High-fidelity spatial and polarization addressing of Ca-43 qubits using near-field microwave control

8.4 MB·

by  D. P. L. Aude Craik

High-fidelity spatial and polarization addressing of 43Ca+ qubits using
near-field microwave control
D. P. L. Aude Craik, N. M. Linke, M. A. Sepiol, T. P. Harty, J. F. Goodwin,
C. J. Ballance, D. N. Stacey, A. M. Steane, D. M. Lucas, and D. T. C. Allcock∗
Clarendon Laboratory, Department of Physics,
University of Oxford, Parks Road, Oxford, OX1 3PU, UK
Individualaddressingofqubitsisessentialforscalablequantumcomputation. Spatialaddressing
6 allows unlimited numbers of qubits to share the same frequency, whilst enabling arbitrary parallel
1 operations. We demonstrate addressing of long-lived 43Ca+ “atomic clock” qubits held in separate
0 zones (960µm apart) of a microfabricated surface trap with integrated microwave electrodes. Such
2 zones could form part of a “quantum CCD” architecture for a large-scale quantum information
processor. By coherently cancelling the microwave field in one zone we measure a ratio of Rabi
c
e frequencies between addressed and non-addressed qubits of up to 1400, from which we calculate a
D spin-flip probability on the qubit transition of the non-addressed ion of 1.3×10−6. Off-resonant
excitationthenbecomesthedominanterrorprocess,ataround5×10−3. Itcanbepreventedeither

4 byworkingathighermagneticfield,orbypolarizationcontrolofthemicrowavefield. Weimplement
1 polarization control with error 2×10−5, which would suffice to suppress off-resonant excitation to
the ∼ 10−9 level if combined with spatial addressing. Such polarization control could also enable

] fast microwave operations.
h
p
-
t The prospect of a quantum computer (QC) transitions, and cryogenically-cooled systems
n
that can solve classically intractable problems such as superconducting circuits [7, 8], dia-
a
u andmakepossiblethesimulationandengineer- mond/silicon defects [9, 10], and semiconduc-
q ing of quantum systems at the atomic level has tor quantum dots [11]. In several of these sys-
[ driven research into many different candidate tems, microwave-driven single-qubit rotations

2 systems [1]. The feasibility of large-scale quan- have been demonstrated with error rates well
v tum computation depends both on our ability belowthe1%level[7,11–14]. Microwave-driven
6 to scale-up prototype systems to parallelized two-qubit quantum logic gates with error rates
9
multi-qubit architectures and to perform qubit slightly below 1% have been achieved in su-
6
operations with error rates that are low enough perconducting circuits [7] and, very recently,
2
0 to allow for the implementation of quantum er- trapped-ion qubits [15]. A critical issue for all
. ror correction protocols without the need for a thesetechnologiesisthesuppressionofcrosstalk
1
prohibitively large number of additional error- between microwave signals targeted at specific
0
6 correcting qubits per logic qubit. Recent work qubits; even if the qubits operate at differ-
1 using surface code error correction places the entfrequencies,thelimitedbandwidthavailable
: errorthresholdforfault-tolerantquantumcom- meansthatfrequency-sharingwillultimatelybe
v
i putation as high as ≈ 1%, but error rates sub- necessary.
X
stantially below this are necessary for realistic
r overheads [2–4]. Trapped atomic ions are one of the most
a
promising QC platforms [16], especially when
Almost all of the present QC technolo- hyperfine ground-level “atomic clock” qubits
gies in which two-qubit quantum logic gates areused. Thesearefreefromspontaneousemis-
have been demonstrated are based on qubits sionerrors,offerverylongcoherencetimes(lim-
which operate in the microwave frequency do- ited only by technical considerations) [14, 17]
main, for example laser-cooled trapped ions [5] with high-fidelity state preparation and read-
and neutral atoms [6] based on hyperfine out [14, 18], and can be directly manipulated
2
by microwave radiation [15, 19–22] as well as eral such electrodes can produce field differen-
by lasers [23–25]. Prospects for scalability of tials at even smaller length scales.
