Quantum Computing with Superconducting Circuits
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Quantum Computing with Superconducting Circuits
Rob SchoelkopfYale 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
2) “We don’t know it’s not going to work…”
1) There is lots of excellent new science!
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Superconducting Qubits
nonlinearity from Josephson junction
(dissipationless)electromagnetic oscillator 01 ~ 5 10GHz
See reviews: Devoret and Martinis, 2004; Wilhelm and Clarke, 2008
Ene
rgy
0
101
1201 12
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)
Several challenges:
4) How to measure the result?
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chargequbit
fluxqubit
phasequbit
Three “Flavors” of SC Qubits
Design your hamiltonian! Inverse problem?Man-made en masse Calibration?Tune properties in-situ Decoh. from 1/f noiseStrong interactions Fast relaxationCouple/control with wires Complex EM design
Strengths Weaknesses
Shared traits of all of these:
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Superconducting QC
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?)
Requirement Status
(after DiVincenzo)
This IS the Hamiltonian of my system“and we really mean it!” (Lehnert, 2003)
Some high fidelity (>90%) readout,not routine and sometimes incompatiblewith best performance
Progress but a LONG way to go!
Naturally strong: learning how to tameSeveral two qubit gates demonstrated
Coupling with photons on wires
Can mass produce qubits Electronic control – a big advantage
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Progress in Superconducting Charge Qubits
Nakamura (NEC)
Charge echo (NEC)
“Quantronium”:sweet spot
(Saclay)
Transmon(Yale)
Similar plots can be made for phase, flux qubits2 1
1 1 12T T T
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Outsmarting Noise: Sweet Spot
sweet spotEn
ergy
Vion et al., Science 296, 886 (2002)
transition freq.1st order insensitive
to gate noise
But T2 still < 500 ns due to second-order noise!
1st coherence strategy: optimize design
Charge (CgVg/2e)
Strong sensitivity of frequency to charge noise
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Ener
gy
EJ/EC = 1 EJ/EC = 25 - 100
“Eliminating” Charge Noise with Better Design
Cooper-pair Box “Transmon”
exponentially suppresses 1/f!
Houck et al., 2008
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Coherence in Transmon Qubit
*2 12 3.0 sT T
1 1.5 sT
Error per gate = 1.2 %
Random benchmarking of 1-qubit opsChow et al. PRL 2009:
Technique from Knill et al. for ions
*01 2 100,000Q T
Similar error rates in phase qubits (UCSB):Lucero et al. PRL 100, 247001 (2007)
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Materials Can Matter…
losses consistent with two-level defect physicsin amorphous dielectrics
Martinis et al., 2005 (UCSB)
Other relaxationmechanisms:
Spontaneous emission?Superconductors?Junctions?Readout circuitry?
Still not clear for most qubits!
Dielectric loss?
phase qubits
2nd coherence strategy: improve materials/fabrication
Progress on origin of 1/f flux noise:
Clarke,McDermott,Ioffe…
quantumregime
, ~ 1kT n is special!
quantum regime
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But High Q May Not Be Impossible!V. Braginsky, IEEE Trans on Magnetics MAG-15, 30 (1979)
Nb films on macroscopic sapphire crystal
Q ~ 109 @ 1 K !
So fundamental limits might be 4-5 orders of magnitude away…
Note: this is not in microfabricated device, and not at single photon level
Qua
lity
fact
or
104
109
T (K)0 5 10 15
105
106
107
108
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Coupling SC Qubits: Use a Circuit Elementa capacitor
Charge qubits: NEC 2003 Phase qubits: UCSB 2006
entangledstates
Con ~ 55%
an inductor
Flux qubits: Delft 2007
tunable element
Flux qubits: Berkeley 2006, NEC 2007
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Josephson-junctionqubits7 GHz in
outtransmissionline “cavity”
Blais et al., Phys. Rev. A (2004)
Qubits Coupled with a Quantum Bus
“Circuit QED”
Expts: Sillanpaa et al., 2007 (Phase qubits / NIST) Majer et al., 2007 (Charge qubits / Yale)
use microwave photons guided on wires!
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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!
• Dozen pulses with sub-ns timing• Per pulse accuracy >> 90%• Many initial calibrations• Many field displacements for W()
Requires:
Shows the beauty of strong coupling + electronic control…
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1 ns resolution
cavity: “entanglement bus,” driver, & detector
transmon qubits
DC - 2 GHz
A Two-Qubit Processor
T = 10 mK
L. DiCarlo et al., cond-mat/0903.2030 (Yale)
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Spectroscopy of Qubits Interacting with Cavity
Qubit-qubit swap interactionMajer et al., Nature (2007)
cavity
left qubit
right qubit
Cavity-qubit interactionVacuum Rabi splittingWallraff et al., Nature (2004)
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Spectroscopy of Qubits Interacting with Cavity
01
Preparation1-qubit rotationsMeasurement
cavity
10
Qubits mostly separatedand non-interacting
due to frequency difference
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Two-Qubit Gate: Turn On Interactions
01
cavity
10
Conditionalphase gate
Use voltage pulse oncontrol lines to push
qubits near a resonance:
A controlled z-z interaction
also ala’ NMR
Adiabatic pulse (30 ns)-> conditional phase gate
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Measuring Two-Qubit States
Joint measurement of both qubits and correlations
using cavity frequency shift
Ground state: 00 Density matrix
leftqubit
rightqubit correlations
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Measuring Two-Qubit States
Apply -pulse to invert state of right qubit
One qubit excited: 01
0001
1011
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Measuring Two-Qubit States
Bell State:
Now apply a c-Phase gate to entangle the qubits
12
00 1
0001
1011
Fidelity: 94%Concurrence: 94%
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Two-Qubit Grover Algorithm
“unknown”unitary
operation:
Challenge: Find the location
of the -1 !!!
10 pulses w/ nanosecond resolution, total 104 ns duration
ORACLE
Classically: 2.25 evaluations QM: 1 evaluation only!
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Grover in action
Begin in ground state:
Grover Step-by-Step
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Grover in action
Create a maximalsuperposition:look everywhere at once!
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A Grover step-by-step movie Grover in action
Apply the “unknown”function, 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 actionGrover 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 actionGrover search in action Grover in action
Final 1-qubit rotations reveal theanswer:
The binary representation of “location 3”!
The correct answer is found
>80% 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 > 107?)
• Cheap waveform generators (16 bits, 10 Gs/sec, $2k/chan?) • Controlled couplings with high on/off ratio (> 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 10’s 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 further1) Design around the decoherence2) 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
• A frequency shift
• Avoided crossing (160 MHz)
Use large on-off ratio of to implement 2-qubit phase gates.
Strauch et al. (2003): proposed use of excited states in phase qubits