Dynamic compensation of stray electric fields in an ion trap using machine learning and adaptive algorithm
Moji Ghadimi, Alexander Zappacosta, Jordan Scarabel, Kenji Shimizu, Erik W Streed, Mirko Lobino
DDynamic compensation of stray electric fields in an ion trap using machine learningand adaptive algorithm
Moji Ghadimi , ∗ Alexander Zappacosta , Jordan Scarabel , Kenji Shimizu , Erik W Streed , , and Mirko Lobino , Center for Quantum Dynamics, Griffith University, Nathan QLD Australia Institute for Glycomics, Griffith University, Southport QLD Australia Queensland Micro Nanotechnology Centre, Nathan QLD Australia (Dated: February 12, 2021)Surface ion traps are among the most promising technologies for scaling up quantum computingmachines, but their complicated multi-electrode geometry can make some tasks, including compen-sation for stray electric fields, challenging both at the level of modeling and of practical imple-mentation. Here we demonstrate the compensation of stray electric fields using a gradient descentalgorithm and a machine learning technique, which trained a deep learning network. We show auto-mated dynamical compensation tested against induced electric charging from UV laser light hittingthe chip trap surface. The results show improvement in compensation using gradient descent andthe machine learner over manual compensation. This improvement is inferred from an increase ofthe fluorescence rate of 78% and 96% respectively, for a trapped Yb + ion driven by a laser tunedto -7.8 MHz of the S / ↔ P / Doppler cooling transition at 369.5 nm.
I. INTRODUCTION
Trapped ions are one of the most promising candi-dates for implementing scalable quantum informationprocessing [1–4]. Traditionally macroscopic rod or nee-dle traps were used for electrically trapping laser cooledions. These Paul traps have a deep potential well thatenables the trapping of multiple ions in a chain, but theirdistant electrodes lack the fine spatial control of electricfields necessary to efficiently split and combine small ioncrystals [5]. One of the proposed architectures for scalingup the number of trapped ions in a quantum processor isthe use of microfabricated surface chip traps with multi-ple DC electrodes that are able to manipulate multipleions individually [6–10].In these chip traps the ions are confined to a potentialformed by the node of an oscillating RF electric field intwo dimensions while a DC field generated from multipleelectrodes provide a finely spatially adjustable potentialin the third dimension. It is well-known in Paul trappingthat stray DC electric fields push the ion off the RF nodeand induce micro-motion that degrades or outright pre-vents effective confinement and laser-cooling [11]. Thesolution to this problem is to use the DC electrodes togenerate an opposite DC electric field that compensatesfor these stray fields [9].Micro-motion amplitude can be measured and dealtwith in multiple ways [9, 12–15]. A simple and quickproxy for small amounts of micromotion is to measure theion’s fluorescence under laser cooling near the Dopplerlimit. In fact for low magnitudes of micro-motion, if alaser is red-detuned near the natural linewidth of theatom, the ion fluorescence rate increases as the micro-motion amplitude decreases (see Section II and Fig. 2).While stray electric fields can be readily compensated in ∗ m.ghadimi@griffith.edu.au simple fixed trap geometries [16], this task becomes morechallenging for multi-electrode designs [17] and in prox-imity of surfaces which are vulnerable to laser inducedcharging [18].Automation, optimization, and machine learning havebeen used to improve different manual tasks in atom andion traps [19–21] and they are also useful tools for op-timizing the individual electrode voltages which gener-ate the trapping electric field. In this work we showhow the voltages of an array of electrodes in a surfacechip trap can be optimized using a fully automated, ma-chine learning driven process to minimize micromotionand maximize florescence. The chip trap in our experi-ment has 44 segmented DC electrodes and 2 RF rails, asshown in Fig. 1. The trap incorporates nearly aberrationfree diffractive mirrors directly fabricated onto the cen-tral ground electrode for efficient fluorescence collectionfrom the ion [22]. A Gradient descent (ADAM [23]) anda machine learning algorithm (MLOOP [20]) were com-pared on the basis of the versatility and time taken tofind the optimal compensation and highest fluorescencerate of the ion. These methods were applied to a trapped Yb + ion and compared to a manual optimization per-formed by an experienced operator.With ADAM we were able to improve the fluorescenceby 78% starting from voltages already optimized by man-ual adjustment, while MLOOP achieved a 96% improve-ment. Subsequently we tested the versatility and adap-tion of this procedure by deliberately charging the trapwith UV light to drop the fluorescence rate by around35% and compensating back to the optimal with ADAM.This was not tested on MLOOP as it was observed to bequite sensitive to the noise in the fluorescence signal anddid not make a solid candidate for final optimization ofthe artificially charged trap. a r X i v : . [ qu a n t - ph ] F e b s P F=1F=0 S F=1F=0