trapped-ionmicrowavequbitswereimprovedby Warring et al. [32] demonstrated near-field
the development of microfabricated “chip” ion addressing by selectively moving one of two
traps with integrated microwave electrodes to ions in a single-zone trap on and off the null
provide all-electronic control of coherent qubit of a large-gradient quadrupole microwave field
operations [21, 26, 27]. Two important chal- (also used to perform two-qubit microwave
lenges remain: performing microwave-driven gates [21]), which was generated by feeding
two-qubit gates with sufficiently high fidelity, high-powermicrowavesignalsintothetrapelec-
and demonstrating a scalable method of indi- trodes. That scheme achieved crosstalk errors
vidually addressing ions using microwaves with of order 10−3; it would require the addition of
sub-threshold crosstalk; we describe work to- further microwave nulling electrodes, similar to
wards the former goal in [15], while the lat- those used in this work, to enable parallel ad-
ter is the subject of this paper. These tech- dressing in a 2D array of traps.
niques could be combined with recent work on
In this paper, we present results from a
large multi-zone trap arrays [37], shuttling of
first experiment to implement the scheme we
ionsbetweenzones[36,39,43],andsympathetic
proposed in [33] for microwave addressing of
cooling using auxiliary ion species [40, 41], to
field-independent trapped-ion qubits. The
realize a “quantum CCD” architecture for a
scheme is a microwave-driven implementation
microwave-based quantum processor.
of the memory section of the quantum charge-
Both far-field and near-field microwaves have coupled device (QCCD) architecture (proposed
previously been used to address trapped ions in [34] and further discussed in [35]) and in-
individually. In the far field, the long wave- volves storing single ions in separate trap zones
length means that differential field amplitudes where individually-addressed single-qubit rota-
cannot be established between neighbour ions tionsareappliedinparallelusinglow-powermi-
and addressing is instead done in frequency crowaves. In this architecture, two-qubit gates
space, using a static magnetic field gradient are performed by shuttling two or more ions to
toZeeman-shiftdifferentiallytheresonancefre- entanglement zones where they are held in the
quenciesofindividualions[29–31]. Thisscheme same trap so that Coulomb-mediated gates can
has achieved crosstalk errors of order 10−5 and be performed via a shared motional-mode. Al-
is suited to a 1D linear array of magnetic-field- though not implemented in this work, the ion
dependent qubits. shuttlingrequiredforthisschemehasbeenper-
Spatial addressing, which allows the use formed in several surface-electrode traps with
of noise-immune magnetic-field-independent minimal motional heating [38, 43]. Here, we
“atomic clock” qubits, and 2D or 3D arrays of focus on implementing the large microwave
ions, is made possible if near-field microwaves fielddifferentialsneededtoperformmicrowave-
are used since, in the near field of current- drivenspatialaddressingofqubitsinneighbour
carrying waveguides, the field decay length- zones.
scales depend on the geometry of the waveg- The demonstration experiments described
uides and of the surrounding structures, rather here are performed in a prototype microfabri-
than on the wavelength of the radiation. It cated surface-electrode dual-zone ion trap de-
is feasible, with a single electrode of width w, signed to provide arbitrary phase, amplitude
to generate differential field amplitudes that and polarization control of the microwave field
can be used to address ions spaced by a few at each trap zone. Fabricated in Oxford clean-
w (provided induced return currents are care- room facilities using methods similar to those
fully routed), while interfering fields from sev- described in [28, 33], the ion trap used in this
3
a) b)
43Ca+ 4P
m 3/2
854 n
4P
1/2
3D
5/2 866 nm m 3 nm
8 7 4 3 3D3/2 7 n 39
-1 0 39
F = 3 +1
RF A B Hz |↑ σ+
RF G π 4S
2 σ- 1/2
6 5 2 1 3. |↓
F = 4 +1
0
-1
MF
1mm
FIG.1. Thesurfaceiontrapand43Ca+ transitions. (a)Top: iontrapchipmountedonaceramicpingrid
array (CPGA). Square gold-chip capacitors seen on the edge of the CPGA are used on DC electrodes (to
shortanymicrowavepick-uptoground)andonmicrowaveelectrodes(toallowDCvoltagestobeappliedto
thesameelectrodes). Bottom: magnifiedviewofthecentreofthedeviceshowingtheseparatetrapzonesA
andB.Theeightmicrowaveelectrodes(numbered)feature‘T’-shapedslotsaroundwhichmicrowavecurrent
flows. The axial electrodes used for the Paul trap radio-frequency (RF) confinement are indicated. A split
centre DC electrode is usedto control the orientation ofthe radial trapaxes [28]. (b) 43Ca+ energy levels,
showing the four optical transitions used for laser cooling, and for qubit state preparation and readout.
