubit
ANOT1
BNOT1 ANOT
1 BNOT1
B−A
1
−B1
−
A
0
1
−
B0
1−
A
−
0
1
B−
01
A−
0
B−
0
A− Logical |0〉
B−A
0
−B0
−
A
1
0
−
B1
0−
A
−
1
0
B−
10
A−
1
B−
1
A− Logical |1〉
Using a slightly differentstructure, we can haveA−B−
1
A−
1
B−
10
A
−
1
0
B1
01
A
1
0
1
B0
1−
A
0
1
−
B1
−
A
1
−B− Control unit
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.8/23
oGlobal Operations
AUf , BU
f , f ∈
{
0, 1, 2 non edge qubit0, 1 edge qubit
ANOT1 BNOT
1
ANOT1 BNOT
1
B−A
1
−B
1
−A
0
1
−
B
0
1
−
A
−
0
1
B
−
0
1
A−
0
B−
0
A− Logical |0〉
B−A
0
−B
0
−A
1
0
−
B
1
0
−
A
−
1
0
B
−
1
0
A−
1
B−
1
A− Logical |1〉
Using a slightly differentstructure, we can haveA−B−
1
A−
1
B
−
1
0
A
−
1
0
B
1
0
1
A
1
0
1
B
0
1
−
A
0
1
−
B
1
−A
1
−B− Control unit
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.8/23
oGlobal Operations
AUf , BU
f , f ∈
{
0, 1, 2 non edge qubit0, 1 edge qubit
ANOT1 BNOT
1 ANOT1
BNOT1
B−A
1
−B
1
−A
01
−B
0
1
−
A
−0
1B
−
0
1
A
−
0B−
0
A− Logical |0〉
B−A
0
−B
0
−A
10
−B
1
0
−
A
−1
0B
−
1
0
A
−
1B−
1
A− Logical |1〉
Using a slightly differentstructure, we can haveA−B−
1
A
−
1B
−
1
0
A
−1
0B
1
0
1
A
10
1B
0
1
−
A
01
−B
1
−A
1
−B− Control unit
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.8/23
oGlobal Operations
AUf , BU
f , f ∈
{
0, 1, 2 non edge qubit0, 1 edge qubit
ANOT1 BNOT
1 ANOT1 BNOT
1
B−A
1
−B
1
−A
01
−B
01
−A
−0
1B
−0
1A
−
0B
−
0A− Logical |0〉
B−A
0
−B
0
−A
10
−B
10
−A
−1
0B
−1
0A
−
1B
−
1A− Logical |1〉
Using a slightly differentstructure, we can haveA−B
−
1A
−
1B
−1
0A
−1
0B
10
1A
10
1B
01
−A
01
−B
1
−A
1
−B− Control unit
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.8/23
oLocal Single Qubit Gates
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.9/23
oLocal Controlled Gates
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.10/23
oRichard Buckminster “Bucky” Fuller
Inventor of geodetic domes (1895 – 1983).
The American Pavilion of Expo ’67, now theBiosphére in Montréal, Quebec, Canada.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.11/23
oFullerenes – 1996 Nobel Prize
C60 – Fullerene Endohedralfullerene
o Harold Kroto, Robert Curl & Richard Smalley.
o Kroto, Heath, O’Brien, Curl & Smalley, Nature318, 162 (1985).
o Yoshida & Osawa, Aromaticity, p. 174 (1971).
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.12/23
oFullerenes – 1996 Nobel Prize
C60 – Fullerene Endohedralfullerene
o Harold Kroto, Robert Curl & Richard Smalley.o Kroto, Heath, O’Brien, Curl & Smalley, Nature
318, 162 (1985).
o Yoshida & Osawa, Aromaticity, p. 174 (1971).
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.12/23
oFullerenes – 1996 Nobel Prize
C60 – Fullerene Endohedralfullerene
o Harold Kroto, Robert Curl & Richard Smalley.o Kroto, Heath, O’Brien, Curl & Smalley, Nature
318, 162 (1985).o Yoshida & Osawa, Aromaticity, p. 174 (1971).
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.12/23
oEndohedral-Fullerene Computer
A B A B A B
15N@C60 |←−−1.1−−→nm| 31P@C60
o An endohedral-fullerene chain on a siliconsubstrate.
o Neighbors interact via electronic spin-spincoupling.[J. Twamley, PRA 67, 052318 (2003).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.13/23
oThe Physical Implementation of QC
D. P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).o A scalable physical system with well
characterized qubits.
o A “universal” set of quantum gates.o Long relevant decoherence times, much
longer than the gate operation time.o The ability to initialize the state of the qubits
to a simple fiducial state such as |000 . . .〉.o A qubit-specific measurement capability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.14/23
oThe Physical Implementation of QC
D. P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).o A scalable physical system with well
characterized qubits.o A “universal” set of quantum gates.
o Long relevant decoherence times, muchlonger than the gate operation time.
o The ability to initialize the state of the qubitsto a simple fiducial state such as |000 . . .〉.
