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XYZ 11/7/2011

Realistic Trapped-Ion Quantum Processing for

Enhanced Computation, Simulation, and Sensing: Addressing Challenges to Scaling Up Processor Speed, Size, and Fidelity

John Chiaverini

This work was sponsored by the Department of the Air Force under contract number FA8721-05-C-0002. Opinions, interpretations,

conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government.

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Quantum computing: small or different?

• Atoms per bit approaching 1 (~2020?)

– Corollary of Moore’s law gives amazingly reliable exponential decrease in size of bits in a computer

– We will need to do something different with conventional computers when we get to this level

– This is still just making a classical bit, however, but using 1 atom instead of many

R. W. Keyes IBM J. R&D 32 (1988)

CMOS

Pentium IV

Intel Core II

100

2020

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XYZ 11/7/2011

Quantum computing: small or different?

• Quantum computing, ~1 atom (etc.) per qubit*

– Reason for this is that we need a coherent quantum system capable of

Superposition Entanglement with other

quantum systems

– Quantum computers do not just do “classical computing, but better”

– QC works in a different way, solving some problems exponentially faster than possible classically

– Requirements for QC are not the same as those for Moore’s law continuation

*It will actually be many atoms per (logical) qubit to really work

102

1

10012

1

Michael Nielsen:

“…[Q]uantum computers cannot be

explained in simple concrete terms; if

they could be, quantum computers

could be directly simulated on

conventional computers, and

quantum computing would offer no

advantage over such computers.”

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Overview

• Trapped ions for quantum processing – Most advanced modality for QIP – Holding tight to a single atom, and the apparatus involved – High-fidelity quantum operations

• Trapped ions v. neutral atoms for quantum applications

• Current challenges for scaling to large-scale processors – Systems need to be smaller to be faster – Anomalous heating of motional modes – Arrays of individual trapped ions – Speeding up high-fidelity operations

• Methods to address these challenges – Low-temperature operation – Trap chip surface quality – Enhanced light collection – RF and MW quantum logic gates

• Outlook

Will be interspersed

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Current state of the art ion QIP demos

• Entanglement of 14 qubits

• Programmable two-qubit quantum processor

• Repetitive quantum error correction

• Quantum simulation of interacting spin systems

• yN force detection

Hanneke et al. Nature Phys. (2009)

Biercuk et al. Nature Nano. (2010)

Islam et al. Nature Comm. (2011)

Schindler et al. Science (2011)

Monz et al. Phys. Rev. Lett. (2011)

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XYZ 11/7/2011

Ion quantum-logic clock

• “…Metrology at the 17th decimal place”

• Al+ ion is controlled and read out via quantum logic operations on an auxiliary Be+ ion

• Currently, inaccuracy smaller than 10-17 (comparing 2 Al+ clocks in 2010)

• Also used to measure grav. redshift due to height difference of only 33 cm

Chou et al. Science (2010)

Rosenband et al. Science (2008)

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Trapping and manipulating individual atomic ions

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Controllable quantum systems

• Internal quantum states have long lifetimes, coherence

• Quantum gates performed by driving transitions

• Ions coupled through Coulomb interaction

• Share quantized vibration modes in trap

• 2-qubit gates performed by inducing internal state-dependent motion

Ion Paul trap

n=0

n=1

n=2

Ion vibrational mode

Dn |0

|1

t ~ 0.5 to >10 s

t ~ 5 ns

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XYZ 11/7/2011

Typical setup in the real world

• Current scale is “small-room” sized (1-2 optical tables)

• Most experiments are single-to-few individually addressable ions

• Classical control is typically a few computers plus a few racks of electronics

• Significant room for integration

Lasers

Classical control

Vacuum

Detectors

Feedthroughs

“dc” m-wave, rf

AOMs/

switches

Bulk optics

Fibers

Windows

Laser

stabilization

Ion

Source Trap

Pump

Resonator Trap

rf

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XYZ 11/7/2011

Keeping ions around

• Vacuum requirements – Ion lifetime typically limited by

background gas collisions – Room temperature UHV

systems – Use only UHV-compatible

materials – After ~1wk bakeout @200-

300C, get to ~10-10 T or less – This can give lifetimes of

several hours to several days – Equipment

St. steel flanges with knife edges

Deformable copper gaskets Bake-able valves or pinch-offs Ion and evaporable getter

pumps Representative UHV system

(MIT LL)

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XYZ 11/7/2011

Systems can be smaller

• Maybe Even portable!

