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Quantum bits based
on superconducting circuits
Martin Weides, Karlsruhe Institute of Technology
Brief history experimental SC qubits
1999
2002
2004
Charge (NEC)+flux (Delft) qubits
Phase qubit (NIST)
cQED with qubits (Yale)
2007
Lasering (NEC)
QND (Delft)
2008
2009
Fock states (UCSB)
Grover and Deutsch–Jozsa (Yale)
Arbitrary quantum states (UCSB)
Bell inequality (UCSB)
2010 3-qubit entanglement
(UCSB & Yale)
2011 Quantum von Neumann
architecture (UCSB)umann architecture
2012 4 qubits and
5 resonators (UCSB)
Shor, ‘15=5x3’
Microstructured quantum processor
(University of California, Santa Barbara)
Qubit
Memory
Signalbus
5 mm
Lucero et al., Nature 2012
Basic potentials
Harmonic oscillator
Anharmonic oscillator
Photons in cavity, atom oscillation
Energy levels equidistant
Large excitation amplitudes
Energy eigenstate
Two level system
if |/w | >>0  two level system
atomic transition, spin, qubit
Nobel price 2012
Nobel Prize in Physics 2012 was awarded jointly to
Serge Haroche and David J. Wineland
"for ground-breaking experimental methods that enable measuring and
manipulation of individual quantum systems"
Controlling a quantum particle
(atoms or ions)
Jaynes–Cummings
Cavity-qubit system
Quantum information processing,
Q-simulation, collective Q-phenomena
Artificial atoms for quantum matter require
C
L
Large interaction strength
 dipole moment
Tunability
 tune transition frequency
Frequency selection
 large anharmonicity
Long coherence
 low loss
High integration density
 scalability
linear LC oscillator
C
Superconducting quantum circuit
LJ, f
2
1
0
non-linear LC oscillator
• Strong coupling w/ EM field, long coherence, fast & local detuning
• simple resonant circuit design, straightforward scalability
• high density, integration w/ std. electronics
2
1
0
Josephson junction  non-linear inductor
Phase difference
1st Josephson eq.:
(DC)
2nd Josephson eq.:
(AC)
From DC:
Insert in AC:
 non-linear inductance:
Capacitively shunted Josephson junction
 Anharmonic oscillator
C
LJ, f
2
non-linear LC oscillator
1
0
w21
w10
Restrict to two lowest
states  Bloch sphere
F
C
LJ
v
LJv
C
Magnetic flux F changes LJ(f)
Superconducting qubit ’zoo’
Junction area (μm2)
Charge
Flux
Phase
1
102
104
0.1-1
1-100
0.01
100 mm
Modern designs
C-shunted flux qubit
3d transmon
Transmon=
C-shunted charge qubit
circuit quantum electrodynamics (cQED):
artificial atom (qubit) coupled to resonator
Resonator
Qubit
Koch et al. PRA 2007, Blais et al. PRA 2004
Transmission |S21|
Strong coupling regime possible
Qubit
readout
Frequency fr
Parasitic two level systems (TLS) in
dielectrics
S
I
E
I
S
S
Josephson tunnel
junction
resonator
Amorphous oxides loaded with uncompensated charges ~ 1016/cm3
Range of energies, coherence and Rabi frequencies , T1, T2, W
Absorption probability goes as ~
Maximized at low E, T
 Dominating loss at low T & E
Schickfus, Hunklinger (1975)
Katz et al., PRL (2010)
Decoherence due to TLS
w10
S
interaction S lifts
degeneracy
E
flux bias
Qubit spectroscopy and time domain
TLS located in tunnel barrier oxide
fluxon@pi.uka.de
Resonator quality factor
power dependence (TLS saturation)
Sage et al.
JAP ‘10
coupler
Coherence threshold quantum error correction
Min. requirement: 0.1‰ error per gate (10 nsec) 100 μsec
Relaxation T1
Limited by: Capacitive and inductive loss, quasiparticles,
environmental coupling, microscopic defect states (TLS)
Dephasing T2*, T2
T2≈2T1 (@ sweet spot), usually shorter
Limited by: 1/f noise (charge, flux)
Materials limited:
Junctions, inductors, capacitors
C LJ
L
Field distribution, filling factor of stored energy
 Etched surface matters, microscopic structure, E-field
 Implications for resonant quantum circuits
vacuum
conductor
Filling factor:
substrate
Fluorine
GND
TiN
Silicon
Chlorine
GND
Chlorine
Ar mill
Sandberg et al.