F=1F=0F=1F=0 D [3/2]
38 ns . n m . n m cooling laserDAC RFPMTDC electrodes (a) (b)
53 ms
FIG. 1. a: Transitions for laser cooling Yb + . The ion is laser cooled on the nearly closed 396.5 nm S / F=1 to P / F=0transition. The small amount of off-resonant scattering into the S / F=0 state is repumped with a 14.7 GHz sideband onthe primary cooling laser. Decays from P / can also populate the D / level, which are repumped using a 935 nm laser. b:Schematics of the ion trap chip and the optimization devices. RF and DC electrodes are used to trap the ion and shuttle itabove the diffracting mirror that collects photons from the ion and sends it to photo multiplayer tube (PMT). The PMT countsare processed by the optimiser and DC electrode voltages and cooling laser position are updated using a digital to analogueconverter (DAC). II. EXPERIMENTAL SETUP
The ion trap used in these experiments and describedin [22, 24], consists of a planar rectangular chip of1400 µ m length and 800 µ m width. It has a set of alu-minum electrodes patterned on top and is schematicallyshown in Fig. 1. The ion is trapped 60 microns abovethe surface, between the two RF electrode rails that ex-tend for the full length of chip, and 44 DC electrodes onthe sides. The DC electrodes are used to create a re-configurable trapping potential along the length of thetrap, compensating stray electric fields, and enabling ioncrystals merging, separation, and shuttling.An atomic oven underneath one end of the trap gener-ates a beam of neutral Yb atoms which passes through aslit in the chip. The Yb is first excited by an isotopi-cally selective 399 nm laser [25], and subsequently non-resonantly ionized by the a 369.5 nm laser. The ion isthen Doppler cooled using the same 369.5 nm laser tunednearly resonant with S / F=1 ↔ P / F=0 transition.Occasionally off-resonant scattering from the P / F=1state will populate the dark S / F=0 ground state,which is repumped by a small amount of light from a14.7 GHz sideband added to the primary 369.5 nm cool-ing laser. There is also a probability of 0.5% for theatom to decay from the P / into the meta-stable D / state. In this case a 935 nm laser repumps the ions backinto the cooling cycle. Figure 1 depicts the cooling andrepumping transitions.After initial trapping near the oven slit region, the ion is shuttled along the length of the trap by properly con-trolling the voltages of the array of DC electrodes witha 12-bit National Instruments PXI-6713 DAQ (outputdoubled to +/-20V with 10 mV resolution). For ourexperiments, the ion was shuttled above the surface ofan integrated diffracting micro-mirror patterned on theground electrode with a focal length of 60 µ m, equal tothe height of the ion above the trap, to improve flores-cence collection and coupling into a single mode fiber[22].For efficient Doppler cooling and subsequent quan-tum information processing experiments, it is importantto minimize any micro-motion induced by stray electricfields. This is done by tuning the voltages of the DCelectrodes so that they generate an opposing electric fieldthat compensates for the stray fields. To generate a com-pensation field in the RF confinement plane xy , we usetwo waveforms (array of DC voltages for individual elec-trodes) which were calculated for generating an electricfield of 100 V/m in the x (horizontal) and y (vertical)directions. Electrode voltages of − x direction and − y direction are needed tocreate electric field of 100 V/m at the location of the ion.These sets of voltages are multiplied by arbitrary weights w x and w y to compensate arbitrary fields in the RF trap-ping plane. In practice this process has imperfectionsand cannot fully compensate for the stray electric fields[17]. Instead, individual electrodes need to be tuned in-dependently for optimal compensation. This optimumcompensation is position dependent and there might bemultiple solutions for a multi-electrode trap.Two other DC waveforms are used and their relativeweights tuned: a harmonic waveform, and RF plane trapaxis rotation waveform. The former creates a harmonicpotential to trap the ion in different locations along thechip length, while the latter rotates the trap’s secularconfinement axes to lift the degeneracy and improve cool-ing [26].We infer the magnitude of the stray electric field fromthe fluorescence rate of the ion when the cooling laser isred-detuned near half its natural linewidth for optimalcooling. When driving an ideal cold two-level atom withthis laser, the fluorescence is proportional to the popula-tion of excited state, P e , that can be calculated from theoptical Bloch equation [27]. The relationship between P e and the strength of the stray electric field is given by [15]: P e ( β ) = C ∞ (cid:88) m = −∞ J m ( β )( δ L γ + m Ω γ ) + (1)where J m is the m th order Bessel function of the firstkind, δ L = ω atom − ω laser is the laser frequency detun-ing, γ is the natural linewidth and Ω is the RF trapfrequency. β is a dimensionless measure of the ion’s co-herently driven motion from the stray electric fields andRF phase imbalances (AC micromotion) [15]. C dependson the strength of the coupling between the levels thatis a constant here since we keep laser intensity and di-rection fixed. Figure 2 shows a graph of P e ( β ) /P e (0) asa function of β . The graph shows that at our detuning(-7.8 MHz) the population decreases monotonically as β P e ( β ) / P e ( ) β FIG. 2. Normalised florescence as a function of the dimen-sionless micromotion parameter β (Eq. 1). Here δ L , the laserfrequency detuning, is -7.8 MHz, γ , the natural linewidth is 20MHz and Ω, the RF trap frequency, is 25.5 MHz. The P / state population and therefore the fluorescence rate dropsmonotonically as β increases as long as its value is not toolarge (smaller than 2.5). Our operating regime is far belowthis threshold. increases if β is less than 2.5. For larger β micromotioninduced local maxima arise that prevents inferring themagnitude of micromotion from fluorescence rate. Sinceour operating regime is below this threshold, we can usethe change in fluorescence rate to detect the change inmagnitude of the stray electric field. III. RESULTS
A gradient descent algorithm (ADAM) and a deeplearning network (MLOOP) were tested for compensat-ing stray fields in different working regimes. The sourcecode used for the experiments is available in [28]. Thesoftware controlled the voltages using the PXI-6713 DAQand read the fluorescence counts from a photo-mutliplier-tube (PMT) through a time tagging counter (IDQ id800).All software was written in python and interfaced withthe DAQ hardware using the library NI-DAQmx Python.A total of 44 DC electrodes and the horizontal positionof the cooling laser were tuned by the program, resultingin a total of 45 input parameters.
A. Gradient Descent optimizer
The first compensation test was performed by ADAMgradient descent algorithm. This is a first order opti-mizer that uses the biased first and second order mo-ments of the gradient to update the inputs of an ob-jective function, and was chosen for its fast conver-gence, versatility in multiple dimensions and toleranceto noise[23]. Our goal was to maximize the fluorescenceof the ion which was described by a function f ( (cid:126)α ), where (cid:126)α = ( α , α , α , . . . α ) represents the array of param-eters to be optimized. To find the optimal (cid:126)α , the algo-rithm needs to know the values of the partial derivativesfor all input parameters. Because we do not have an an-alytic expression for f ( (cid:126)α ), the values of its derivativeswere estimated from experimental measurements by se-quentially changing each input α i , and reading the asso-ciated change in fluorescence f . This data were used asinputs to ADAM for finding the optimal (cid:126)α which maxi-mized f .Before running the automated compensation, we man-ually adjusted the 4 weights of the waveforms used forcompensation described in the previous section. We alsotried to run ADAM to optimize these 4 parameters butthe increase in fluorescence was limited to 6%. Aftermanual compensation, we ran ADAM on all 45 inputswith the algorithm parameters given in the source code[28]. Each iteration took 12 s, where 9.8 s were the pho-ton readout (0.1 s × × ±
1% (Fig. 3) when starting froma manually optimized configuration.The ADAM algorithm was fast and reliable (the ionwas never lost during optimization), even in extremelyvolatile conditions like having time-dependent chargingand stray electric field buildup. Figure 4a shows acolourmap of the voltages and laser position adjustments,where most of the improvement came from adding thesame voltage to all DC electrodes indicating the ion wasnot at optimal height. The volatility of the ion-trap envi-ronment causes the fluorescence rate to oscillate aroundthe optimal point. To get the best value, instead of us-ing the values of the final iteration, the software savedall voltage combinations and applied the setting with the P ho t on C oun t ( k c oun t s / s ) Iteration Number + % Photon count from different DC values found by ADAM Final Photon CountInitial Photon Count
FIG. 3. The photon count improvement using ADAM start-ing from manually optimized waveform weights. This graphdemonstrates a 78 ±
1% improvement in ion fluorescence.The error bars are a combination of the readout error ofthe PMT and peak to peak variations in the photon countwhilst not optimizing. The background photon count here is1184 ±
34 counts/s. highest photon count after all iterations were finished.Despite picking the best value it can be seen in Fig. 3that the fluorescence for some iterations during the opti-mization are higher than the final point selected by thesoftware. This is because when the settings are changed,the ion fluorescence rate may transiently increase andsubsequently stabilize to a slightly lower value for thesame voltage settings.
