A. Wallraff, Control and measurement of multiple qubits - PTB

Control and Measurement of Multiple Qubits
in in Circuit Circuit Quantum Quantum Electrodynamics
Electrodynamics
Andreas Wallraff (ETH Zurich)
www.qudev.ethz.ch
M M. Baur, BBaur, D D. B BBozyigit Bozyigit, i i , R RR.
. Bi Bianchetti Bianchetti, h i i, C C. Ei Eichler Eichler, hl , S SS.
. Fili Filipp Filipp, , J J. Fi Fink, k
T. Frey, CC.
. Lang, P. Leek, G. Littich, G. Puebla-Hellmann,
Puebla Hellmann,
L. . Steffen, A. van Loo (ETH ETH Zurich)
A A. Bl Blais i (Sh (Sherbrooke
Sh Sherbrooke, b k , C Canada) d )
J. Gambetta (Waterloo, Canada Canada)

Controlling the Interaction of Light and Matter ...
... is challenging on the level of single (artificial) atoms and single photons
• dipole moment d (usually small in atoms ~ ea 0)
• single photon fields E 0 (small in 3D)
• photon/atom interaction (usually small)
d and E 0 can be controlled in superconducting circuits:
• perform basic quantum optics experiments
D. Walls, G. Milburn, Quantum Optics (Spinger-Verlag, Berlin, 1994)

Cavity Quantum Electrodynamics

Circuit Realization of Cavity QED
... in superconducting circuits:
with individual photons and qubits ...
A. Blais, et al., PRA 69, 062320 (2004)
A. Wallraff et al., Nature (London) 431, 162 (2004)

elements:
• the cavity: a superconducting 1D transmission line resonator
with large vacuum field E 0 and long photon life time 1/
• the artificial atom: a superconducting qubit with large dipole
A. Blais et al., PRA 69, 062320 (2004)

Resonant Vacuum Rabi Mode Splitting …
first demonstration in a solid: A. Wallraff et al., Nature (London) 431, 162 (2004)
this data: J. Fink et al., Nature (London) 454, 315 (2008)
R. J. Schoelkopf, S. M. Girvin, Nature (London) 451, 664 (2008)

5 Years of Quantum Electrodynamics with Circuits
Quantum AC-Stark Shift
D. Schuster et al., Nature 445, 515 (2007)
Lamb Shift
A. Fragner et al., Science 322, 1357 (2008)
Fock and Arbitrary Photon States
MM. HHofheinz fh i et t al., l NNature t 454, 30(2008)
310 (2008)
M. Hofheinz et al., Nature 459, 546 (2009)
Root n Nonlinearityy
J. Fink et al., Nature 454, 315 (2008)
Two Photon Nonlinearities
F. Deppe et al., Nat. Phys. 4, 686 (2008)
Super Splitting and Root n Nonlinearity
L. Bishop et al., Nat. Phys. 5, 105 (2009)
Vacuum Rabi Mode Splitting
A. Wallraff et al., Nature 431, 162 (2004)
Coherent Flux-Qubit / SQUID Coupling
I. Chiorescu et al., Nature 431, 159 (2004)
Single Photon Source
A. Houck et al., , Nature 449, 449,3 328 (2007) ( 7)
Single Qubit MASER
O. Astafiev et al., Nature 449, 588 (2007)
Cooling and Amplification
M. Grajcar et al., Nat. Phys. 4, 612 (2008)
Quantum Bus
M. Sillanpaa et al., Nature 449, 438 (2007)
H. Majer et al., Nature 449, 443 (2007)
L. DiCarlo et al., Nature 460, 240-244 (2009)

Cavity QED with Multiple Photons Atoms
li N t t i l h t
. Rev. Lett. 103, 083601 (2009)
coupling nn photons to single atom

Multi-Atom Cavity QED

Multi-Qubit Circuit QED Schematic

Three Qubit Circuit QED Setup

Three Qubit Circuit QED Sample

N = 1, 2, 3 Qubit – Cavity Anti Crossing
, Phys. Rev. Lett. 103, 083601 (2009)

• th the spectrum: t
• the states:
states equally shared
between photon and qubit

• th the spectrum: t
• the states:
bright states: superposition
of a photon and a Bell state
dark state

• th the spectrum: t
• the states:
one photon h t plus l th three
qubit entagled W-state
two dark states

• th the spectrum: t
• scaling of collective coupling with
J. Fink et al., Phys. Rev. Lett. 103, 083601 (2009)

This work:
• excitation spectrum of 4 coupled quantum systems measured
• Tavis-Cummings model tested in the discrete limit
• a step towards multi-qubit QIPC in circuit QED
The future:
• investigate collective excitations with small but fixed number of
qubits
• Dicke states
• ssuperradiance perradiance
• generate complex entangled states using collective interactions

quantum bus
g g g
Leek et al., Phys. Rev. B 79, 180511(R) (2009)
• controlling photon life times on the quantum bus
P. Leek, M. Baur et al., Quantum Device Lab (2009)
• measuring i entanglement t l t bby joint j i t read-out d t with itha single i l ddetector t t
Filipp et al., Phys. Rev. Lett. 102, 200402 (2009)

Circuit QED for Quantum Information Processing
benefits of architecture:
• isolation of qubits from environment
•maintains i i addressability
dd bili
• quantum non-demolition qubit read out
• conversion of quantum information between qubits and photons
• long-range photon mediated qubit/qubit interactions

