the$quantum$computer$roadmap,$...
TRANSCRIPT
![Page 1: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/1.jpg)
The Quantum Computer Roadmap, and “going off road”
David DiVincenzo 27.06.2012
Varenna Course CLXXXIII
![Page 2: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/2.jpg)
An architecture of the large-scale quantum computer is taking shape
- “roadmap” as given by N. C. Jones et al. How can we do better than Jones (“going off road”)
- Majorana wires? - Direct multiqubit parity measurements - Codes that directly embody universal quantum
computation
Outline
![Page 3: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/3.jpg)
Physical Review X, In press
![Page 4: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/4.jpg)
![Page 5: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/5.jpg)
![Page 6: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/6.jpg)
![Page 7: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/7.jpg)
![Page 8: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/8.jpg)
An architecture of the large-scale quantum computer is taking shape
- “roadmap” as given by N. C. Jones et al. How can we do better than Jones (“going off road”)
- Majorana wires? - Direct multiqubit parity measurements - Codes that directly embody universal quantum
computation
Outline
![Page 9: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/9.jpg)
Proposal for realiza>on B. M. Terhal, F. Hassler, and D. P. DiVincenzo, "From Majorana Fermions to
Topological Order," arXiv:1201.3757, Physical Review LeRers, in press.
Light-grey areas are superconducting (SC) islands, each with two InAs nanowires on top at the end of which are Majorana bound states: 4 Majorana fermions (in yellow), representing a single qubit. Tunneling coupling of strength ! for Majorana fermions between islands.
![Page 10: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/10.jpg)
arXiv:1205.1910
![Page 11: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/11.jpg)
s1, s2, s3 are the states of the three qubits (0,1) χi is dispersive shift parameter Dispersive coupling is the same for each qubit and the same on both resonators (a and b)
χ=g2/Δ
![Page 12: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/12.jpg)
Wave impedance “looking into” port A (transmission line theory)
Reflection coefficient of full structure NB
(Z0=50Ω)
![Page 13: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/13.jpg)
arg(r(ω)) for different qubit states
θ is the same for all even states (mod 2π) θ is the same for all odd states (mod 2π)
θeven≠θodd
![Page 14: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/14.jpg)
Alternative solution of Mabuchi and coworkers
![Page 15: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/15.jpg)
An architecture of the large-scale quantum computer is taking shape
- “roadmap” as given by N. C. Jones et al. How can we do better than Jones (“going off road”)
- Majorana wires? - Direct multiqubit parity measurements - Codes that directly embody universal quantum
computation
Outline
![Page 16: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/16.jpg)
Quantum Circuits for Measuring Levin-‐Wen Operators
With N.E. Bonesteel
Florida State University
a
c e b
d
a
e b
d
c
c
e
a
b a
b
a
e b
d
c
a
e b
d
c
a
c e b
d
a
e b
d
c a
b
a
e b
d
c
a
e b
d
c
X 0
c
e
a
b
6
1
2
4
3
12
9
10
11
7
8
5
p
arXiv:1206.6048:
![Page 17: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/17.jpg)
Levin-‐Wen Models
∑∑ −−=p
pv
v BQH
Trivalent lattice: Qubits live on edges
![Page 18: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/18.jpg)
Levin-‐Wen Models
∑∑ −−=p
pv
v BQH
i j
k v vQ ijkδ= i
j
k v
Trivalent lattice: Qubits live on edges
0001010100 === δδδAll other 1=ijkδ
“Doubled Fibonacci” Model Vertex Operator
![Page 19: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/19.jpg)
Levin-‐Wen Models
∑∑ −−=p
pv
v BQH
( ) fmnmns
elmlms
dklkls
cjkjks
bijijs
aninmlkjisijklmn FFFFFFabcdefB ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′
ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ = nis,,p
i j
k v vQ ijkδ= i
j
k v
sBp f
a b
d
c
m
j k
l n
i
e
p ( )∑ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′
ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′=nmlkji
nmlkjisijklmn abcdefB ,,p f
a b
d
c
m’
j’ k’
l’ n’
i’
e
p
2
10
1 ϕ
ϕ
+
+= pp
p
BBB
Vertex Operator
Plaquette Operator
Horrible 12 spin interaction!