o A qubit-specific measurement capability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.14/23
oThe Physical Implementation of QC
D. P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).o A scalable physical system with well
characterized qubits.o A “universal” set of quantum gates.o Long relevant decoherence times, much
longer than the gate operation time.
o The ability to initialize the state of the qubitsto a simple fiducial state such as |000 . . .〉.
o A qubit-specific measurement capability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.14/23
oThe Physical Implementation of QC
D. P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).o A scalable physical system with well
characterized qubits.o A “universal” set of quantum gates.o Long relevant decoherence times, much
longer than the gate operation time.o The ability to initialize the state of the qubits
to a simple fiducial state such as |000 . . .〉.
o A qubit-specific measurement capability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.14/23
oThe Physical Implementation of QC
D. P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).o A scalable physical system with well
characterized qubits.o A “universal” set of quantum gates.o Long relevant decoherence times, much
longer than the gate operation time.o The ability to initialize the state of the qubits
to a simple fiducial state such as |000 . . .〉.o A qubit-specific measurement capability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.14/23
oThe 1st Criterion
A scalable system with well characterized qubits.
o The spins of the trapped atoms’ nuclei are thequbits.
o All operations are global→ scalability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.15/23
oThe 1st Criterion
A scalable system with well characterized qubits.
o The spins of the trapped atoms’ nuclei are thequbits.
o All operations are global→ scalability.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.15/23
oThe 2nd Criterion
A universal set of logic gatesA demonstration of AU
1 :(a) Initial state – electrons in |0〉.
(b) Swap B nuclei with electrons.(c) Electronic ANOT
1 .(d) Swap B nuclei with electrons.(e) Control-U on A, the electrons as
controls and nuclei as targets.
Elec. Nuc.A B A B
|0〉 � • � •
|1〉 � # � ◦
Gray – |0〉Black – |0〉White – |1〉Stripes – |1〉
White/Stripes – |1〉, Black/Gray –|0〉
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.16/23
oThe 2nd Criterion
A universal set of logic gatesA demonstration of AU
1 :(a) Initial state – electrons in |0〉.(b) Swap B nuclei with electrons.
(c) Electronic ANOT1 .
(d) Swap B nuclei with electrons.(e) Control-U on A, the electrons as
controls and nuclei as targets.
Elec. Nuc.A B A B
|0〉 � • � •
|1〉 � # � ◦
Gray – |0〉Black – |0〉White – |1〉Stripes – |1〉
White/Stripes – |1〉, Black/Gray –|0〉
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.16/23
oThe 2nd Criterion
A universal set of logic gatesA demonstration of AU
1 :(a) Initial state – electrons in |0〉.(b) Swap B nuclei with electrons.(c) Electronic ANOT
1 .
(d) Swap B nuclei with electrons.(e) Control-U on A, the electrons as
controls and nuclei as targets.
Elec. Nuc.A B A B
|0〉 � • � •
|1〉 � # � ◦
Gray – |0〉Black – |0〉White – |1〉Stripes – |1〉
White/Stripes – |1〉, Black/Gray –|0〉
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.16/23
oThe 2nd Criterion
A universal set of logic gatesA demonstration of AU
1 :(a) Initial state – electrons in |0〉.(b) Swap B nuclei with electrons.(c) Electronic ANOT
1 .(d) Swap B nuclei with electrons.
(e) Control-U on A, the electrons ascontrols and nuclei as targets.
Elec. Nuc.A B A B
|0〉 � • � •
|1〉 � # � ◦
Gray – |0〉Black – |0〉White – |1〉Stripes – |1〉
White/Stripes – |1〉, Black/Gray –|0〉
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.16/23
oThe 2nd Criterion
A universal set of logic gatesA demonstration of AU
1 :(a) Initial state – electrons in |0〉.(b) Swap B nuclei with electrons.(c) Electronic ANOT
1 .(d) Swap B nuclei with electrons.(e) Control-U on A, the electrons as
controls and nuclei as targets.
Elec. Nuc.A B A B
|0〉 � • � •
|1〉 � # � ◦
Gray – |0〉Black – |0〉White – |1〉Stripes – |1〉
White/Stripes – |1〉, Black/Gray –|0〉
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.16/23
oReversing the Unitaries
The rest of AU1 :
(d) Swap B nuclei with electrons.
(c) Electronic ANOT1 .
(b) Swap B nuclei with electrons.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.17/23
oReversing the Unitaries
The rest of AU1 :
(d) Swap B nuclei with electrons.(c) Electronic ANOT
1 .
