Trapped Atom-RF Interaction: MAGIC L = , "Carrier" L = - - PowerPoint PPT Presentation

MAGIC IN THE LAB

Trapped Atom-RF Interaction: MAGIC

ωL = ω, "Carrier" ωL = ω − ν, "red sideband" ωL = ω + ν, "blue sideband"

L

ω

ω − ω ν + ω ν

MAGIC – Experiment

369nm

2P1/2

935nm

[3/2]1/2

2D3/2 2S1/2

Yb+

RF-optical double resonance spectroscopy

π- polarized PRL 102 (2009)

MAGIC – Experiment

Spin-Motion coupling using RF radiation

Zeeman Resonance Yb+ D3/2 state

∂

PRL 102 (2009)

Zeeman Resonance Yb+ D3/2 state

∂ ∂

PRL 102 (2009)

MAGIC – Experiment

Spin-Motion coupling using RF radiation

• 200
• 150
• 100
• 50

50 100 150 0.2 0.4 0.6 0.8

Excitation probability

Detuning from Carrier (kHz)

|↑ ›

12.6 GHz

|↓ ›

171Yb+

MAGIC – Experiment

Spin-Motion coupling using RF radiation

Single Qubit Gates Using RF-waves

• K. R. Brown et al., PRA 84 (2011)

Gate error O(10-5) Gate error O(10-6)

• T. P. Harty et al., PRL 113 (2014)

MAGIC QUANTUM TOOLBOX

• RF (MW) for all coherent operations
• Individual Addressing
• Spin-Spin Coupling:
• Adjust Magnitude
• Simultaneous
• On and Off
• Change Sign

Addressing a Quantum Byte

10 µm 1 2 3 4 5 6 7 8

Magnetic Gradient 19 T/m

Addressing a Quantum Byte

1

Magnetic Gradient 19 T/m

Addressing a Quantum Byte

10 20 30 40 0.2 0.4 0.6 0.8 1

pulse duration (µs) excitation probability

10 20 30 40 0.2 0.4 0.6 0.8 1

pulse duration (µs) excitation probability

10 µm 1 2 3 4 5 6 7 8

• Nat. Commun. 5 (2014)

Addressing a Quantum Byte

Benchmarking

10 µm 1 2 3 4 5 6 7 8

C5,4 = 7.6(1.3)·10-5

F5,4 500 1000 1500 0.85 0.9 0.95 1 sequence length N state fidelity 500 1000 1500 0.85 0.9 0.95 1 sequence length N F5,1 state fidelity

C5,1 = 1.9(9)·10-5 Example:

• Nat. Commun. 5 (2014)

addressed qubits (rows); observed qubits (columns)

Ci,j (10-5)

• 3.0(9)

1.9(8) 2.2(9) 2.3(9) 1.0(8) 0.7(6) 0.7(7) 3.8(1.4)

• 4.1(1.1)

2.3(9) 2.3(1.1) 1.6(1.1) 0.9(8) 0.9(9) 2.1(1.0) 3.7(1.2)

• 4.5(1.2)

1.6(7) 2.1(6) 0.8(7) 1.1(6) 0.9(9) 1.7(6) 2.7(1.1)

• 3.1(9)

0.8(7) 0.6(6) 0.6(6) 1.9(9) 1.6(9) 3.1(1.0) 7.6(1.3)

• 3.1(1.0)

1.8(9) 0.5(5) 1.5(5) 1.2(8) 1.5(8) 1.0(8) 5.5(1.4)

• 3.6(1.3)

0.8(8) 0.8(8) 1.4(8) 1.5(7) 1.2(8) 1.2(8) 2.9(1.1)

• 2.6(8)

0.8(6) 1.1(5) 0.6(6) 0.8(8) 2.5(9) 1.1(8) 3.4(1.2)

• 1

2 3 4 5 6 7 8

Addressing a Quantum Byte

Measured cross-talk matrix for interacting ions

• Nat. Commun. 5 (2014)

