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