B. Deep Learning Network for the Ion trap
The second algorithm tested was a deep learning net-work using the python based optimization and experi-mental control package MLOOP[20]. MLOOP uses Dif-ferential Evolution [30] for exploring and sampling data.The blue points in Fig. 5 corresponds to these samplesand it can be seen that even at the end of optimization,they can have non-optimum fluorescence rates.MLOOP also trains a neural network using the datacollected by Differential Evolution and creates an ap-proximate model of the experimental system. It thenuses this model to predict an optimum point. The redpoints in Fig. 5 shows the optimum points predicted bythe neural network model. It can be seen that this sec-tion starts later than Differential Evolution, as it requiressome data for initial neural network training, and gradu-ally finds the optimum and stays near it. For training ofthe neural network, the inbuilt ADAM optimizer is usedto minimize the cost function.The sampling in MLOOP does not require a gradientcalculation which greatly improves the sampling time.Even though the sampling is fast, training the network tofind an optimal point requires a minimum of 100 samplesand that makes MLOOP slower than ADAM. With oursettings for MLOOP, each iteration took 0.7 s on aver-age and therefore 700 s was needed to take 1000 samplesshown in Fig. 5.In our test the neural network in MLOOP had 5 layerswith 45 nodes each, all with Gaussian error correction.The neural network structure was manually optimizedand tested on a 45-dimensional positive definite quadraticfunction before being used for the experiment.Once the ion was trapped, positioned above the in-tegrated mirror [22], and photon counts were read, theprogram started sampling 100 different voltage combina-tions around its initial point. Then, the network startedtraining on the initial data and making predictions forthe voltages that maximise fluorescence.Since the ion trap setup is very sensitive to changes inthe electric field, the voltages were set to move a max-imum of 1% of their previous value in each iteration toreduce the chance of losing the ion. As a step size valuecould not be explicitly defined, this percentage was cho-sen to make the changes similar to the step size used forADAM.A small percentage of our initial trials with the max-imum change of a few percent (instead of 1%) led to E l ec t r od e ( odd e l ec t r od e s ) E l ec t r od e ( e v e n e l ec t r od e s )
143 5 10 15 20 25 30 143244244 (a) (b) -0.04-0.02+ 0.02+ 0.04
Iteration FIG. 4. Voltage deviation from the original starting point during optimization with ADAM. a: uncharged trap (section III A).b: During UV charging (section III D). Top graphs show odd electrode numbers corresponding to top DC electrodes in Fig.1 and the bottom graphs show the even electrode numbers. The values were determined by subtracting the voltage at eachiteration by the starting voltage ∆ V = V n − V . Changes can be seen in almost all the electrodes of the trap. an unstable ion during the parameter search sequence.This is because MLOOP is a global optimizer and can setthe voltages to values far from the stable starting point.Since the ion trap is a complicated system that can onlybe modelled for a specific range of configurations, movingaway from these settings can lead to unpredictable andusually unstable behavior.MLOOP also has an in-built mechanism that handlesfunction noise using a predefined expected uncertainty.We set this uncertainty to the peak-to-peak noise of thephoton readout when no optimization was running.Since MLOOP is a global optimizer it was able tofind optimum points different from the points found byADAM. For trials where low numbers of initial trainingdata points were used, these configurations proved to beunstable and in most cases resulted in the loss of theion. Unstable states were also observed occasionally ifthe optimizer was run for too long. With moderate-sizetraining sets, MLOOP was able to find voltage settingswith fluorescence rates similar or higher than optimumpoints found by ADAM as shown in Fig. 5.Considering the long duration of the MLOOP iterationsequence and the possibility of finding unstable settingsin volatile conditions, the test of optimization with in-duced changing stray fields (section III D) was only per-formed with the ADAM optimizer as the gradient basedsearch method proved to be more robust against fluctu- P sat ( µW ) η (%) ¯ Bkg (1 /s )Initial 4.11(1) 0.971(2) 1184(34)ADAM-45 1.86(1) 0.938(1) 1227(35)MLOOP-45 1.86(1) 0.989(1) 1291(35)TABLE I. Saturation power ( P sat ), detection efficiency ( η )and average background count rate ( Bkg ) before and afteroptimization with different methods. P sat and η values arecalculated by fitting the theoretical formula for FluorescenceRate vs Laser Power to the experimental data [31–33]. Aclear drop in saturation power is observed after ADAM andMLOOP optimization of individual electrodes indicating areduction of the micromotion. ations in the ion environment. C. Ion Properties before and after optimization
