Overview and System Design
Experimental quantum computing is beginning to realize its potential for computational speedup through recent demonstrations of specialized algorithms with as few as 50 qubits [1], [2]. These machines are considered noisy intermediate-scale quantum (NISQ) computers [3], and though their ability to solve relevant real-world problems is limited by their size and fidelity, they are very useful for investigating the best way to build and operate a future fault-tolerant quantum computer. While access to NISQ hardware has become available over the past few years [4]–[6], it is still scarce and highly constrained to a small set of fixed physical operations. We have developed the Quantum Scientific Computing Open User Testbed (QSCOUT) platform to reduce these two barriers in order to accelerate progress by the scientific community.
QSCOUT's user program begins with a call for proposals, where the details of the upcoming system are described. Up-to-date information about proposal calls and current capabilities is available on the website: https://qscout.sandia.gov. Proposals are reviewed by a committee external to the QSCOUT program and judged on their scientific merit and feasibility given the capabilities of the current system. Selected proposals are guaranteed run time on the machine as well as access to QSCOUT scientists if desired, for collaboration. Additionally, complete specifications of the system can be provided for each algorithm run, including, but not limited to, pulse lengths and secular frequencies. Other specifications requested by the user can also be provided. There is no fee to use the QSCOUT system.
The QSCOUT platform consists of a small number of Ytterbium (171Yb+) ion qubits. The first round of user experiments has two to three ions, with plans to expand to a linear chain of 32 ions in later rounds. Trapped ions have long coherence times [7], [8], high gate fidelities [9], and very low state preparation and measurement (SPAM) errors [10], making them an ideal system to build a quantum processor. The targets for the QSCOUT are to provide up to 32 qubits with
To trap a linear chain of ions, we are using a high optical access (HOA-2.1) surface trap fabricated at Sandia National Laboratories [13], because it is capable of precisely controlling ion spacing and manipulating chains of ions. Additionally, it has demonstrated heating rates above the slotted portion of the trap in the range of 100–200 quanta/s [14] at the radial secular frequencies used in QSCOUT experiments (see Table 6). To maintain a linear chain for enough time to perform many quantum operations, the trap must be under ultra-high vacuum (UHV) to limit collisions that “melt” the ion crystal or eject ions from the trap. The vacuum chamber must have windows for optical access as well as electrical feedthroughs for radio frequency (rf) and dc voltages to reach the trap. The details of the vacuum chamber are described in Section II. Section III discusses the specific laser frequencies and locks needed for trapping, cooling, and detecting 171Yb+ ions, as well as our optomechanical system for minimizing vibrations and drift that degrade the quality of the delivered light. Quantum gates are performed using a 355-nm pulse train [15], which has tight spatial tolerances to achieve individual addressing of closely spaced ions. Our technique for pulse train spacing compensation and optical delivery is outlined in Section IV. Distinguishable detection of ions is achieved by imaging light from each ion into a separate core of a multimode fiber array, with each core coupled to it own photomultiplier tube (PMT) for counting photons. Section V describes this detection method in more detail. We also developed new electrical hardware to control the timing, frequency, and amplitude of the rf pulses needed to modulate the optical signals that are delivered to the ions. This device and corresponding firmware are described in Section VI. The high-level programming language for users to interface with our hardware, Jaqal, has been described in [16], and design decisions described in [17]. In Section VII, we describe the resulting ion performance achieved in preparation for the first round of user experiments, and finally, in Section IX, we provide full specifications of the QSCOUT system.
UHV Chamber
Because the QSCOUT relies on the realization of multi-ion chains, the background gas pressure in the system is of paramount importance. While an individual ion lifetime in a surface-electrode trap is typically hours-long (even a few days), as we scale up to larger chains, the chain lifetime reduces as more ions are subject to background gas collisions [18]. Since most collisions at room temperature are of sufficient energy to destabilize the ion chain, limiting collisions results in fewer ion losses, fewer quantum algorithm restarts, and faster processing time. To this end, we develop a UHV system intended to realize long-lived ion chains incorporating vacuum practices from other fields to achieve lower background pressure.
UHV has been a standard of vacuum technology for decades. It has relied on the use of stainless steel components, copper gasketing, limiting organics to low-outgassing plastics, welding and brazing of components such as viewports, and utilizing ion pumps to maintain the necessary vacuum pressure. Additionally, a vacuum bake is a standard procedure to remove water vapor and other outgassing residues from the internal environment.
In trapped-ion systems, the vacuum chamber must support an ion trap, an ion source, and have viewports for laser access. In our chamber, the central experimental region is a Kimball Physics 6-in CF (ConFlat flange) Spherical Square (see Fig. 1). A feedthrough flange containing electrical and rf connections is attached at the top of the chamber. A stainless steel platform anchored to the feedthrough is suspended inside the chamber. The platform and its various components are all machined from Grade 316L stainless steel and electropolished. The microfabricated surface-electrode ion trap is attached to this platform, facing downward to make it less likely dust particles will attach to the surface [see Fig. 2(a)]. The trap uses an rf signal on a single large electrode to generate the radial trapping pseudopotential, as well as a number of smaller dc electrodes to shape the potential and confine the ion to a particular region of the trap [13], [19], [20]. A thermal oven is used to create a neutral Yb flux, which is then photoionized to generate ions for trapping (more details are provided in Section III-A). Imaging is performed from the bottom of the chamber and utilizes a re-entrant viewport to allow for the small working distance of the imaging lens assembly (more details are given in Section V). The spherical square has an octagonal structure, and viewports are affixed to seven of the eight sides to optically access the trap. One of the viewports that allow for optical access perpendicular to the trap axis is also a re-entrant viewport, visible in Fig. 1. This is needed for individual ion addressing using lasers, described in Section IV. The transition to the pumping region of the chamber consists of a stainless steel vacuum cross and tee. This supports a 50-L/s ion pump (Agilent Varian VacIon Plus 55 StarCell), an ion gauge (Agilent Varian UHV-24P Nude Bayard–Alpert Ion Gauge with dual Ir-Th filament), a titanium sublimation pump (TSP), and all-metal bakeable valve. To prevent titanium film from sputtering on the trap surface, the TSP is positioned out of direct line of sight from the trap. For convenience, we constructed two chambers so that the backup, already baked with a trap, can be swapped as needed.
UHV chamber for trapped ion quantum operations. The chamber consists of an experimental region (left) and a pumping region (right). The chamber has rf and dc feedthroughs that support trap potential generation as well as viewports for laser addressing of the ions.
(a) Trap platform attached to the feedthrough flange. The trap platform, on which the trap will be mounted, is machined from stainless steel. The dc signals are routed via bare copper wires from a Micro-D feedthrough to an Al
A. Requirements
The dc and rf wiring that convey the voltages for trap generation traditionally use organic materials in the form of insulation, multipin connectors, and circuit boards. The materials include polyether ether ketone (PEEK), polyimide films such as Kapton (DuPont), and RO4350B (Rogers Corporation). While these materials are typically classified as low-outgassing materials (total mass loss
B. Hydrogen Mitigation
In an effort to decrease the amount of hydrogen within the stainless steel components, we subject all of the purely stainless steel components to a high-temperature bake process. This includes the trap platform, the experimental chamber, and all of the nipples, tees, crosses, adapters, and blanks. Prior to baking, the parts are cleaned with solvents and degreasers that include 3M Novec 72DE, acetone, and isopropanol. Initially, they are baked in a dry H
The stainless steel elements of other components, such as viewports and feedthrough flanges, were subjected to a vacuum bake at 800
After assembling the chamber, we bake it without the trap for several weeks at 200
C. Elimination of Organics
For every element in the system in which the typical component contains organic material, we developed a suitable replacement using ceramic materials, such as the machinable ceramic MACOR (Corning), aluminum nitride (AlN), and aluminum oxide (Al
1) DC Delivery
To bring the 100 dc signals to the trap control electrodes, we use a 100-pin Micro-D vacuum feedthrough. The standard commercial connector for this feedthrough on the vacuum side consists of a PEEK connector with 100 Kapton coated wires. Instead, we use a MACOR version of the connector (Winchester Interconnect) and a series of bare oxygen-free high-conductivity (OFHC) copper wires (AWG28) soldered into the receptacle pins of the connector. These wires are
2) Signal Delivery Circuit Board
The circuit board, manufactured by Millennium Circuits, consists of a 0.059-in-thick substrate of an aluminum-based ceramic. The first chamber built was outfitted with an AlN circuit board [see Fig. 2(b)], while the second has a Al
3) Trap Mounting
Our trap package consists of a microfabricated surface-electrode trap attached to a ceramic package. For future iterations, we plan to use a trap that is attached via a solder process described in [20] as part of the effort to remove all organics. However, the trap currently in the system is attached to its package with an epoxy.