The inset shows relevant states within the ground level hyperfine structure, with the 3.2GHz π polarized
qubit transition highlighted (green). σ+ and σ− polarized transitions out of the qubit states used in the
polarization-controlexperimentarealsoindicated(redandblue). ZeemansplittingsbetweenadjacentM
F
states are ≈0.98MHz at B =2.8G.
0
work is a gold on fused-silica surface-electrode scheme could be scaled up to large arrays of
chip (fig. 1a). The zone spacing of 960µm (≈9 trap zones, each of which could be addressed
ion-electrode distances) was chosen to facilitate independently and in parallel. Further details
thegenerationoflargezone-to-zonemicrowave- relatingtotrapdesign,fabricationandthescal-
field differentials, but making it smaller than abilityoftheaddressingschemecanbefoundin
a few ion-electrode distances would also hin- [33, 42].
der our ability to easily generate the electric
Using the Doppler recool method [28], we re-
potentials required for inter-zone splitting and
cently measured an axial-mode heating rate for
shuttling,shouldwechoosetoimplementthem.
an ion trapped in between zones A and B of
The trap features two microwave addressing 105phonons/s, for an axial trap frequency of
zones (denoted A and B), each with four inte-
0.5MHz.
grated microwave control electrodes, which can
We use the transition at frequency f =
be used to drive coherent single-qubit opera-
3.226GHz between the |↓(cid:105) = 4S4,0 (where the
tions on an ion trapped 110µm from the chip 1/2
superscript in the atomic term denotes the
surface. Crosstalk fields in neighbouring zones
F, M quantum numbers of the level) and
are nulled by generating cancelling fields using F
|↑(cid:105) = 4S3,0 hyperfine ground-state levels of
the microwave electrodes in those zones. The 1/2
43Ca+ as our qubit transition (fig. 1b). At
4
low static fields (here, B = 2.8G), this tran- Rabi flops on an ion trapped in that zone. A
0
sition is robust to magnetic field fluctuations second electrode located in the neighbouring
(df/dB = 6.8Hz/mG; ambient lab field fluc- “nulledzone”isusedtonullthemicrowavefield
0
tuations are of order 1mG). For increased co- along the spatial direction that couples to the
herence times, intermediate-field clock qubits qubit transition in that zone. We choose to
can also be used (for example, 4S4,0 ↔ 4S3,+1 use electrodes 1 and 8 because these produce
1/2 1/2
at B = 146G [14], or 4S4,+1 ↔ 4S3,+1 at the largest single-electrode Rabi frequency ra-
0 1/2 1/2
B = 288G). We prepare |↓(cid:105) using a 397nm tios (r = 3.6 and r = 2.9, see table I). The
0 1 8
π-polarizedbeamwith3.2GHzsidebandstoop- nulling is achieved by driving Rabi flops on the
tically pump on the 4S3 ,4S4 ↔4P4 transi- qubit transition, and minimizing the observed
1/2 1/2 1/2
tions(theselectionrulethatforbidsM =0→ Rabi frequency as a function of the relative
F
M(cid:48) = 0 when ∆F = 0 causes population to phase and amplitude of the microwave signals
F
buildupinthe|↓(cid:105)state). Readoutisperformed fed to the two electrodes (fig. 2c). With nulling
by first using a σ+ circularly-polarized 393nm optimized, we then measure the qubit Rabi fre-
beam to optically pump population from |↓(cid:105) to quencies in both the driven and nulled zones,