• Similarly to smaller neutral atoms systems, not a lot is required for basic functionality

– Ion pump – Source of atoms – Optical access for lasers and light collection – Electrical feed-throughs – Magnetic field coils

Cold Quanta, Inc.

• Commercial system for

producing Rb MOT

• ~ 30 cm in longest dimension

Caveat: Does not include lasers!

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XYZ 11/7/2011

Going cold

• Cryogenic traps – Helps the vacuum

Cryopumping: most gases plate out, rapidly producing low pressures w/o a bake

Larger range of materials can be used – Helps with anomalous motional state

heating (more later)

• He bath cryostats – Trap sits in vacuum space in contact with

LHe bath, 4.2 K (or below if pumped) – High cooling power, relatively quiet

(acoustically and vibrationally) – LHe, and usually LN2 also, must be

transferred every couple of days

• Closed-cycle cryocoolers – Trap attached to cold plate cooled by He

gas cooled in heat-engine cycle (e.g. Gifford-McMahon or Pulse-tube)

– Can operate continuously, no liquid cryogens

– Vibration, acoustic noise can be appreciable

– Cooling power typically lower than bath cryostats

MIT campus group

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XYZ 11/7/2011

Holding onto ions

• RF traps – Ponderomotive trapping with

rapidly varying quadrupole electric field

– Linear traps use a static electric field in one dimension

• Trapping fields – Need high amplitude RF

voltage (~100V at 10s of MHz) – Static voltage usually a few

volts

• Trap frequencies (linear trap) – Typically several MHz radially – A few MHz axially – Ions line up along RF null line RF RF

Positive ions

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Surface electrode traps

• Unfold the quadrupole electrodes onto a surface

• RF null above the surface

• Depth/trap frequencies smaller for same applied RF voltage

• Fabrication greatly simplified

• Integration more straightforward

JC et al., QIC 5, 419 (2005)

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Surface electrode traps in practice

• SETs are being used in many labs

• SETs are the primary (but not sole) format for integration

• Less shielding than standard designs

First NIST SETs

Oxford MIT Campus Seidelin, JC, et al. PRL ‘06

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Atoms to ions

• Direct production from hot atomic beam

• Atoms are typically several 100’s to 1000 deg C

• Trap electrodes must be shielded

• Ablation also used

• Photo-ionization – Typically two-step

process – Requires 1-2 lasers, or

laser + LED, or pulsed laser, etc.

– Ion-species dependent – Can provide isotope

selectivity

DC current

S

P Neutral atom

structure

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XYZ 11/7/2011

Getting light to the ions

• Bulk optics – Usual setup has free-space

light for frequency stabilization, switching, frequency shifting, etc.

– Beams in air with long lever arms between mirrors leads to acoustic sensitivity for beam pointing

– Also index of refraction effects

• Fibers – Bring fibers to vacuum

system – Bring fibers into vacuum

system to trap – May need fiber noise

cancellation techniques if narrow linewidth light

• Better idea might be integration of sources and waveguides on-chip Kim et al. (MIT campus) arXiv:1103.5256

Typical optics set up (MIT LL)

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Switching of beams

• Shutters are typically too slow (ms), but are used when total extinction required

• Typically done with acousto-optic modulators (AOMs) – Acoustic wave in crystal causes deflection of light beam – Can be switched in ~100 ns or less – Requires relatively high RF power (Watts at 100’s of MHz)

• Thermal management problems – Diffraction efficiency is duty-cycle dependent – Switching latency variations if beam pointing changes – Light scatter even when “off” can lead to decoherence (follow

AOM with shutter, but slow) – Water cooling?

