999999-1 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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999999-1
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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XYZ 11/7/2011
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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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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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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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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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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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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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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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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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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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