the metastable 3D “shelf” state via 4P5 . without further adjustment of the phase and
5/2 3/2
Thestateisthenreadoutusingthe397nmand amplitude. We achieve a Rabi frequency ra-
866nm Doppler cooling lasers to look for fluo- tio between nulled and driven zones of R =
A
rescenceonthe4S ↔4P 397nmtransition Ωnulled = 1.2(1) × 10−3 when zone A is the
1/2 1/2 Ωdriven
(thepopulationtransferredfrom|↓(cid:105)totheshelf nulled zone (fig. 2a), or R = 7.2(3) × 10−4
B
willnotfluoresce,whilstanypopulationremain- when zone B is the nulled zone (fig. 2b). Fol-
ingin4S will). Thispreparationandreadout lowing [32], we quantify the addressing error
1/2
scheme, chosen here for its technical simplicity, by the probability of exciting a spin-flip on the
achieves ≈90% net state preparation and mea- qubit transition of the neighbour ion when we
surement (SPAM) fidelity. If desired, this can drive a π-pulse (spin-flip) on the addressed ion.
bestraightforwardlyincreasedto>∼99.8%using With this definition, these ratios imply an ad-
anextralaserat850nm(torepumppopulation dressing error (cid:15) = π2R2 = 3.4(7)×10−6 and
A 4 A
from 3D to 4P ) and microwave pulses, as (cid:15) =1.27(7)×10−6 for zone A nulled and zone
3/2 3/2 B
we implemented in [14, 18]. B nulled respectively.
Single-qubit rotations are achieved by apply-
However, we note that two additional er-
ing3.2GHzsignalstotheintegratedmicrowave
ror sources arise in these experiments because
trap electrodes. Consider driving a single mi-
we did not null the σ components of the mi-
crowave electrode i, with all other electrodes
crowavepolarization,whichcoupletospectator
50Ohm terminated. We define Ω to be the
near transitions out of the qubit states: (i) a non-
Rabi frequency measured on the qubit transi-
zeroprobabilityofoff-resonantexcitationtothe
tion when the ion is trapped in the zone where
neighbouringM =±1statesinthe4S man-
F 1/2
theelectrodeissituatedandΩ tobethatmea-
far ifold (fig. 1b); and (ii) an AC Zeeman shift on
sured when the ion is trapped instead in the
thequbittransition. WealsomeasuredtheRabi
neighbour zone. Thus ri = ΩΩnear is the Rabi frequencies of σ transitions and, from these, we
far
frequencyratioproducedbetweentrapzonesby
canestimatetheorderofmagnitudeofbother-
a single microwave electrode i. Measured val-
rors. For the conditions of the present exper-
ues for r for all eight microwave electrodes are
i iments, the off-resonant excitation error (i) is
given in table I.
more significant, causing excitation out of the
To demonstrate spatial addressing, we use qubitmanifoldwithprobabilityestimatedtobe
a single electrode in the zone where we wish between0.6×10−3 and5×10−3 (dependingon
to address qubits (the “driven zone”) to drive whether the σ field components from each elec-
5
a) 8 b) 8
A B A B
zoneyAynulled zoneyAydriven
zoneyBydriven B0 zoneyBynulled B0
1 1
1 1
0.75 0.75
. .
↓ 0.5 ↓ 0.5
P6 P6
0.25 0.25
0 0
0 40 80 120 160 0 40 80 120 160 200
microwaveypulseylengthy/yμs microwaveypulseylengthy/yμs
1 1
0.75 0.75
. .
↓ 0.5 ↓ 0.5
P6 0.25 P6 0.25
0 0
0 20 40 60 80 0 20 40 60 80
microwaveypulseylengthy/yms microwaveypulseylengthy/yms
c) variableyphase/shifter
computerycontroly6TTL.