AOM heats up

AOM cools down

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State readout

• Look at photons coming from ion in some detection time

– Set threshold – Ions typically put out >10

MHz rate of photons – These are not all collected

(see following)

• Detectors – CCDs for imaging and array

readout Good QE, but slow Will need larger arrays that

are faster for larger systems

– PMTs for photon counting Very sensitive Somewhat low efficiencies

– APDs? VLPCs? SNSPDs?

Oxford group

Maryland group

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XYZ 11/7/2011

High-fidelity quantum state manipulation

• Required error rates – Threshold in the

neighborhood of 10-4, maybe

– Should be much lower than this for reasonable resource requirements

• Achieved error rates – Ions are ahead of the

pack – Still a long way to go,

however – Also, somewhat slow

(particularly measurement)

• Algorithmic figure of merit 105-106

– Other modalities <104 or so

Operation Error Time demonstrated for high-fidelity

Preparation ~1x10-4 ~2 us

Single-qubit operation (microwaves)

2x10-5 10 us

Two-qubit op. 7x10-3 50 us

Measurement 1x10-4 150 us (avg)

Demonstrated coherence time: >10 s

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Cold Neutrals v. Trapped Ions

• Similarities – All atoms/ions are identical – Laser cooling used in both cases to prepare and

readout quantum info. – Both can be trapped “on-chip” – UHV generally required

• Differences – Trapping provided via RF v. laser/magnetic trapping

Strong trapping much easier in ions Only one laser beam needed for cooling bound particle No large magnetic coils needed RF voltage required Lower temperatures in atoms

– Charged particles Strong interaction between ions Lower numbers (Coulomb repulsion)

– Lasers a bit toward blue and UV for ions, technologically a bit harder

– Lifetimes nominally similar, but ions demonstrated somewhat longer due to better trapping

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+Ze +(Z+1)e

Lasers: wavelengths

• Singly-ionized hydrogenlike species:

– Unscreened (or not-quite-as-well screened) extra proton

– Makes energy somewhat higher than in typical neutral alkalis that are used for ultracold atom work

• For D1 & D2 lines, near-IR goes to blue or UV

• Blu-ray wavelength is close, but not enough screw-ups left

– Early mistakes made ion trappers happy

-(Z-1)e

-1e

-(Z-1)e

-1e

Alkali atom Alkali-earth ion

Lybarger, PhD thesis (2009)

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XYZ 11/7/2011

Pushing toward useful, large-scale devices

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XYZ 11/7/2011

Smaller, Faster, but Probably Not Cheaper

• Multi-qubit operation speed limited to motional frequency

• Frequency ~ 1/d2

• So shrink the trap! – Surface traps can scale right down to

micron scale, leading to GHz or higher frequencies

– Lithography still won’t be that hard, and voltages go down

• But there is noise – Johnson noise of the electrodes is not

appreciable – However, anomalous heating has been

seen in all ion trap experiments – Heating scales as ~ 1/d4 (!) – This heating rate leads directly to error

in multi-qubit quantum logic gates – Not a major obstacle now, but… – It is the biggest fundamental obstacle to

large-scale QIP with ions Epstein et al. PRA 76, 033411 (2007)

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XYZ 11/7/2011

What is it?

• Fluctuating potentials from insulating patches

– Patches are smaller in size than distance from ion to electrode

– Charge moves around on patches – Could be insulating or not-as-conductive

regions: oxides, dirt, fabrication detritus, etc.