APL 2012
Microstrip transmon qubit
1. Best Josephson junction (T1)  Sub-micron Al-AlOx-Al
2. Best capacitor (d)  TiN microstrip w/ low loss silicon substrate
3. Negligible Al/TiN interface loss  Merge sub-micron junctions and TiN capacitor
Loss participation analysis:  expected lifetime dominated by TiN
qubit 1:
Purcell limit 20 msec
Radiation limit 17 msec
Combined limit 9.7 msec
qubit 2:
Purcell limited
Re-designed qubit T1=40 msec
Sandberg et al., APL 2013
expect >100 msec (error correction threshold)
Engineered quantum elements
Resonator design and simulation
Current distribution
Flux tunable
junction
10 mm
Kiselev, BA thesis ‘13
F
Transmission |S21|
Qubit (Transmon) coupled to
resonator
Braumüller, MA thesis ‘13
100 mm
Frequency fr
Deposition tools
Fast turnaround, flexibility, reliability, good control
Deposition, cleaning, oxidation
Al-AlOx-Al tunnel junctions
• Sputter tool Plasma 1
• Al, Nb, NbN, AlOx resonators
• Shadow evaporation tool Plassys
• E-beam evaporator
• Al-shadow evaporated junctions
• Ti/Au markers, AuPd resistors
• Sputter tool Plasma 2
• Nitride superconductors
• Heating stage (500°C)
Sputtered thin films
• Fast turnaround, flexibility,
reliability, good control
• Deposition
• Cleaning
• Oxidation
• Al, Nb, NbN, AlOx resonators
• Al-AlOx-Al tunnel junctions
• Toolbox of designs and materials
50 mm
Bottom electrode
200 mm
Neuwirth, BA thesis ‘13
10 mm
Top electrode
Tunnel area
DFG Center for Functional Nanostructures
Nanostructure Service Laboratory
Schematic fabrication
1. Design software
2. Film deposition,
optical litho, etch
3. E-beam markers
optical litho
3” wafer
(Si,
Al2O3)
4. Dice into
20x20 mm2
Get 6 chips w/
same designs
Inductor, capacitor, flux bias…
(1 µm+ feature sizes)
Markers (crosses etc.)
5. E-beam litho, Al-AlOxAl shadow evaporation
6. Dice into
5x5mm2
‘Dolan’ bridges,
Tunnel junctions, …
Get 9 chips w/
different designs
12 qubit chip ‘cavemon’
Flux bias
Qubit
Transmission line
150 µm
Readout resonator
3He/4He
dilution refrigerator
400 mm cold plate
18 coax lines, 24 filtered DC lines
6 HEMTs (2x LNF)
2-port, 4-port microwave switches,
circulators, filters, infrared shield…
Fits 9 samples
Multi-tone spectroscopy, flux bias,
time domain measurements
Materials for quantum circuits
- specific properties for capacitive and inductive
regions -
Superconductors
Aluminium
Niobium
Niobium nitride
Aluminium oxide
Josephson junctions
Cross junctions (optical & e-beam, sputtered)
Shadow junctions (e-beam, evaporated)
Josephson tunnel junctions
Al-AlOx-Al junctions
• Ultra-small shadow evaporated (aka Dolan JJs)
• Micron-sized cross JJs, evaporated and sputtered
Current-voltage characteristic at 300mK
Dolan JJ
200 nm
10 mm
F
Cross JJ
Microwave resonators
Internal quality factor versus power
NbN λ resonator
Al, Nb, NbN, and AlOx resonators
quality factors Q:100k @single photon, 1M+ @high power
Designs: Geometric, lumped element, spiral,
coplanar waveguide, microstrip
Microstrip transmon qubits
(non-tunable and tunable)
10 mm
F
100 mm
Flux F to qubit
resonator response
Qubit spectroscopy
Increase drive power  higher level visible
½(0↔2)
1↔2
Braumüller, MA thesis ‘13
0↔1
0↔1
The team
Egor Kiselev
Kai Kleindienst
Marcel Langer
Markus Neuwirth
Alexander Stehli
Tobias Bier
Joel Cramer
Amadeus Dieter
Peter Fehlner
Marco Pfirrmann
Steffen Schlör
Jochen Braumüller
Saskia Meißner
Sebastian Skacel
Ping Yang
Hannes Rotzinger
Sasha Lukashenko
Michael Meyer
Roland Jehle
Lucas Radtke
Gernot Goll
Alexey Ustinov
Georg Weiß
Thanks for your attention
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