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Towards programmable quantum simulation at computationally relevant scales IQsim13
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Transcript of Towards programmable quantum simulation at computationally relevant scales IQsim13
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