Michael J. BiercukQuantum Control LaboratoryCentre for Engineered Quantum

SystemsSchool of Physics, The University of

Sydney

Formerly, NIST Ion Storage Group

Towards programmable quantum simulation at computationally relevant scalesIQsim13

www.physics.usyd.edu.au/~mbiercuk

Outline

• Motivation• 9Be+ crystals in Penning Ion Traps• Engineering tunable coupling in ion

crystals• A path to programmable simulation by

coherent control

Aim: Build a useful quantum simulator where a user may program in a desired interaction to

be simulated.

Problems in condensed matter

All of this physics comes from noninteracting models

Lattice models of interacting electrons

http://large.stanford.edu/courses/2008/ph373/hughes2/images/f1.gif

Frustration: Antiferromagnetic interaction

?

Exotic quantum states• Gapless fermi/bose spin liquids• Gapped spin liquids

Nature 471, 612 (2011), Francis Pratt /ISIS/ SFTC

Potential explanation for High-Tc superconductivity

Candidate materials

Herbertsmithite

Nature 492, 406 (2012)

Quantum simulation

It’s like this…but quantum

Lattice models from the bottom up.

Scaling up Ion-trap Quantum Simulation

Courtesy C. Monroe (UMD), M.G. Blain (Sandia); Amini et al., NJP 12, 033031 (2010).

2.5 mm

Simulation at computationally relevant scales

N>300

The NIST Penning TrapB=4.5 T

c ~ 7.6 MHz, m ~ 20-50 kHzz ~ 600-800 kHz

9Be+

Forthcoming…the Sydney Penning Trap

Toy Ising-type Hamiltonian

Spin-spin interactions Spin rotations

?

Beryllium Ion Qubit

Fiel

d Se

nsiti

veMJB et al,. Nature 458, 996 (2009). MJB et al., Quant. Info. Comp. 9, 920 (2009).

Fluo

resc

ence

Cool

ing

9Be+ at 4.5T

F=1

F=2124 GHz

Repu

mp

Hi-Fi Wave (124 GHz) Coherent Control

MJB et al,. Nature 458, 996 (2009). MJB et al., Quant. Info. Comp. 9, 920 (2009).

Rabi

Osc

illat

ions

Larm

or P

rece

ssio

n

Average Error: 8 ± 110-4

(99.92% Fidelity/Gate)

Motional bus for coupling spins

State-dependent ac stark shift

Spatially varying light field

Nature 422, 412 (2003). Nature 438, 639 (2005).

Harmonic confinement

Transverse COM-Mode

Trap

Axi

s

MJB et al., Nature Nanotechnology 9, 646 (2010); MJB et al., Op. Ex. 19, 10304 (2011)

Phase-coherent Doppler velocimetry via RF tickle

Spin-Motional Entanglement with COM

Sawyer et al., PRL 108, 213003 (2012)

Implementation in the Penning trap

MJB et al., Op. Ex. 19, 10304 (2011), Sawyer et al., PRL 108, 213003 (2012), Britton et al, Nature 484, 489 (2012)

The mean-field limit

http://www.southampton.ac.uk/~fangohr/research/vortex1/subs/subs.html

Measurement: B-induced precession

Nature 484, 489 (2012)

“Tipping angle”, q

Tune coupling by spatial asymmetry

Nature 484, 489 (2012)

Tunable coupling to asymmetric modes gives control over interaction range

Mean-field benchmarking of tunable interaction

Extra

cted

Mea

n Fie

ld

Laser Detuning

N~300

No Free Parameters

Nature 484, 489 (2012)

Ion-dipole

Coulomb

Infinite

Moving beyond the mean field

Increase interaction strength

Predictability breaks down

What have we accomplished so far…

Britton, Sawyer…MJB, Bollinger, Nature 484, 489 (2012).

Hilbert space ~ 2300

Tunable Engineered Spin-

Spin Coupling

What if this functional form

doesn’t give access to physics we care about?

Richness of Physics

PRL 107, 077201 (2011)

Increasing NNN-to-NN interaction strength

Background• Arbitrary simulation proven possible

(a la universal QC)• Decoupling/Recoupling protocols in

NMR• Recent ion-specific protocols

NJP 14, 095024 (2012).

Towards programmable analog simulators

• Only basic resources required– Single-qubit Paulis with individual addressing– Long-range coupling

• Technology independent• Addresses the problem of “programming”

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

Programmable Quantum Simulation

Apply control protocols to modify interactionsQuantum Simulation Program realized in form

of control protocols, their scaling, and their sequencing

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

CONTROL Arbitrary

Error suppression & control…

Spin Echo:Engineering in the time domain

Hahn 1950, NMR

y(t)-1

+1

SU(2) ops can modify effective coupling

time

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

Sum on timesteps

Stroboscopically engineer a new effective spin coupling

Distance dependence revealed by symmetry of control propagator

For multiqubit system, H (P) is periodic in number of timesteps

t

NN

NNN NNNN

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

Pulsed control filters interaction strength

Filte

r Wei

ght:

H(P

)

d

Coupling changes sign!

d

FM

AFM

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

Break evolution into more timesteps…

Build program by combining filters

Combine by sequential application and concatenation

Tuning knobs:– Specific pulse sequence applied– Filter duration (sets “Fourier” coefficient)– Number of timesteps (sets triangle periodicity)– Addition of free-evolution (can “decouple” terms)– Addition of p/2 pulses to shift basis (X, Y, Z)

CONTROL Arbitrary

Universal couplings achievable

“Universal” filter space

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

Non-native adiabatic evolutions can also be engineered

Adiabatic evolutions

Hayes, Flammia, MJB, arXiv:1309.6736 (2013).

Approach is resource efficient• Concatenation scaling (Universal filter)• Runtime scaling

• Calculating control is a problem in linear programming

ArbitraryHayes, Flammia, MJB, arXiv:1309.6736 (2013).

Interqubit distance

Wor

st-c

ase

coup

ling

stre

ngth

Testing in a 1D Paul trap

Yb+ Ion strings for Quantum Simulation

Outlook...programming ion-based quantum simulators

Acknowledgements

http://tf.nist.gov/ion

Ion Storage Group

Joe Britton, Brian Sawyer,Hermann Uys, Aaron

VanDevenderChristian Ospelkaus, John

Bollinger,David Wineland

Quantum Control Lab

David Hayes, Steve Flammia,Alex Soare, MC Jarratt,Kale Johnson, James

McLoughlin, Karsten Pyka

Acknowledgements & Collaborators

Lorenza ViolaKaveh Khodjasteh

Hendrik BluhmAmir Yacoby

Chingiz Kabytaev

Ken Brown

PhD opportunities and postdoctoral fellowships available at Sydney

michael.biercuk@sydney.edu.au