MAGIC QUANTUM TOOLBOX

• RF (MW) for all coherent operations
• Individual Addressing
• Spin-Spin Coupling:
• Adjust Magnitude
• Simultaneous
• On and Off
• Change Sign

B

MAGIC: Spin-Spin Interaction

• 1. Individual Addressing
• 2. Spin-Spin Coupling

− ! 2 σz,iσz,j Jij

i<j N

∑

MAGIC: Spin-Spin Interaction

| > | >

ω h

| > | >

ω h

B

MAGIC: Spin-Spin Interaction

| > | >

ω h

B

MAGIC: Spin-Spin Interaction

| > | >

ω h

B

In Laser Physics at the Limit, Springer, 2002, p. 261; also: quant-ph/0111158

• Adv. At. Mol. Opt. Phys.49, 295 (2003); also: quant-ph/0305129

−  2 Jij σz,iσz,j

i<j N

∑ MAGIC: Spin-Spin Interaction

MAGIC Example: Two Ions

B

MAGIC Example: Two Ions

Spin flip ⇒ dz = Fz / (mν 2)

B

dz J12 = −Fzdz = −Fz

2 / (mν2) ∝ (∂zB / ν)2.

J 2

• J. Phys. B 42, 154009 (2009)

MAGIC Example: Two Ions

B

dz

J12 ∝ (∂zB / ν)2

J 2

• J. Phys. B 42, 154009 (2009)

MAGIC: Outline of Math (1d)

= … − F qn

n=1 N

∑

σz

(n)

Vharm = Ai,jqi

n=1 N

∑

qj

Potential (external + Coulomb) Interaction N uncoupled normal modes

⇒

Unitary transformation

⇒

with and

In Laser Physics at the Limit, Springer, 2002,

• p. 261. also: quant-ph/0111158

1. Qubit resonances shifted individually 2. Spin-Spin coupling between individual qubits

−  2 σz,iσz,j Jij

i<j N

∑

B

Magnetic Gradient Induced Coupling: MAGIC

Interlude: Ramsey-type measurements

π/2 π 3/2π

phase: 0

Ramsey measurement

state

π/2 π 3/2π

phase: π/2

Ramsey measurement

state

π/2 π 3/2π

phase: π

Ramsey measurement

state

π/2 π 3/2π

phase: 3/2π

Ramsey measurement

state

Interlude: Quantum Gates using J-coupling

|↑ ›

12.6 GHz

|↓ › |↑ ›

12.6 GHz

|↓ ›

2 ⎛ ⎞ ⎜ ⎟ ⎝ ⎠y π

J-type coupling – CNOT Gate

Schematic

12 1 2

( ) exp 2 ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

z z gate gate

i U J τ σ σ τ

12

2 ⋅ =

gate

J π τ

J-type coupling – CNOT Gate

Schematic

↑↑ ⎯⎯⎯ → ↑↑

CNOT

2 ⎛ ⎞ − ⎜ ⎟ ⎝ ⎠x π

J-type coupling – CNOT Gate

Schematic

12

2 ⋅ =

gate

J π τ

J-type coupling – CNOT Gate

Schematic

12 1 2

( ) exp 2 ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

z z gate gate

i U J τ σ σ τ

↓↑ ⎯⎯⎯ → ↓↓

CNOT

2 ⎛ ⎞ − ⎜ ⎟ ⎝ ⎠x π

J-type coupling – CNOT Gate

Schematic

MAGIC QUANTUM TOOLBOX

• RF (MW) for all coherent operations
• Individual Addressing
• Spin-Spin Coupling:
• Adjust Magnitude
• Simultaneous
• On and Off
• Change Sign

Measuring MAGIC

1/2 1 3/2 2 0.25 0.5 0.75 1 Ramsey phase at conditional evolution time 4 ms excitation probability Ramsey phase / p (rad) 1/2 1 3/2 2 0.25 0.5 0.75 1 Ramsey phase at conditional evolution time 4 ms excitation probability Ramsey phase / p (rad) 1/2 1 3/2 2 0.25 0.5 0.75 1 Ramsey phase at conditional evolution time 4 ms excitation probability Ramsey phase / p (rad)