To test the effectiveness of the protocols, the satura-tion power, P sat , was measured before and after the op-timization process. The P sat is the laser power at whichthe fluorescence rate of a two-level system is half the flu-orescence at infinite laser power. We also measured theoverall detection efficiency η , the fraction of emitted pho-tons which resulted in detection events. Table. I shows P sat decreased (ion photon absorption was improved) us- P ho t on C oun t ( k c oun t s / s )
70 Iteration Number2030405060
Differential EvolutionNeural Network + % FIG. 5. MLOOP deep learning network. Differential Evo-lution explores the input space (blue points) and the neuralnetwork creates a model of the data and predicts an optimum(red points). Maximum photon count of the neural networkpoints is 96 ±
1% higher than manual optimization. Differen-tial Evolution continues to explore the input space and hasvaried photon counts. The beginning point for the process(found by manually adjusting the 4 waveform weights) wasat 33700 counts/s and the highest photon count found by theneural network was at 66200 counts/s. ing both ADAM and MLOOP. The detection efficiencywas approximately the same for all runs as expected.Another test was done by measuring fluorescence vslaser detuning before and after optimization. Figure 6shows that the measured values follows the expectedLorentzian profile [31–33] and associated linewidth be-fore and after optimization. This indicates that the ini-tial micromotion magnitude β was sufficiently small forfluorescence to be a good optimization proxy. Clear in-crease in florescence can be seen after optimizing 44 elec-trodes individually both with ADAM and MLOOP. Thefit residual curve (difference between the experimentalvalues and the theoretical fit) shows that optimizing in-dividual electrodes, resulted in slight increase in heatinginstability near the resonance. D. Testing under poor trap conditions
To test the live performance of the optimization proto-col in a non-ideal situation, we deliberately charged thetrap by shining 369.5 nm UV laser light onto the chipfor 70 minutes. The power of the laser was 200 ± µW and the Gaussian diameter of the focus was 120 ± µm .This process ejects electrons due to the photo-electriceffect [34] and produces irregular and potentially unpre-dictable slow time varying electric fields within the trap. The process charged the trap significantly and made anoticeable reduction to the photon count. The ADAMalgorithm was then tested both during charging and aftercharging was stopped. In both cases an improvement offluorescence rate was observed.The first experiment was performed to test the opti-mizing process after charging. In this test, starting withthe optimal manual setting, ADAM individual electrodeoptimizer was able to obtain 27% improvement in thefluorescence rate (blue points on the left side of Fig. 7).Then charging was induced onto the trap for 70 min anda clear decrease in photon count was seen that went evenlower than the initial value (red points in Fig. 7). At thispoint charging was stopped and ADAM was run againand fluorescence rate returned back to the previous op-timum, within the error, in approximately 12 min. Dur-ing the second optimization, the fluorescence goes higherthan the stable final value for some iterations before thefinal. This is because of the same effect explained in sec-tion III A that the fluorescence might spike right after a F i t R e s i d u a l (a)40 30 200 Laser Detuning l (MHz) I o n F l u o r e sc e n c e ( k c o un t s / s ) Laser Detuning δ L (MHz) P ho t on C oun t ( k c oun t s / s ) Heating instability
Initial F it R e s i du a l ( k c oun t s / s ) s ca l e (b) InitialADAM-4ADAM-48M-LOOP (a)40 30 20 10 0 Laser Detuning l (MHz) I o n ( k c o un t s / s ) (b) InitialADAM-44M-LOOP InitialADAM-45MLOOP-45 (a)(b)
FIG. 6. Fluorescence vs laser frequency detuning from theresonance for inital setting and after different optimizations.It can be seen from (a) that the experimental values are veryclose to the theoretical Lorentzian fit [31–33]. This showsthe heating is low before and after optimization and thereforethe change in fluorescence can be used to infer the change inheating. Deviation from the theory near the resonance shownin (b) is a sign of small heating instability.
