o

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