DCyDAC
φ drivingyelectrode
~
DCyDAC
nullingyelectrode
synth isolator RFyswitch amp isolator
powerysplitter variableyattenuator bias/Ts
FIG. 2. Spatial addressing experiments. (a) Zone B is the ‘driven’ zone and zone A is the ‘nulled’ zone.
Top: Rabi flops in the driven zone (blue points, solid curve) with Ω =15.29(2)kHz are seen when we
driven
scanthedurationofamicrowavepulsefedintoelectrodes1and8. Onthistime-scale,theioninthenulled
zone is unaffected (red points, dashed line). Bottom: for longer pulse lengths, we are able to measure a
small Rabi frequency in the nulled zone of Ω = 18(2)Hz before decoherence reduces the contrast of
nulled
the Rabi flops. (b) Similarly, with zone A as the driven zone and zone B as the nulled zone, we measure
Ω =10.07(3)kHzandΩ =7.2(3)Hz. Inboth(a)and(b),thecontrastoftheRabiflopshasbeen
driven nulled
normalized to correct for the ≈10% state preparation and measurement errors. (c) The microwave system
usedtodrivethetwoelectrodes. Thepowerlevelsatthevacuumfeed-throughforthedatainplot(b)were
≈170mW at the driving electrode (8) and ≈9mW at the nulling electrode (1).
trode interfere destructively or constructively). phase. Assumingsimilarstabilityoftheσ fields
The high-resolution data measured in zone B as found for the π fields (fig. 3), we estimate
(fig. 2b) set an upper limit of ≈ 2×10−3 on fluctuations in the phase error δφ < 1mrad,
this error for that case. The differential AC leadingtoareductionofthequbitstatefidelity
Zeeman shift (ii) is at most 340Hz (calculated ∼(δφ)2<10−6 which is negligible compared to
∼
by assuming the worst-case phase relationship the off-resonant excitation error. Both error
between σ components) leading to a phase er- sources can be straightforwardly reduced either
ror φ = 70mrad on the nulled qubit when a by decreasing the Rabi frequency, shaping the
π-pulse is applied on the driven qubit. Pro- microwave pulses in time, or by increasing the
vided the AC Zeeman shift is stable, this can staticmagneticfield. Inpracticeonewouldide-
be corrected for by keeping track of the qubit allywishtouseanintermediate-fieldclockqubit
6
such as that at B = 288G where, without 3.5 30
0
reexdcuitcattiioonn ienrroRrabwioufrledqubeen∼cy,5×the10o−ff7-raensodnathnet 3 20inferre
AtoifvCtehlZye,eefitmehlaedncusanhnwifaatnls<∼toe4dbHepznou(lasllereiezdat,ataiboslnedeIcImo)m.oAnpslottnrearetnneatds- -3/Ω/(10)driven 12..255 510d//addressin
bgieblolewl,ewvehlsicehvwenoualtdlroewdustcaettichefiseeldesrraonrsd/toornhegiglih- Ωnulled 1 g/erro
Rabi frequencies. 0.5 nulling/in/zone/A,/addressing/in/zone/B 1 r/(1
The decoherence seen in the “nulled zone” nulling/in/zone/B,/addressing/in/zone/A 0)-6
0 0
Rabi flops (fig. 2) most likely occurs due to rel- 0 20 40 60 80 100
time/(mins)
ativephaseandamplitudefluctuationsbetween
the two arms of the microwave drive interfer-
FIG. 3. The Rabi frequency in the ‘nulled’ zone,
ometer (which cause the minimized Rabi fre-
Ω , was monitored for more than an hour. For
nulled
quency to change from shot to shot of the ex- each zone, the nulling parameters were optimized
periment). We confirm that this decoherence before t = 0; thereafter no further adjustments
is not a property of the qubit by performing a to the nulling parameters were made. The ra-
controlexperiment, whereweeliminaterelative tio (Ωnulled/Ωdriven) is plotted, assuming constant
Ω , for nulling in zone A (blue) and in zone B
phaseandamplitudefluctuationsbyusingasin- driven
(red). Bothratiosremainbelow3×10−3,whichim-
gle microwave line to drive only one of the mi-
pliesthespin-fliperrorscanbekeptbelow2×10−5
crowaveelectrodeswithanattenuatedsignalso
without the need to recalibrate nulling over these
as to produce very low Rabi frequency (18Hz). time-scales. Lines are to guide the eye.
