Quantum Computing with Superconducting Circuits Rob Schoelkopf Yale Applied Physics QIS Workshop,...
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Transcript of Quantum Computing with Superconducting Circuits Rob Schoelkopf Yale Applied Physics QIS Workshop,...
Quantum Computing with Superconducting Circuits
Rob Schoelkopf
Yale Applied Physics
QIS Workshop, Virginia April 23, 2009
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!
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?
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:
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
Progress in Superconducting Charge Qubits
Nakamura (NEC)
Charge echo (NEC)
“Quantronium”:sweet spot
(Saclay)
Transmon(Yale)
Similar plots can be made for phase, flux qubits
2 1
1 1 1
2T T T
Outsmarting Noise: Sweet Spot
sweet spotE
nerg
y
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
En
erg
y
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
Coherence in Transmon Qubit
*2 12 3.0 sT T
1 1.5 sT
Error per gate = 1.2 %
Random benchmarking of 1-qubit ops
Chow 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)
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
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
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
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!
Recent Highlights: Arbitrary States of Oscillator
Hofheinz et al., Nature 2008 (UCSB)
Wigner Functions of Complex Photon States
Thy. Expt.
Hofheinz et al., Nature in press 2009 (UCSB)
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…
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)
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)
Spectroscopy of Qubits Interacting with Cavity
01
Preparation1-qubit rotationsMeasurement
cavity
10
Qubits mostly separatedand non-interacting
due to frequency difference
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
Measuring Two-Qubit States
Joint measurement of both qubits and correlations
using cavity frequency shift
Ground state: 00 Density matrix
leftqubit
rightqubit correlations
Measuring Two-Qubit States
Apply -pulse to invert state of right qubit
One qubit excited: 01
0001
1011
Measuring Two-Qubit States
Bell State:
Now apply a c-Phase gate to entangle the qubits
1
2
00 1
0001
1011
Fidelity: 94%Concurrence: 94%
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!
Grover in action
Begin in ground state:
Grover Step-by-Step
Grover in action
Create a maximalsuperposition:look everywhere at once!
A Grover step-by-step movie Grover in action
Apply the “unknown”function, and mark the solution
Grover in action
Some more 1-qubitrotations…
Now we arrive in one of the four
Bell states
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!
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.
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…
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…
Two-Excitation Manifold of System
“Qubits” and cavity both have multiple levels…
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