Our package for these traps previously consisted of a 104-pin grid array (PGA), which contained Kovar pins that are then inserted into a zero-insertion-force (ZIF) socket, which is typically manufactured from PEEK. While the ZIF socket could potentially be manufactured out of a machinable ceramic such as MACOR, there was concern that the insertion and removal of traps may be hampered by brittleness of the ceramic with potential damage to the trap and the socket. As such, we replaced the PGA package with a land grid array package consisting of gold-coated pads on the backside of the package.
The trap is then placed on a machined MACOR spacer. The 0.1-in-thick spacer sits on the circuit board and consists of an array of holes matching up with the array of pads, as well as additional holes for ground connections in the center of the package. Gold-plated beryllium copper 0.12-in-long FuzzButtons (Custom Interconnects) are inserted into each slot in the MACOR spacer [see Fig. 2(b)]. The FuzzButtons provide both the path for the signal (or ground) and the elasticity necessary to ensure contact. In addition, the FuzzButtons eliminate the use of the magnetic Kovar pins found on the PGA packages, thus eliminating a potential source of stray magnetic fields near the ion. The trap is placed on top of the MACOR spacer and FuzzButtons, and a custom clamp machined from 316L stainless steel pushes down on the trap to ensure contact. The clamp is designed to ensure that there is no loss of optical access around the trap. It consists of a series of fingers, which clamp onto the package outside of designed laser path [see Fig. 2(c)].
4) Trap rf Delivery
The rf is delivered to the circuit board via an AWG11 bare OFHC copper wire. This rf wire is connected through a barrel connector to another similarly gauged wire affixed to a feedthrough. The chamber serves as the rf ground. The air side of the feedthrough also consists of a ground shield around the extruding wire, with an air gap (custom MPF P/N A19619-1). A helical resonator can is attached to the air side [27].
Given that the qubit splitting in 171Yb+ is 12.642 GHz, it is not feasible to drive the qubit transition using an internal microwave antenna, as any signal would be attenuated drastically without the use of an internal coaxial cable. Because of our restriction on the use of organics inside the chamber, we instead use an external microwave horn to drive transitions.
D. Characterization of Vacuum
We utilize a variety of measurements to characterize our background pressure. The most rudimentary approach, and least informative, is a measurement of the pressure via the ion gauge, as the reading varies considerably based on the controller used and its particular calibration. Additionally, the ion gauge may underestimate the vacuum pressure since it is calibrated to the nitrogen ionization rate, which is larger than that of helium and hydrogen [28]. The two assembled chambers measured pressures of 6e-12 and 4e-12 Torr via their respective ion gauges, but with the same controller. We measure pressures using this controller in other chambers used by our group that do not undergo the organic elimination or the hydrogen mitigation. We find that our QSCOUT chambers outperform the others by factors of 2–5.
Another method we use to examine the background pressure is through background gas–ion collision measurements using a double-well potential [29]. We generate a series of double-well trapping potentials with a variable height barrier [see Fig. 3(a)]. Because hydrogen is the dominant residual gas, we begin with a low enough energy barrier to capture a significant portion of all collisions, 60
(a) Series of slices of the axial potentials used to probe background gas collisions. The central barrier can be increased up to
We monitor the number of distinct jumps that occur at several different barrier heights. At each height, we wait for at least 6 h or 20 distinct jumps before increasing the barrier. Fig. 3(b) is a typical response over one 6-h time window. For each potential, we count the number of jumps a single ion makes between the two sites and estimate the collision rate as twice the observed jump rate to account for collisions in which the ion returned to its original site [18], [29]. This collision rate corresponds to all background gas collisions with the ion that have a kinetic energy along the trap axis that is greater than the barrier height. By raising the barrier height, we aim to understand more about the residual gas species remaining in the chamber. Using a Langevin collision model, we estimate partial pressures of these gases [18]. These pressures may be underestimations since the ion jumps are most sensitive to collisions along the trap axis, and off-axis collisions may not result in an ion jump. As we increase the barrier height, the number of collisions decreases until it flattens out around 2 meV [see Fig. 3(c)]. This behavior suggests that the collisions are dominated by hydrogen, but there are some residual collisions at higher energies. Typically (90% of instances), during experimental runs with chains of ions, a collision will destroy the entire chain. A small fraction of the time, a single ion will go dark, but the chain will remain roughly intact. Regardless of that, the pressure suggested by these collisions is suitable for the purposes of this experiment and shows an improvement of a factor of roughly 2 over other chambers in our group.