We observe no significant loss of contrast in a
microwave pulse time scan up to 55ms, which
is consistent with the expected coherence time
quency (1.6kHz splitting at B =2.8G), hence
0
forthesequbitstates,elsewheremeasuredtobe
off-resonantexcitationlimitsthespeedatwhich
T∗ = 6(1)sat B = 2.0G [25]. To investigate
2 0 this transfer can be performed. A similar diffi-
slow drifts in the nulling quality, we monitored culty arises for readout of the 4S4,+1 ↔ 4S3,+1
thestabilityofthenullingover>1hourineach 1/2 1/2
field-independent qubit at B = 288G. Here
0
zone(fig.3)andfoundthatbothRAandRB re- we demonstrate selective nulling of the σ+ po-
main below 3×10−3 over this period, sufficient
larization component of the microwave field in
to maintain (cid:15) <2×10−5 without recalibra-
A,B∼ zone A by using two microwave control elec-
tion of the nulling field.
trodes in that zone (electrodes 7 and 8) and
With four electrodes per zone, the ion trap the same drive system used in the experiment
used here gives us more than enough degrees described above. Nulling is achieved by adjust-
of freedom to control the microwave field in all ing the phase shifter and variable attenuator
three spatial dimensions and hence to null un- while minimizing the ion’s Rabi frequency on
wanted polarization components. This could the 4S4,0 ↔ 4S3,+1 σ+ transition. To measure
1/2 1/2
enablesignificantlyfastermicrowaveoperations the Rabi frequency on the 4S4,+1 ↔ 4S3,0 σ−
1/2 1/2
byeliminatingtheoff-resonantexcitationerrors transition, we first prepare the |↑(cid:105) qubit state
discussed above. It is also useful, for example, by optically pumping to |↓(cid:105) and then driving
for performing high-fidelity read-out at low B , a microwave π−pulse on the qubit transition
0
which involves selectively transferring popula- using a third electrode. We achieve a Rabi
tion in one of the qubit states to the stretch frequency ratio of Ω /Ω = 2.77(8)×10−3
σ+ σ−
state 4S4,+4: the σ+ and σ− transitions out of (fig. 4), implying a polarization addressing er-
1/2
the qubit states are nearly degenerate in fre- ror of (cid:15) = 1.9(1) × 10−5. Combining the
pol
7
1 mainingthreedidnot. Larger aredesirableso
i
) 00..68 nudlrliivnigng σ- driven thatcrosstalkbetweenzonesislocal,improving
↓ σ+ nulled the ease of scalability to a large array of zones.
P( 0.4 Numerical simulations predicted r ∼5 for all
0.2 σ- B i
0 0 microwave electrodes. We believe that the dis-
0 25 50 75 100
crepancy between simulated and measured ra-
microwavedpulsedlengthd/dμs
tiosmaybeduetothefactthattheionsarenot
1 directly above the microwave electrodes, and
0.8 hence are removed from the points where each
)
0.6
↓ electrode produces the greatest field strength.
P( 0.4 At the ion positions, the electrode fields have
0.2
already decayed to approximately one-tenth of
0
0 20 40 60 80 their maximum value and are then of the same
microwavedpulsedlengthd/dms
orderofmagnitudeasthefieldsproducedbyre-
turn currents coupled across the trap. The ra-
FIG. 4. To demonstrate polarization control,
tio of field amplitudes between the two zones is
we null the σ+ component of the microwave po-
larization. We are then able to drive the σ−- verysensitivetotheprecisedistributionofthese
polarized transition that is indicated in blue on stray currents, which may be strongly affected
fig. 1b, without exciting the nearly-degenerate σ+- by fabrication inaccuracies and any other dif-
polarizedtransitionindicatedinredonfig.1b. Top: ferences between the simulated and fabricated
wedriveRabiflopsonthedrivenσ−-polarizedtran- trap(suchastheCPGApackage,ortheelectri-
sition(bluepoints,solidcurve)withRabifrequency
cal loading of the RF drive system, neither of
Ω = 11.6(1)kHz by scanning the length of the
σ− which we attempted to simulate).