Single ion Control |0> Control |1>

τ φ 2

ij ij

J Δ =

Science Advances 2 (2016) PRL 108, 220502 (2012)

120 130 140 150 160 170 180 10 20 30 40 50 60

νz (kHz) J12

2π (Hz)

19 T/m

Magnitude of MAGIC

Variation of trapping potential

J ∝ ∂zB νz ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

B

PRL 108, 220502 (2012)

1

Q

3

Q

2

Q

MAGIC: Spin-Spin Interaction

MAGIC: Spin-Spin Interaction

J12σ 1

zσ 2 z

J23σ 2

zσ 3 z

J13σ 1

zσ 3 z

1

Q

2

Q

3

Q

Simultaneous Coupling

1 2 3 4 5 6

• 180
• 120
• 60

60 120 180

Phase shift of qubit 2 due to qubit 1 and qubit 3

conditional evolution time (ms) phase angle (deg) 1 2 3 4 5 6

• 180
• 120
• 60

60 120 180

Phase shift of qubit 2 due to qubit 1 and qubit 3

conditional evolution time (ms) phase angle (deg) 1 2 3 4 5 6

• 180
• 120
• 60

60 120 180

Phase shift of qubit 2 due to qubit 1 and qubit 3

conditional evolution time (ms) phase angle (deg) 1 2 3 4 5 6

• 180
• 120
• 60

60 120 180

Phase shift of qubit 2 due to qubit 1 and qubit 3

conditional evolution time (ms) phase angle (deg)

|00> |01> |10> |11> 3 1,Q

Q

2

Q

3

Q

1

Q

Science Advances 2 (2016)

Turn coupling off

Recoding

2,3 2,3

→ ψ ψ

t

1

Q

2

Q

3

Q

2S

1/2

F=1 F=0

0' 1

+

pQ mQ

1 1 1 1

0 and 1 0' → →

Qubit 1: Isolation by Recoding

1

Q

2

Q

3

Q

1 2 3 4 5 6 7

• 120
• 60

60 120 conditional evolution time (ms) phase angle (deg) 1 2 3 4 5 6 7

1

Q3 :

Science Advances 2 (2016)

Sign of Coupling

= F 1 = F 1 − 1 +

Hz ) 7 ( 39 ) 7 ( 27 ) 7 ( 39 ) 7 ( 34 ) 7 ( 27 ) 7 ( 34 2 ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = π

ij

J

1

Q

2

Q

3

Q

Science Advances 2 (2016)

Sign of Coupling

= F 1 = F 1 − 1 +

Hz ) 7 ( 34 ) 5 ( 27 ) 7 ( 34 ) 5 ( 39 ) 5 ( 27 ) 5 ( 39 2 ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − = π

ij

J

3

Q

1

Q

2

Q

Science Advances 2 (2016)

MAGIC QUANTUM TOOLBOX

• RF (MW) for all coherent operations
• Individual Addressing
• Spin-Spin Coupling:
• Adjust Magnitude
• Simultaneous
• On and Off
• Change Sign

Coherent QFT Using Multiple Coupling

• single-qubit gates: rotations and Hadamard gate
• conditional dynamics: all mutual couplings
• conditional dynamics: selected coupling

Science Advances 2 (2016)

Coherent QFT Using Multiple Coupling

§ Total time 8.6 ms ≈ one CNOT gate

Science Advances 2 (2016)