Continuous-Wave Laser Delivery
The 171Yb+ ion is one of the predominant ion qubits due to its magnetically insensitive hyperfine states for ultrastable qubit transitions [7], relatively simple hyperfine structure (nuclear magnetic spin
A. Level Diagram and Required Lasers
We load ions into our trap via a two-photon transition of neutral Yb atoms sublimated from a heated source of solid Yb. The two-photon transition first requires a resonant 399-nm photon, which (with isotope selectively) drives the atom into an excited state. If this excitation is followed by another high-frequency photon (
The lasers needed to keep the ion in the qubit subspace [2
Energy-level diagram of 171Yb+ (not to scale) showing lasers used to drive transitions and to keep the ion in the qubit manifold (solid arrows). The magnetic sublevels are shown only for the 2
During Doppler cooling, 14.7-GHz sidebands are added to the 370-nm beam via a Qubig free-space electrooptic modulator (EOM) to prevent the ion from becoming trapped in 2
Applied 370-nm light and sidebands for cooling, optical pumping, and detection (solid blue arrows). Also shown are ion relaxation channels (black dotted lines) and applied 935-nm tones (red solid arrows). (a) For cooling, the 370-nm light is detuned
Finally, the 370-nm laser is also used for state detection, as shown in Fig. 5(c). For state detection, in order to keep the ion in a cycling transition between the 2
The 370-nm light alone is not sufficient to prevent the ion from decaying into nonqubit states. In particular, from the 2P
Collisions can cause the ion to relax to the 2
Finally, another laser that is used for characterization of our system is the 435-nm laser. It is used to perform transitions between the 2
In summary, Table 1 lists the cw lasers used with 171Yb+ and the sidebands applied for various stages of ion initialization and readout. The 399-, 935-, and 760-nm lasers are part of the Toptica MDL-PRO rack mountable system. Fibers route light from these lasers to the experiment.
B. 370-nm Laser Path
The 370-nm laser is the most complicated in terms of locking, modulation, and delivery requirements. The light needs to be referenced to an atomic source and have a linewidth narrow enough (
1) Transfer Cavity Module
The transfer cavity lock module consists of three separate locks. All three objects being locked (two lasers and a transfer cavity) are mounted on a minus-K 100BM-8 benchtop vibration isolation system inside a Herzan acoustic enclosure to protect them from acoustic noise and provide passive temperature stability.
A schematic of the transfer cavity locking system is shown in Fig. 6. The Toptica DLC Pro 780-nm laser is first locked to a stable Rubidium source. We use a side of fringe lock on the lower frequency side of the 5
Schematic of the transfer cavity module. Red and Blue (solid) arrows represent optical connections and dotted black lines represent electrical feedback signals.
The stabilized light from the 780-nm laser is used to lock an SLS-PZT cavity from Stable Laser Systems. The mirror substrates were coated by FiveNine Optics, Inc., to have a finesse of 1000–3000 for 370 and 780 nm; the cavity length is scanned with a piezo. We use a standard Pound–Drever–Hall (PDH) technique [37], [38] to lock the cavity by adding
Next, the stabilized cavity is used to lock the “parent” 370-nm laser (Toptica DL PRO), also using a PDH lock. 19.76-MHz sidebands are added to the light using a free-space Qubig EOM. The cavity reflection is mixed with a stable frequency source equal to the applied sideband frequency, and the resulting signal is used to lock the laser via a Toptica DLC-PRO Lock. The frequency of the parent laser is chosen to be roughly centered between the 171Yb+ and 174Yb+ Doppler cooling transitions. Therefore, the same locking electronics can be used to lock 370-nm experiment lasers to either isotope for diagnostics, calibration, or perhaps sympathetic cooling [40], [41]. Light from the parent 370-nm laser is split in free space and then coupled into fibers that are sent to various experiments and a Toptica High Finesse wavemeter (HF-ANGS WS8-2+1X8PCS) for monitoring.