microwave pulse applied to electrodes 7 and 8. On
this time-scale, the nulled σ+-polarized transition We identify three critical improvements that
is not visibly excited (red points). Both datasets should be incorporated into future near-field
on this plot were taken with microwaves resonant microwave addressing experiments that will al-
with the σ+ transition (which is 1.6kHz detuned
low for control of larger numbers of ions with
from the σ− transition). Bottom: on the mil-
lower levels of crosstalk. Firstly, the address-
lisecond time-scale, we observe slow Rabi flops on
the nulled σ+-polarized transition with Rabi fre- ing electrodes need to be placed as close to
quency Ω = 32.0(8)Hz, driven by residual σ+- the ion on the trap as possible (for example,
σ+
polarization. Data have been corrected for the within the centre control electrode). To do
≈10% state preparation and measurement errors. this for more than a few electrodes will re-
quire moving from a single-layer to a multi-
layer electrode fabrication technology, for ex-
polarization control with the spatial addressing ample as proposed in [33, 42]. Secondly, a low
would, for the typical 10kHz Rabi frequencies crosstalk and impedance-controlled package for
used here, suppress the off-resonant transition the trap should replace the CPGA. Thirdly,
errorsoutofthequbitstatestonegligiblelevels a microwave drive system with many digitally
(∼10−9), as the off-resonant σ transitions are controlled channels is required so that calibra-
≈1MHz detuned from the qubit transition at tion of field nulling can be automated.
B0 =2.8G. Inconclusion,thisworkreportsafirstdemon-
In considering what improvements can be stration of a near-field microwave addressing
made for a next-generation trap, we note the scheme which can enable arbitrary operations
data in table I shows that five of this trap’s mi- to be performed in parallel on “atomic clock”
crowaveelectrodesproducedRabifrequencyra- memory qubits stored in different zones of a
tiosr >1betweenaddressingzones,butthere- surface-electrode QCCD-type processor. The
i
8
Electrode i 1 2 3 4 5 6 7 8 controlwouldpermithigh-fidelityaddressingto
r = Ωnear 3.6 0.93 2.6 1.7 0.43 1.5 0.78 2.9 be performed even in low-field qubits. Further-
i Ωfar
more, we verify that the field nulling used to
TABLE I. Measured Rabi frequency ratios for all suppress crosstalk between trap zones is pas-
microwave drive electrodes. For each electrode i, sively robust to laboratory environmental fluc-
thequantityrigivestheratiooftheRabifrequency tuations for over an hour, indicating that, after
Ω measuredforaniontrappedinthezonenear
near an initial calibration, it is feasible to perform
electrode i, to the Rabi frequency Ω measured
far single-qubit addressing operations with errors
for an ion trapped in the zone far from electrode i.
<10−5 for long periods using this scheme.
TheRabifrequenciesaremeasuredonthe|↓(cid:105)↔|↑(cid:105) ∼
qubit transition, for a static magnetic field applied These error rates are two to three orders of
parallel to the trap axis (as shown in figure 2). Es-
magnitude below the threshold rates necessary
timated measurement errors are ≈ 8%. (If we in-
for fault-tolerant quantum computation. The
steadalignthestaticfieldperpendiculartothetrap
techniquesusedtonullthequbit-qubitcrosstalk
axis, we measure r ≈1 for all electrodes, possibly
i
becausestraycurrentstravellingdowntheRFelec- here will be applicable to the wide variety of
trode produce a π-polarized microwave field that physical systems which use qubits based on mi-
drives the qubit transition with similar strength in crowave frequency transitions, and are likely to
both trap zones.) be essential if these systems are to be scaled
up to the large numbers of qubits required for
general-purpose quantum computing.