Trivalent lattice: Qubits live on edges
0001010100 === δδδAll other 1=ijkδ
“Doubled Fibonacci” Model
![Page 20: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/20.jpg)
Levin-‐Wen Models
∑∑ −−=p
pv
v BQH
( ) fmnmns
elmlms
dklkls
cjkjks
bijijs
aninmlkjisijklmn FFFFFFabcdefB ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′
ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′ = nis,,p
i j
k v vQ ijkδ= i
j
k v
sBp f
a b
d
c
m
j k
l n
i
e
p ( )∑ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′
ʹ′ʹ′ʹ′ʹ′ʹ′ʹ′=nmlkji
nmlkjisijklmn abcdefB ,,p f
a b
d
c
m’
j’ k’
l’ n’
i’
e
p
2
10
1 ϕ
ϕ
+
+= pp
p
BBB
Vertex Operator
Plaquette Operator
Horrible 12 spin interaction!
Trivalent lattice: Qubits live on edges
0001010100 === δδδAll other 1=ijkδ
“Doubled Fibonacci” Model
![Page 21: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/21.jpg)
“Fibonacci” Levin-‐Wen Model
• Excitations are Fibonacci anyons: Universal quantum computation can be carried out purely by braiding.
• Active approach: Ground states of Fibonacci Levin-Wen model can be used as a quantum code (the Fibonacci code). Qv and Bp are stabilizers which are measured to diagnose errors.
Question: How hard is it to measure Qv and Bp?
Koenig, Kuperberg, Reichardt, Ann. of Phys. (2010).
![Page 22: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/22.jpg)
1
2
3
v
X X X X 0
1
2
3
v1 Q−
Quantum Circuit for Measuring Qv
That was easy! What about Bp?
NB: 4-qubit Toffoli gate
![Page 23: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/23.jpg)
A Useful Resource: The F Move a b
c d
e Fdb !eace
!e" e’
b
d
a
c
Koenig, Kuperberg, Reichardt, Ann. of Phys. (2010).
Levin-Wen Ground State
![Page 24: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/24.jpg)
A Useful Resource: The F Move a b
c d
e e’
b
d
a
c
Levin-Wen Ground State
Koenig, Kuperberg, Reichardt, Ann. of Phys. (2010).
Fdb !eace
!e"
![Page 25: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/25.jpg)
A Useful Resource: The F Move a b
c d
e e’
b
d
a
c
Levin-Wen Ground State Levin-Wen Ground State on New Lattice
Koenig, Kuperberg, Reichardt, Ann. of Phys. (2010).