(b) Swap B nuclei with electrons.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.17/23
oReversing the Unitaries
The rest of AU1 :
(d) Swap B nuclei with electrons.(c) Electronic ANOT
1 .(b) Swap B nuclei with electrons.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.17/23
oReversing the Unitaries
The rest of AU1 :
(d) Swap B nuclei with electrons.(c) Electronic ANOT
1 .(b) Swap B nuclei with electrons.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.17/23
oThe 3rd Criterion
Dephsing times much longer than gate timeo C60 cages the qubit, making it inert→ long
dephasing time T e2
?∼ 1sec, TN
2
?∼ 1000sec.
o The electron cloud is compressed→stronghyperfine-coupling: 21.2MHz(15N@C60)
o A global operation involves ∼ 15 hyperfinecouplings occurrences; simplest gates require∼ 30 global operations→ Tgate ∼
30·1521.2×106 = 21.2µsec⇒ T e
2
Tgate∼ 47, 000
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.18/23
oThe 3rd Criterion
Dephsing times much longer than gate timeo C60 cages the qubit, making it inert→ long
dephasing time T e2
?∼ 1sec, TN
2
?∼ 1000sec.
o The electron cloud is compressed→stronghyperfine-coupling: 21.2MHz(15N@C60)
o A global operation involves ∼ 15 hyperfinecouplings occurrences; simplest gates require∼ 30 global operations→ Tgate ∼
30·1521.2×106 = 21.2µsec⇒ T e
2
Tgate∼ 47, 000
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.18/23
oThe 3rd Criterion
Dephsing times much longer than gate timeo C60 cages the qubit, making it inert→ long
dephasing time T e2
?∼ 1sec, TN
2
?∼ 1000sec.
o The electron cloud is compressed→stronghyperfine-coupling: 21.2MHz(15N@C60)
o A global operation involves ∼ 15 hyperfinecouplings occurrences; simplest gates require∼ 30 global operations→ Tgate ∼
30·1521.2×106 = 21.2µsec⇒ T e
2
Tgate∼ 47, 000
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.18/23
oThe 4th Criterion
The ability to initialize the qubits’ state to |0n〉.At a low temperature a high magnetic field,electrons are highly polarized.
T = 1KP e
|0〉 = 0.999B = 10Tesla
d A cooling algorithm can increase P N|0〉 further.
[SV, STOC (1999); BMRVV, PNAS (2002); FLMR,IJQI (2004).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.19/23
oThe 5th Criterion
A qubit-specific measurement capability.
ZB
SpinFilter Source Island Drain Filter
SpinDetector
Inside Spin
Outside Spin
M. Feng and J. Twamley, PRA 70, 030303 (2004)Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.20/23
oThe 5th Criterion
Inside Spin Outside Spins Transition Freq.|3/2〉 |1/2〉 ↔ |−1/2〉 2ν1 + 2δ + 3J/2
|1/2〉 |1/2〉 ↔ |−1/2〉 2ν1 + 2δ + J/2
|−1/2〉 |1/2〉 ↔ |−1/2〉 2ν1 + 2δ − J/2
|−3/2〉 |1/2〉 ↔ |−1/2〉 2ν1 + 2δ − 3J/2... ... ...
A proper rf pulse of frequency 2ν1 +2δ +3J/2 canflip the outside spin iff the inside spins are |↑↑↑〉.A change in the current will be observed.
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.21/23
oSummaryo Quantum cellular automata can solve the
addressability problem in large computers.
o Endohedral-fullerene based quantum cellularautomaton was suggested.
o The implementation meets all fiverequirements set by David DiVincenzo.
o For the fifth requirement, a fulleren-basedsingle-electron transistor was suggested.
o A record was set straight. Fullerenes werecredited to Yoshida and Osawa [J. MolecularGraphics and Modelling, 19, 185 (2001).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.22/23
oSummaryo Quantum cellular automata can solve the
addressability problem in large computers.o Endohedral-fullerene based quantum cellular
automaton was suggested.
o The implementation meets all fiverequirements set by David DiVincenzo.
o For the fifth requirement, a fulleren-basedsingle-electron transistor was suggested.
o A record was set straight. Fullerenes werecredited to Yoshida and Osawa [J. MolecularGraphics and Modelling, 19, 185 (2001).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.22/23
oSummaryo Quantum cellular automata can solve the
addressability problem in large computers.o Endohedral-fullerene based quantum cellular
automaton was suggested.o The implementation meets all five
requirements set by David DiVincenzo.
o For the fifth requirement, a fulleren-basedsingle-electron transistor was suggested.
o A record was set straight. Fullerenes werecredited to Yoshida and Osawa [J. MolecularGraphics and Modelling, 19, 185 (2001).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.22/23
oSummaryo Quantum cellular automata can solve the
addressability problem in large computers.o Endohedral-fullerene based quantum cellular
automaton was suggested.o The implementation meets all five
requirements set by David DiVincenzo.o For the fifth requirement, a fulleren-based
single-electron transistor was suggested.
o A record was set straight. Fullerenes werecredited to Yoshida and Osawa [J. MolecularGraphics and Modelling, 19, 185 (2001).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.22/23
oSummaryo Quantum cellular automata can solve the
addressability problem in large computers.o Endohedral-fullerene based quantum cellular
automaton was suggested.o The implementation meets all five
requirements set by David DiVincenzo.o For the fifth requirement, a fulleren-based
single-electron transistor was suggested.o A record was set straight. Fullerenes were
credited to Yoshida and Osawa [J. MolecularGraphics and Modelling, 19, 185 (2001).]
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.22/23
oThe end
Yossi Weinstein, Physics Department, Technion – Israel Institute of Technology – p.23/23
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