implementationofthisschemewithhighfidelity
We thank D. MacDougal for helpful MATLAB
hinges on the achievement of a large field dif-
scripts, L. Stephenson for technical assistance,
ferential between processor zones (which are
and C. J. Stevens, A. D. Karenowska and
spaced by 960µm, a mere 1% of the wave-
P. J. Leek for useful discussions. This work
length of the qubit-driving microwaves) using
is supported by the U.S. Army Research Of-
relatively low microwave powers and an elec-
fice (contract W911NF-14-1-0217), and by the
trode geometry which offers independent field
U.K. EPSRC “Networked Quantum Informa-
control at each zone. Such independent con-
tion Technology” Hub.
trol is achieved by interfering fields generated
by microwave electrodes integrated into each
trap zone so as to null residual crosstalk in
neighbour zones. For technical simplicity, the
scheme was demonstrated here using a low- ∗ Present address: National Institute of Stan-
field 43Ca+ qubit at 2.8G, with which the ad- dardsandTechnology,325Broadway,Boulder,
dressing error was limited by off-resonant ex- CO 80305, USA
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(2010).
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(2014).
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bined with crosstalk-nulling, this polarization 339, 6124, 1169 (2013).
9
TABLE II. Error budget table summarizing the metrics used in this work to asses the performance of
the field-nulling addressing scheme. The second column details which metrics were directly measured and
which were calculated from measurement. The last column of the table lists the projected errors for the
scheme when implemented on an intermediate-field 43Ca+ clock qubit at 288G (both the low-field clock
transition used here and the 288G transition are π-polarized). The 288G qubit was not used in this work
because it requires a magnetic field strength beyond the capabilities of the present setup. The σ-polarized
146Gclockqubit(previouslyusedtoimplementhigh-fidelitysingle-qubitandtwo-qubitmicrowave-driven
gates[14,15])canalsobeusedwiththisaddressingscheme,withaprojectedtotaladdressingerroroforder
10−5. All errors given here relate to addressing performed with a single microwave electrode per zone. As
wasseparatelydemonstratedinthiswork,moreelectrodesperzonecanbeusedtocontrolthepolarization
ofthemicrowavefield,atechniquewhichwouldreduceoreliminateoff-resonantexcitationandACZeeman
shift errors if combined with addressing. These errors are quoted below for the nulled qubit, but similar
levels of off-resonant excitation and light-shift also occur in the driven qubit.
Projected error for
Value for this
Metric How was it evaluated? intermediate-field
experiment
qubit at B =288G
0
≤ 1.2(1) × 10−3
Ratio of qubit-transition Rabi fre-
Measured ≤1.2(1)×10−3 (sameasforlow-field
quencies, R = Ωnulled
A,B Ωdriven qubit)
Probabilityofspin-fliponthequbit
≤ 3.4(7) × 10−6
transition of nulled qubit when we Calculated from measured
≤3.4(7)×10−6 (sameasforlow-field
flip the spin of the driven qubit, R
A,B qubit)
(cid:15) = π2R2
A,B 4 A,B
Calculated from measured
Off-resonant excitation error on ratioofσtoπRabifrequen-
≤5×10−3 ≤5×10−7
nulled qubit ciesforelectrodes1and8in
each zone
Calculated from measured
ratioofσtoπRabifrequen-
AC Zeeman shift on nulled qubit <340Hz <4Hz
ciesforelectrodes1and8in
each zone
Calculated from measured
Phase error on the nulled qubit
ratioofσtoπRabifrequen-
when we drive spin-flip on ad- <70mrad <0.7mrad
ciesforelectrodes1and8in
dressed ion
each zone
Estimated from measured
ratioofσtoπRabifrequen-
Stability of phase error on nulled cies for electrodes 1 and 8
<1mrad <0.01mrad
qubit in each zone and from mea-
sured drift of nulled qubit
Rabi frequency
Measured from high-
Total addressing error resolution data taken in <2×10−3 ≤4×10−6
zone B (see fig. 2b top)
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