Fdb !eace
!e"
![Page 26: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/26.jpg)
F Quantum Circuit
⎟⎟⎠
⎞⎜⎜⎝
⎛
−=
−−
−−
12/1
2/11
ϕϕ
ϕϕF
a b
c d
e e’
b
d
a
c
215 +
=ϕ
a
c
e
b
dX
X F
X
X
X =
Fdb !eace
!e"
First gate: Locally equivalent to 5-qubit Toffoli gate
F is a pi-rotation around a funny axis
![Page 27: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/27.jpg)
Pentagon Equa>on
1 2 3 4
5 6
7
![Page 28: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/28.jpg)
Pentagon Equa>on
1 2 3 4
5 6
7
1 2 3 4
5 6
7
![Page 29: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/29.jpg)
Pentagon Equa>on 1 2 3 4
1 2 3 4
5 6
7
5 6
7
1 2 3 4
5 6
7
![Page 30: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/30.jpg)
Pentagon Equa>on
1 2 3 4
5 6
7
1 2 3 4
5
6
7
1 2 3 4
5 6
7
1 2 3 4
5 6
7
![Page 31: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/31.jpg)
Pentagon Equa>on
1 2 3 4
5
6
7
1 2 3 4
5
6
7
1 2 3 4
5 6
7
1 2 3 4
5 6
7
1 2 3 4
5 6
7
![Page 32: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/32.jpg)
Pentagon Equa>on
1 2 3 4
5
6
7
1 2 3 4
6 5
7
1 2 3 4
5 6
7
1 2 3 4
5
6
7
1 2 3 4
5 6
7
1 2 3 4
5 6
7
![Page 33: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/33.jpg)
Pentagon Equa>on 1 2 3 4
1 2 3 4
5 6
7
5 6
7
1 2 3 4
5
6
7
1 2 3 4
5
6
7
1 2 3 4
6 5
7
1 2 3 4
5 6
7
SWAP
![Page 34: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/34.jpg)
3
4
5
6
1
2
7
c
e
a
b
d
b
e
d
c
a
d
e
c
a
b
a
e
b
d
c
d
e
c
a
b
=
SWA
P
Pentagon Equa>on as a Quantum Circuit
Equality holds if Qv = +1 on each vertex
![Page 35: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/35.jpg)
3
4
5
6
1
2
7
c
e
a
b
d
b
e
d
c
a
d
e
c
a
b
a
e
b
d
c
d
e
c
a
b
=
SWA
P
Pentagon Equa>on as a Quantum Circuit
1111
1
![Page 36: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/36.jpg)
Pentagon Equa>on as a Quantum Circuit
= F
F
F
F
F SWA
P
⎟⎟⎠
⎞⎜⎜⎝
⎛
−=
−−
−−
12/1
2/11
ϕϕ
ϕϕF
215 +
=ϕ
Simplified Pentagon Circuit
![Page 37: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/37.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 38: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/38.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 39: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/39.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 40: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/40.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 41: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/41.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 42: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/42.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 43: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/43.jpg)
Reducing a PlaqueRe to a Tadpole
Koenig, Reichardt, Vidal, Phys. Rev. B (2009).
![Page 44: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/44.jpg)
S
X X =
a
b
⎟⎟⎠
⎞⎜⎜⎝
⎛
−+=
11
11
2 ϕ
ϕ
ϕS
a
b
X 0
p1 B−
a
b
a
b
Measuring Bp for a Tadpole is Easy!
S Quantum Circuit
![Page 45: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/45.jpg)
Restoring the PlaqueRe
![Page 46: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/46.jpg)
Restoring the PlaqueRe
![Page 47: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/47.jpg)
Restoring the PlaqueRe
![Page 48: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/48.jpg)
Restoring the PlaqueRe
![Page 49: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/49.jpg)
Restoring the PlaqueRe
![Page 50: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/50.jpg)
Restoring the PlaqueRe
![Page 51: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/51.jpg)
3 4 5 6
1 2
9 10 11 12
7 8
X 0
a
ceb
d
a
eb
dc
ce
a
bab
a
eb
d
c
a
eb
d
c
a
ceb
d
a
eb
dc
ce
a
bab
a
eb
d
c
a
eb
d
c
p1 B−
Quantum Circuit for Measuring Bp
6
1
2
4
3
12
9
10
11
7
8
5
p
82 Toffoli gates 43 CNOT gates 26 Single Qubit gates
or 20 n-qubit Toffoli gates 10 CNOT gates 24 Single Qubit gates
![Page 52: The$Quantum$Computer$Roadmap,$ …static.sif.it/SIF/resources/public/files/va2012/divincenzo_0627.pdf · An architecture of the large-scale quantum computer is taking shape - “roadmap”](https://reader031.vdocuments.mx/reader031/viewer/2022021823/5b32eac87f8b9a744a8d1522/html5/thumbnails/52.jpg)
An architecture of the large-scale quantum computer is taking shape
- “roadmap” as given by Cody Jones et al. How can we do better than Cody Jones (“going off road”)
- Majorana wires? - Direct multiqubit parity measurements - Codes that directly embody universal quantum
computation
Outline