• Dipoles of adsorbed atoms – Less than a monolayer of adsorbates can

form reasonable-sized dipole moments – These can fluctuate leading to noise – With multiple levels (i.e. more than 2-level

systems) can reproduce empirical data somewhat

• Varies quite a bit with preparation, but not clear yet

– Presence of atoms from hot vapor (used to load ions) seems to be bad

– Inconsistent results from varying electrode material and preparation

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XYZ 11/7/2011

Attacking Anomalous Heating

• Cooling electrodes seems to help

– Orders of magnitude reduction in heating rates

– Thermal activation of bound charges

– Superconductors not an improvement on cold metal

Heating is due to surface effects, not bulk

• There is lots of garbage on the surface

– Leftovers from fab – Oxides – Metal atoms from vapor

Deslauriers et al. PRL ’06

~5K points from MIT

Campus group

Surface oxides, organic

contaminants, metal from atomic

vapor used for loading

(Supposedly) ideal electrode metal

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XYZ 11/7/2011

In-situ Surface Preparation

• Surface oxides, fabrication byproducts, and adsorbates are present

• Surface cleaning in vacuum at low temperature

– Develop ion milling capability to remove surface contaminates

– Trap ions and measure heating rates in just-cleaned trap at low temperature

• NIST, LL groups planning on exploring this

– NIST: room temperature, but with many analysis tools

– LL: low temperature

Ion milling

Surface contaminants

OCI Vacuum

Incorporate into

UHV system

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XYZ 11/7/2011

Speeding Up Readout

• Current ion readout is very good, but somewhat slow

– 99.99% accuracy in 150 us

– Can be even a bit better and slower, or worse and faster

• The big bottleneck is light collection

– Atom can emit at >10 MHz, but into 4p str

– Only a few % is collected

– Detectors are also not perfect

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XYZ 11/7/2011

Enhanced collection technologies

• Coupling to photons (and faster measurement) requires better collection

• Schemes – Fibers nearby – Microlenses – Macroscopic reflectors – Microscopic reflectors – Mirrors on the trap

substrate

• Also a bit to be gained by increasing detector efficiency

Shu et al. PRA 81, 042321 (2010)

VanDevender et al.

PRL 105, 023001

(2010)

Herskind et al.

arXiv:1011.5259

(2010)

Noek et al. Opt.

Lett. 35, 2460

(2010)

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Fresnel Reflector Integration

• Parabolic Fresnel optics – Can be integrated with

surface trap – Some zones identified

with RF to bring about trapping

– Gray tone lithography for definition of zones

– All metal, won’t charge like refractive optics

MIT LL, U. of Washington

Areva Solar

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Low-Fi?

• Gate fidelity must be improved to “fault-tolerant” levels

– 10-6 to 10-4 error per gate is a ballpark figure

– In terms of resources, better to have even lower error

• Biggest technical errors during quantum logic gates: Laser intensity fluctuations

– Gate performance requires pulse area to be constant

– Intensity noise from several sources Frequency doubling process Beam pointing instability Thermal effects in AOMs for switching

• A fundamental source comes along with fast laser operations

– Spontaneous emission during gate – Incoherence due to decay from virtual

atomic level, rather than coherent absorption and re-emission

– Can be reduced with bigger detuning, but need more power

S1/2

P1/2

P3/2

Virtually excited levels…

Lead to decohering

scattering process

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Higher Fidelity Operations

• Microwaves for hyperfine qubit rotations

– No spontaneous emission

– Much more stable in power and frequency than optical sources

– Acoustic-sensitive lock not required

– Easy to switch

• Some drawbacks to MW/RF radiation

– Individual addressing? – Generally no ability to

apply a force to ions (gradient comes for free with optical field)

• Solution: Create a gradient on chip!

S1/2

P1/2

P3/2

RF or MW

~20 nm

lopt

lRF

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Near-field RF and Microwaves

• Gradient coils co-located with trapping structure (possibly in array)

• More robust due to better RF phase coherence

• More scalable due to lower error rate

• Also, ions don’t necessarily need ground state cooling

JC and Lybarger, PRA 77, 022324 (2008)

Ospelkaus et al., PRL 101, 090502 (2008)

