Quantum Computing with Superconducting Circuits

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Quantum Computing with Superconducting Circuits

• Rob Schoelkopf
• Yale Applied Physics

QIS Workshop, Virginia April 23, 2009
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Overview

• Superconducting qubits in general and where they
  stand
• Improving decoherence
• Coupling/communicating between multiple qubits
• Snapshot of current state of the art
• - Arbitrary states/Wigner function of an
  oscillator (UCSB)
• - Implementation of two-bit algorithms (Yale)
• Outlook/Future Directions

1) There is lots of excellent new science!
2) We dont know its not going to work
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Superconducting Qubits
Energy
nonlinearity from Josephson junction (dissipation
less)
electromagnetic oscillator
See reviews Devoret and Martinis, 2004 Wilhelm
and Clarke, 2008
Several challenges
1) Each engineered qubit is an individual
2) Can they be sufficiently coherent?
3) How to communicate between them? (i.e. make
two-bit gates)
4) How to measure the result?
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Three Flavors of SC Qubits
charge qubit
flux qubit
phase qubit
Shared traits of all of these
Weaknesses
Strengths
Design your hamiltonian! Inverse
problem? Man-made en masse Calibration? Tune
properties in-situ Decoh. from 1/f noise Strong
interactions Fast relaxation Couple/control
with wires Complex EM design
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Superconducting QC
Requirement
Status
1. Make and control lots of qubits.
2. Measure the result
3. Avoid decoherence
4. Make qubits interact with each other (gates)5. Communicate quantum information (w/ photons?)
This IS the Hamiltonian of my system
Can mass produce qubits Electronic control a
big advantage
and we really mean it! (Lehnert, 2003)
Some high fidelity (gt90) readout,not routine
and sometimes incompatible with best performance
Progress but a LONG way to go!
Naturally strong learning how to tameSeveral
two qubit gates demonstrated
Coupling with photons on wires
(after DiVincenzo)
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Progress in Superconducting Charge Qubits
Transmon (Yale)
Quantronium sweet spot (Saclay)
Charge echo (NEC)
Nakamura (NEC)
Similar plots can be made for phase, flux qubits
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Outsmarting Noise Sweet Spot
1st coherence strategy optimize design
sweet spot
Energy
transition freq. 1st order insensitive to gate
noise
Charge (CgVg/2e)
Strong sensitivity of frequency to charge noise
But T2 still lt 500 ns due to second-order noise!
Vion et al., Science 296, 886 (2002)
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Eliminating Charge Noise with Better Design
EJ/EC 1
EJ/EC 25 - 100
Energy
exponentially suppresses 1/f!
Cooper-pair Box
Transmon
Houck et al., 2008
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Coherence in Transmon Qubit
Random benchmarking of 1-qubit ops
Chow et al. PRL 2009Technique from Knill et al.
for ions
Error per gate 1.2
Similar error rates in phase qubits (UCSB)
Lucero et al. PRL 100, 247001 (2007)
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Materials Can Matter
2nd coherence strategy improve
materials/fabrication
Dielectric loss?
Martinis et al., 2005 (UCSB)
phase qubits
losses consistent with two-level defect
physicsin amorphous dielectrics
quantum regime
quantumregime
is special!
Progress on origin of 1/f flux noise
Spontaneous emission? Superconductors? Junctions?
Readout circuitry?
Other relaxationmechanisms
Clarke, McDermott, Ioffe
Still not clear for most qubits!
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But High Q May Not Be Impossible!
V. Braginsky, IEEE Trans on Magnetics MAG-15, 30
(1979)
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Q 109 _at_ 1 K !
108
107
Quality factor
106
105
Nb films on macroscopic sapphire crystal
104
0
5
10
15
T (K)
Note this is not in microfabricated device, and
not at single photon level
So fundamental limits might be 4-5 orders of
magnitude away
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Coupling SC Qubits Use a Circuit Element
a capacitor
entangledstates
Con 55
Charge qubits NEC 2003
Phase qubits UCSB 2006
an inductor
tunable element
Flux qubits Delft 2007
Flux qubits Berkeley 2006, NEC 2007
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Qubits Coupled with a Quantum Bus
use microwave photons guided on wires!
Circuit QED
Blais et al., Phys. Rev. A (2004)
transmissionline cavity
out
Josephson-junctionqubits
7 GHz in
Expts Sillanpaa et al., 2007 (Phase qubits /
NIST) Majer et al., 2007
(Charge qubits / Yale)
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Recent Highlights Arbitrary States of Oscillator
Hofheinz et al., Nature 2008 (UCSB)
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Wigner Functions of Complex Photon States
Thy.
Expt.
Hofheinz et al., Nature in press 2009 (UCSB)
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Wow!
Requires