2) Laser Breakout Board With Beatnote Lock Module
The final laser is the “child” 370-nm laser (Toptica DL-PRO), which is shown on the breakout board in Fig. 10. A small portion of the light from this laser (
Locking electronics and signal for 370-nm child laser beatnote lock. (a) Beatnote lock schematic for stabilizing child laser frequency relative to parent laser (amplifiers and filters not shown). (b) Signal used for locking the child 370-nm laser generated from the electronics in (a). We lock to the downslope of the dip with the highest contrast, as marked with the red circle.
Schematic of 370-nm breakout board (left) and modulation board (right). PBS indicates a polarizing beam splitter, WP is waveplate. AOM SP indicates an acoustooptic modulator in the single pass configuration, while AOM DP is in the double pass configuration (also apparent from the beam path arrows).
The breakout board also sends the light through an IntraAction AOM, which serves as a switch to add extra extinction to the 370-nm light on the ion as needed. The first-order output from the AOM is coupled into a fiber and sent to a modulation board. The zeroth-order output is sent to the wavemeter for monitoring.
3) Modulation Board
At the modulation board, the 14.7- and 2.105-GHz signals are added to the 370-nm light, as outlined in Table 1. As shown in Fig. 10, the light is first directed to the free-space Qubiq EOMs [43] after which it is split into two paths. Each path goes through a double-passed AOM for wideband (up to
4) Light Delivery
Once at the experiment, light exits the fiber and focuses on the ion. Our current layout has two 370-nm beams each at a 45
Schematic of chamber as seen from above, showing layout of lasers. The gold “bowtie” in the center of the chamber shows the trap orientation and the arrow labeled “B field” shows the direction of the magnetic field.
We chose lenses to yield a specific spot size at the ion, such that some beams are elliptical while others are round based on their purpose and angle of incidence. Table 2 summarizes the lenses chosen for each beam and the expected beam size at the ion. For the elliptical beams, the shorter focal length cylindrical lens determines the size of the beam in the direction perpendicular to the trap. The longer lens is aligned so the ion is several millimeters behind the focus of the beam and controls the beam size parallel to the trap. This arrangement results in a beam with minimal scatter on the trap surface, but large enough extent to simultaneously address multiple ions.
We also created custom pieces to stably hold our beam launch optics, which can be seen in Fig. 12. The mounts each start with a Newport 561D-XYZ ULTRAlign stage attached to a custom adapter plate that has a hole pattern allowing us to match the stage position to the holes of the optical breadboard (which differs depending on the position around the chamber). Next, a custom L-bracket is attached to the vertical short side of the translation stage, which holds a goniometer for adjusting the beam's angle (“tip”) as it is focused on the trap. On top of the goniometer is another custom piece, which serves as the adaptor to a Thorlabs cage mount system. For the cage mount rods, we use carbon fiber instead of steel for its stiffness and low temperature sensitivity (though it is unclear if this has been beneficial). The cage system holds and centers the collimators with the lenses and waveplates necessary for light delivery. We use Newport picomotors for remote position adjustment in
Example fiber launch assembly, showing custom pieces for attaching the translation stage to the breadboard, attaching the goniometer to the side of the translation stage, and attaching the cage assembly above the goniometer.
Laser-Based Qubit State Manipulation
While incoherent techniques for manipulating ions, as outlined in the previous section, are important for cooling, state preparation, and detection, quantum computing requires coherent manipulation of qubit states. As mentioned previously, we use the 171Yb+ hyperfine clock transition (
Cartoon of the relevant energy levels for the Raman transition in 171Yb+. The 355-nm light used in the Raman beams spans from the
A. Pulsed 355-nm Laser
We use the Coherent Paladin Compact 355 as our pulsed Raman laser. It is a commercial laser that has a repetition rate around 120 MHz [49] with individual pulses roughly 15 ps long. The pulse repetition rate was selected such that no pair of frequency comb teeth generated by a single pulse train would be resonant with any transition in 171Yb+. This includes the carrier transitions ((
B. Locking
To drive transitions between the
Graphical representation of the AOM-shifted frequency comb and repetition rate feedforward scheme. To drive ion transitions, two frequency combs offset by
Because the laser cavity length sets the repetition rate and thus the frequency comb spacing, it is sensitive to thermal drift, such that
C. Optical Beam Paths
As discussed in the previous sections, our qubit operations are performed using two-photon Raman transitions. Since there are two photons involved, the beam propagation direction(s),
The counterpropagating configuration requires two optical beam paths be directed to our ion chain. When designing these optical beam paths, there are several considerations.