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On-Chip Generated Fields

• Integrate microwave waveguide among trap electrodes

• Quantum logic gates without lasers

– Single qubit gates in 19 ms – Includes sidebands for

cooling – Two qubit gates as well

• Considerations – Must make high gradient in B,

with low overall B – Trap frequency fluctuations – Power consumption can be

large – Crosstalk will require

compensating fields with multiple zones

Ospelkaus et al. (NIST) arXiv:1104.3573

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XYZ 11/7/2011

Scaling the whole thing up

• Need many ions, all somewhat addressable

• A few ideas – Movable ions

throughout a 1+e dimensional maze-like structure with branches

– 2D array of individually trapped, mostly static, ions

– Medium-scale 1D arrays joined together via photonic interconnects

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Arrays of traps

• 1D maze-like traps

• Electrostatic movement

• Based on Kielpinski, Monroe, and Wineland suggestion (QCCD)

• Move ions to/from processing zones

• Store in other zones

Leibfried (NIST)

Blakestad et al. (NIST)

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Surface trap arrays

• To date, similar to arrays of 1D maze structures as in more traditional traps

• Junctions are key difficulty

Sandia

NIST

GTRI

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Reconfigurable arrays

• 2D arrays without junctions

• Reconfigurable RF – Can move a ions while

always at RF null – Flexible layout – Can bring ions closer than

lattice spacing for gates

• Considerations – More RF signal overhead – Many channels, depending

on pixelation

Kumph et al. (Innsbruck) arXiv:1103.5428

JC and Lybarger, 2009

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Leave the ions alone

• Photonic interconnects

• Each node has a few qubits

• Entanglement can be generated between nodes

• Gates can be teleported after entanglement is set up

• Recent results 12 minutes to do one entangling op. – Strongly limited by collection efficiency

• So far, getting strong coupling with photons is the big challenge

Chris Monroe, Jungsang Kim, et al.

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Booting up

• For large-scale QIP (QC, simulation, or high SNR quantum sensing), large arrays will be needed

• Ion loss rates at UHV pressures can be appreciable with many 1000’s of ions

• Typical ion trap loading rates are 1/s

– This is due to trapping low-velocity tail of 400 – 1000 C thermal distribution

– Faster loading is required

• Use a pre-cooled source – Lower velocities – Higher efficiencies

Typical Loading

Required Loading

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Start with cold atoms

• Start with cold neutral atom source

• Avoids contamination of trap surface

• Extra level of isotope selectivity

• More efficient trapping

• Much faster loading rates possible – Ions from MOT: faster by orders

of magnitude (Vuletic/Chuang)

• Need an additional laser for MOT

e-

atom

ion

MOT

ion chip

Collect atoms in

MOT

Push atom(s)

to trap region

with resonant

beam

Photoionize atom

above surface trap

Magneto-Optical Trap SET for ions

MIT LL

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XYZ 11/7/2011

• Sr MOT achieved – Cooled and trapped 105 to

106 atoms – T ~ 7 mK – Atoms successfully

pushed to trap (60 mm away)

– Next, ionize them there

MOT atoms

Untrapped

atom

fluorescence

MOT achieved, atoms pushed

w0 ~ 2 mm

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Outlook: One medium-term vision

• Array loaded from pre-cooled neutral source

– Either directly or via a holding zone

• Logic using MW – Array has interspersed CPWG

for signal delivery – Ions moved as necessary with

reconfigurable electrodes

• Ions read out with integrated collection

– Either relay optics or built-in photodetection

• For simulation and sensing, most movement can be eliminated, many operations done in parallel

• Substrate may need to be cleaned in vacuum, cryogenics may be required

• There are many routes, however!

Pre-cooled

neutrals ionized

to load trap array

Embedded MW

electrodes used

for gates, ions

moved as

necessary

Integrated optics

collect light from

ion for

measurement

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XYZ 11/7/2011

END

• MIT Lincoln Lab team – Jeremy Sage – Andrew (Jamie) Kerman – JC

• Collaborators – Warren Lybarger (Los

Alamos National Lab, Aerospace Corp.)

– Harvard

• Funding – Lincoln Lab internal funds

for capability development