• Dozen pulses with sub-ns timing
• Per pulse accuracy gtgt 90
• Many initial calibrations
• Many field displacements for W(a)

Shows the beauty of strong coupling
electronic control
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A Two-Qubit Processor
1 ns resolution
DC - 2 GHz
T 10 mK
cavity entanglement bus, driver,
detector
transmon qubits
L. DiCarlo et al., cond-mat/0903.2030 (Yale)
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Spectroscopy of Qubits Interacting with Cavity
right qubit
Qubit-qubit swap interaction Majer et al., Nature
(2007)
left qubit
Cavity-qubit interaction Vacuum Rabi
splitting Wallraff et al., Nature (2004)
cavity
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Spectroscopy of Qubits Interacting with Cavity
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Qubits mostly separated and non-interacting due
to frequency difference
Preparation 1-qubit rotations Measurement
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cavity
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Two-Qubit Gate Turn On Interactions
Use voltage pulse oncontrol lines to push
qubits near a resonance
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A controlled z-z interaction also ala NMR
Conditional phase gate
10
cavity
Adiabatic pulse (30 ns)-gt conditional phase gate
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Measuring Two-Qubit States
Joint measurement of both qubits and
correlations using cavity frequency shift
rightqubit
leftqubit
correlations
Density matrix
Ground state
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Measuring Two-Qubit States
Apply p-pulse to invert state of right qubit
00
01
10
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One qubit excited
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Measuring Two-Qubit States
Now apply a c-Phase gate to entangle the qubits
00
01
10
11
Fidelity 94 Concurrence 94
Bell State
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Two-Qubit Grover Algorithm
Challenge Find the location of the -1 !!!
unknown unitary operation
Classically 2.25 evaluations
QM 1 evaluation only!
ORACLE
10 pulses w/ nanosecond resolution, total 104 ns
duration
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Grover Step-by-Step

Grover in action
Begin in ground state
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Grover in action
Create a maximal superpositionlook everywhere
at once!
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A Grover step-by-step movie

Grover in action
Apply the unknownfunction, and mark the
solution
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Grover in action

Some more 1-qubitrotations
Now we arrive in one of the four Bell states
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Grover in action
Grover search in action

Grover in action
Another (but known) 2-qubit operation now undoes
the entanglement and makes an interferencepattern
that holds the answer!
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Grover in action
Grover search in action

Grover in action
Final 1-qubit rotations reveal the answer
The binary representation of location 3!
The correct answer is found gt80 of the time.
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Future Directions

• Analog quantum information
• parametric amplifiers, squeezing, continuous
  variables QC
• Topological/adiabatic QC models??
• Multi-level quantum logic (qudits), or level
  structures?
• Hybrid systems (combine SC with spin, ion,
  molecule,)?
• Quantum interface to optical photons?
• A really long-lived solid-state memory

Engineering Wish List

• A low-electrical loss fab process (with Q gt
  107?)
• Cheap waveform generators (16 bits, 10 Gs/sec,
  2k/chan?)
• Controlled couplings with high on/off ratio (gt
  40 dB?)
• Quantum-limited amplifiers/detectors in GHz
  range (readout!)
• Stable funding!
• Reliable dilution refrigerators

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Summary Superconducting Qubits

• Can make, control, measure, and entangle qubits,
• in several different designs
• Play moderately complex games with 10s of
  pulses, and error per pulse 1
• Coherence times microseconds, operation times
  few ns (improved x 1,000 in last decade!)
• Two complimentary approaches for improving this
  further
• 1) Design around the decoherence
• 2) Make better materials, cleaner systems
• Immediate future multi-partite entanglement,
  rudiments of error correction

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Two-Excitation Manifold of System
Qubits and cavity both have multiple levels
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Adiabatic Conditional Phase Gate
Avoided crossing (160 MHz)
A frequency shift
Use large on-off ratio of z to implement
2-qubit phase gates.
Strauch et al. (2003) proposed use of excited
states in phase qubits