1/2 1 3/2 2 0.25 0.5 0.75 1

|000>

1/2 1 3/2 2 0.25 0.5 0.75 1

|100>

Ramsey phase (π rad) excitation probability

1/2 1 3/2 2 0.25 0.5 0.75 1

|001>

1/2 1 3/2 2 0.25 0.5 0.75 1

|010>

1/2 1 3/2 2 0.25 0.5 0.75 1

|011>

1/2 1 3/2 2 0.25 0.5 0.75 1

|101>

1/2 1 3/2 2 0.25 0.5 0.75 1

|110>

1/2 1 3/2 2 0.25 0.5 0.75 1

|111>

Coherent QFT: Experiment

___ Fit

• - - Theory

qubit 1 qubit 2 qubit 3

Science Advances 2 (2016)

probability probability

SSO = 0.99(3) SSO = 0.84(3) SSO = 0.54(2) SSO = 0.64(2)

S(p,q) = piqi

i

∑

( )

2

Coherent QFT: Period Finding

See also:

• J. Chiaverini et al., Science 308 (2005)
• P. Schindler et al., New. J. Phys. 15 (2013)

Science Advances 2 (2016)

Nature 476, 185 (2011) University of Sussex (W. Hensinger):

• S. C. Webster et al. PRL 111 (2013)
• I. Cohen et al., NJP 17 (2015)
• J. Randall et al., PRA 91 (2015)

High-Fidelity 2-Qubit Gate:

• S. Weidt et al., PRL 117 (2016)

MAGIC using Dressed State Gates

Dynamic Magnetic Field Gradient

B t,z

( ) = B0 z ( ) cos ωt ( )

Theory and Experiments: NIST, Boulder (D. Wineland): Ospelkaus et al., PRL 101 (2008). Ospelkaus et al., Nature 476 (2011). University of Oxford (D. Lucas): Aude Craik et al., Appl. Phys. B 114 (2014). High-Fidelity 2-Qubit Gate: Harty et al., PRL 117 (2016) Leibniz University Hannover (Ch. Ospelkaus):

• M. Carsjens et al., Appl. Phys. B 114 (2014)

Dynamic Gradient <-> Static Gradient: New J. Phys. 19 (2017)

Optical Dipole Force: Spin-Spin Interaction

≈ ≈ λ/2

!J12 = −Fzdz = −Fz

2 / (mν2)

Spin flip ⇒ dz = Fz / (mν 2)

• D. Porras and I. Cirac PRL 92 (2004)

Optical Dipole Force: Spin-Spin Interaction

≈ ≈ λ/2

• D. Porras and I. Cirac PRL 92 (2004)

Standing wave: static force

Optical Dipole Force: Spin-Spin Interaction

≈ ≈ λ/2

• D. Porras and I. Cirac PRL 92 (2004)

Two waves with relative detuning ωOpt: F

0 cos(ωOptt) qnσn z

Optical Spin-Spin Interaction

… − F

0 cos ωOpt

( )

qn

n=1 N

∑

σn

z

∝ Ji,jσi

zσ j z i<j N

∑

Coupling

⇒ Jij ∝ Si,nSj,n ωOpt

2

− ωn

2 n

∑

! !

with

ωOpt − ωn ≪ ηi,nΩi

under the condition

Optical Spin-Spin Interaction

−Bx σi

x i N

∑

+ J σi

zσ j z i<j N

∑

• A. Friedenauer et al., Nat. Phys. 4 (2008).

Optical Spin-Spin Interaction

• J. W. Britton et al., Nature 484 (2012).

Optical Spin-Spin Interaction

• J. W. Britton et al., Nature 484 (2012).

Optical Spin-Spin Interaction

with

• K. Kim et al., PRL 103 (2009).

Bichromatic force Transverse modes

Optical Spin-Spin Interaction

Entanglement Propagation after Global Quench

• P. Richerme et al., Nature 511 (2014).

Trapped Atomic Ions in QIS

§ High Fidelity Single- and Multi-Qubit Gates § Programmable Small-Scale Quantum Computer § Quantum Simulations using Spins and Phonons Outlook: § Integrated Micro-Structured 2-D Trap Arrays § Scalable Quantum Computer

• B. Lekitsch et al.,

Science Advances 3 (2017)

• J. Chiaverini et al.,
• Quant. Inf. Comput. 5, 419 (2005).
• C. Monroe et al.,

PRA 89, 022317 (2014)