Time (min) P ho t on C oun t ( k c oun t s / s )
20 40 60 806101418 0 % % ADAM ONCharging ON ADAM OFFCharging ON ADAM ONCharging OFFPhoton Count during ADAMPhoton Count while charging trap
FIG. 7. Real time compensation with ADAM of laser charg-ing induced stray electric field. The ion was optimized usingADAM (left blue points) then the photon count was notedwhilst charging for 70 minutes (red points) then re-optimized(right blue points). Initial improvement from manually opti-mized settings was 27%. The second optimization improvedthe fluorescence by 58% from the charged conditions and re-turned it back to the optimum value of the first optimizationwithin the error. P ho t on C oun t ( k c oun t s / s ) ADAM ONCharging ONPhoton count from ion + Disturbing laser - ADAM ONProposed Photon count - ADAM OFF
FIG. 8. The trap was charged by hitting a UV laser to destabi-lize the ion and individual electrodes optimized using ADAMsimultaneously for 70 minutes. The photon count fluctuatesas a result of combination of fluctuations of power of the cool-ing laser power, algorithm search and charging irregularities.The optimizer keeps the fluorescence at the photon count sim-ilar to the case of optimizing after the charging is stopped(third section of Fig.7). change but go down slightly after stabilizing. Looking atthe changes of individual electrodes, shown in Fig. 4b, wesee that the main electrodes adjusted were those aroundthe ion and some throughout the trap. The change inthe laser horizontal position was negligible.Another experiment was done by running ADAMduring continuous charging for real-time compensation.Since we induce charging via laser scattering from thetrap, the collected photons are both from the ion andthe scattered laser and fluctuations in the intensity ofscattered light confuses the optimizer. Despite that theoptimizer did not lose the ion nor needed to abort theprocess. Figure 8 shows that the fluorescence rate, evenafter a 70-minute charging session, remained near theoptimum value. After stopping the charging, the ion re-mained trapped for more than 8 hours and was intention-ally removed from the trap after this time.
IV. CONCLUSION
Comparing the results of the gradient descent methodand MLOOP shows that ADAM, the local optimizer, wasa better performer in volatile conditions. This is becauseunlike MLOOP, ADAM does not need any training andcan react faster to changes. MLOOP as a global opti-mizer was able to find settings with higher fluorescencebut occasionally optimums were unstable if the definedparameter search range for the settings were large or ifthe machine learner ran for too long. The main drawbackof MLOOP was that it was much slower than ADAM. Inboth cases photon collection times were the limiting fac-tor.Optimizing the individual electrodes improved the flu-orescence by 78% for ADAM and 96% for MLOOP.ADAM showed its reliability in the charging test, return-ing the ion to the optimal fluorescence in 12 minutes af-ter 70 minutes of purposely charging the trap with a UVlaser. Improvement amounts depended greatly on theoverall stability of the cooling laser and efficiency of thephoton counting system.To improve the speed of the gradient based optimizer,shorter readout times can be used although this increasesvariability in the value of the photon count. It is alsopossible to try local optimizers like SPSA [35] that ap-proximate the gradient using only 2 readouts instead of90. This improves the time needed for each iteration butbecause using this approximate gradient reduces the im-provement in each iteration, the overall speed comparisonto reach the same optimum can only be made when bothare tried in practice. One possible problem with SPSAis that it cannot handle noise like ADAM and multiplereadouts and averaging are needed in noisy conditions. Ifhigh amount of averaging is required, the algorithm maybecome very slow.
A. Acknowledgement
This research was financially supported by the Grif-fith University Research Infrastructure Programme, theGriffith Sciences equipment scheme, and Australian Re-search Council Linkage (LP180100096) Projects, ML is supported by Australian Research Council Future Fel-lowship (FT180100055), AZ was supported by Centre forQuantum Dynamics, Griffith University, Summer Schol-arship, JS, and KS were supported by the AustralianGovernment Research Training Program Scholarship. [1] S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman,K. Wright, and C. Monroe, Demonstration of a smallprogrammable quantum computer with atomic qubits,Nature , 63 (2016).[2] B. Lekitsch, S. Weidt, A. G. Fowler, K. Mølmer, S. J.Devitt, C. Wunderlich, and W. K. Hensinger, Blueprintfor a microwave trapped ion quantum computer, ScienceAdvances , e1601540 (2017).[3] C. Monroe and J. Kim, Scaling the Ion Trap QuantumProcessor, Science , 1164 (2013).[4] B. B. Blinov, D. Leibfried, C. Monroe, and D. 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