Out of Single Qubit
L. Steffen et al., Quantum Device Lab, ETH Zurich (2008)

Qubit Coherence: Tomography of Ramsey Experiment

qubit A
qubit A
qubit B
• Two near identical
superconducting qubits
~ 8 mm • Local control of
coupling bus
~
selective qubit drive line
magnetic flux allows
independent p selection of
qubit transition
frequencies
• Local drive lines allow
selective excitation of
individual qubits

Resonator Sideband Transitions
simultaneous excitation of qubit and resonator: |g,0> |e,1>
entangle a qubit with a photon on the bus: |g,0> |g,0> + |e,1>

standard resonator configuration coupled at in and output:
all modes:
• nominally yidentical Q
• identical photon life time
P. Leek et al., Quantum Device Lab (2007-2009)

Engineering Mode–Dependent Photon Life Times
center coupled resonator configuration:
odd modes are decoupled:
•high g Q
• long photon life time
• coherent manipulation
P. Leek et al., Quantum Device Lab (2007-2009)

Engineering Mode–Dependent Photon Life Times
center coupled resonator configuration:
even modes are strongly coupled:
• low Q
• short photon life time
• dispersive qubit measurement
P. Leek et al., Quantum Device Lab (2007-2009)

Realization
P. Leek et al., Quantum Device Lab (2007-2009)

fundamental:
• odd mode
• decoupled
•high Q
• long life time
1st harmonic:
•even mode
•coupled
• low Q
• short life time
2nd harmonic:
•odd
• decoupled
•high Q
• long life time
storage mode measurement mode
storage mode
P. Leek et al., Quantum Device Lab (2007-2009)

• low Q mode (T 1 1 ~ 39 ns)
• high Q mode (T 2 • high Q mode (T1 ~1600ns)
~ 1600 ns)
M. Baur, P. Leek et al., Quantum Device Lab (2009)

:
• create Fock state with
blue sideband pulse
• return qubit to |g>
•wait
• bring qubit to |e>
• annihilate Fock state with
blue sideband pulse
• measure qubit state
:
Fock-State (n=1)
high Q photon
T 1, ~ 1.45 s
M. Baur, P. Leek et al., Quantum Device Lab (2009)

pulse sequence:
high Q photon
T *
2, ~ 19s 1.9 s
M. Baur, P. Leek et al., Quantum Device Lab (2009)

Side Band Rabi Oscillations with Fock-States n = 0, 1, 2
p p
states with BSB
• scaling of Rabi
frequency
Ωn ∝ √ nΩ1
• imperfections due
to preparation
MB M. Baur, P. PLLeekket t al., l
Quantum Device Lab (2009)
Ω
Ω1
√ 2Ω1
√ 3Ω1
prospects:
p p
towards ion-trap style 2-qubit gates (sideband CNOT gate):
Cirac/Zoller, Sorensen/Molmer, Chuang, ...

Two-Mode Bell-State Generation and Measurement

Two-Mode Bell-State Generation and Measurement
storage
measurement
P. Leek, M. Baur et al., Quantum Device Lab (2009)

Photons Photons: Weihs et et al., al PRL 81 (1998) (1998); supercond supercond. qubits qubits: Steffen et et al., al Science 313 (2006) (2006).

Correlation Measurement with Individual Readout
table of single shot values (±1):
k σ z k ⊗ 1
1 +1
2 -1
… …
K -1

Correlation Measurement with Individual Readout
table of single shot values (±1):
k σ z k ⊗ 1 1 ⊗ σz k
1 +1 +1
2 -1 -1
… … …
K -1 +1

Correlation Measurement with Individual Readout
table of single shot values (±1):
k σ z k ⊗ 1 1 ⊗ σz k σ z k ⊗ σz k
1 +1 +1 (+1).(+1) = +1
2 -1 -1 (-1).(-1) = +1
… … … …
K -1 +1 (-1).(+1)=-1

Correlation Measurement with Individual Readout
rotation of qubit: h σ x ⊗ 1i, h 1 ⊗ σ zi and h σ x ⊗ σ zi are measured

Correlation Measurement with Individual Readout
orh σ x ⊗ 1i, h 1 ⊗ σ yi and h σ x ⊗ σ yi, a.s.o.
-> all combinations of {σ x, σ y, σ z} give full information about the state

Correlation Measurement with Joint Readout
• only single detection device
• plus single qubit operations
Circuit QED-Setup:

Homodyne Measurement of Cavity Frequency Shift
Amplitude difference (δQ) depends on state of both qubits:
qubit-qubit correlations can be determined from
transmission measurement
& Schoelkopf, PRA 69, 062320 (2004)

experimental
state fidelity:
F = 86%
concurrence: Pure
F 0.541 = 100%
entanglement
of formation :
0.371
overlap with
calculation l l ti
F = 99%

experimental
state fidelity:
F = 86%
Pure
concurrence:
F = 100%
0.518
entanglement
of formation :
0.374
overlap with
calculation l l ti
F = 99%
P. Leek et al., Phys. Rev. B 79, 180511(R) (2009)
S. Filipp et al., Phys. Rev. Lett. 102, 200402 (2009)

N atom t cavity it QED ...
• test of Tavis-Cummings model
... generation of all 4 Bell states using sidebands ...
• towards a universal gate
... realization of two qubit tomography
• correlations w/o single-shot g measurement
• using joint dispersive read-out

The ETH Zurich Quantum Device Lab
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