Individual pulses from the laser are 15 ps long; thus, for the pulses to overlap at the ion from separate beam paths, the beam path lengths must match on the submillimeter scale.
Relative beam path lengths must not change due to vibrations or air currents.
We must be able to shift the frequency combs relative to each other in frequency space to address different transitions.
Copropagating and MS gates require two frequency combs from the same direction; thus, alignment needs to hold for a broad range of frequencies.
At least one of the beam paths must be able to individually address the ions.
Each ion requires a laser with distinct frequency, amplitude, and phase control.
Beams must be tightly focused to not overlap with nearby ions.
In the following, we will describe our design and how it allows us to achieve the above requirements. A schematic of the beam paths is shown in Fig. 15. The beam paths include a method for: path length matching on the micrometer scale; carefully designed optical mounts to prevent vibrations; AOMs in both paths to shift the frequencies; optics designed to reimage a wide range of frequencies; one path with multiple beams with independent control of frequency, amplitude, and phase; and finally, optics to create tightly focused beams at the ions with low crosstalk and scatter. To minimize air currents and other environmental disturbances, the entire system is enclosed.
3-D rendering of the optical path for the Raman beams as seen from above. The chamber is mounted to an optical breadboard, with the laser on the optical table below it (not shown). The shared path between the global and individual setups is shown in green, where the light travels from the laser below through the optical breadboard and then passes through polarization optics to set the total laser power and to an AOM, which is used for power stabilization. Then, the light passes through a beamsplitter, where it is split into the two separate paths. The global path (teal) goes to a mirror pair mounted on a stage allowing for path length matching of the beams and then its own AOM for frequency control. The individual addressing beam path (magenta) passes through the 32-channel Harris AOM, where it is first split into 33 beams by a diffractive element. Each beam goes to its own AOM crystal, which modifies the frequency, amplitude, and phase of that beam based on the driving rf signal. After the AOM in each path, there are optics to shape the beams and image all frequencies to the same locations at the ion chain. Also shown are the placement of cw-laser beam delivery subsystems around the vacuum chamber.
1) Global Beam Design
The global beam (represented by the teal beam in Fig. 15) is designed to work either alone, to drive motionally insensitive gates on the entire ion chain, or, with individual beams, to drive motionally sensitive gates on specific ions. To that end, the beam needs to have a nearly uniform spatial profile, the alignment must be stable, and the timing must be aligned to the individual beams.
After splitting the individual path and the global bath at a beamsplitter, the global beam is diverted to a pair of mirrors on a linear translation stage to allow for fine-tuning of the path length without affecting downstream beam alignment. Next, the beam passes through an AOM, allowing for full amplitude, phase, and frequency control of the beam.
To select the global beam size, we needed to ensure that we would not scatter on the surface of the trap and that we would be able to roughly equally illuminate 32 ions. We calculated that a Gaussian horizontal beam with a waist of 160
To achieve these beam waists, we use a cylindrical telescope to change the aspect ratio of the beam by using a concave/convex lens pair, which avoids putting the beam through any unnecessary focal planes. A spherical lens is used to reimage the beam near the final focusing optics to minimize the effects of vibrations and diffraction.
2) Individual Addressing Beam Path
The individual addressing beam path is more complicated than the global beam path, due to the extra requirements of splitting the beam many times, separately controlling each beam, and then imaging each beam on one and only one ion.
We use an illumination module from Harris Corporation, which is a multichannel AOM, which was specifically designed for this application [50] and pioneered at the University of Maryland [51]. It has integrated diffractive optics that splits the single beam into 33 equal and parallel beams, which are sent to 32 separate integrated miniature AOMs (the last beam is blocked internally). Each AOM has an independent rf input from a dedicated rf amplifier. The control signal to the amplifier is generated by an rf system on chip (RFSoC) (or an Octet; more details are in Section VI). It can generate multitone rf signals with arbitrary amplitude, frequency, and phase modulation capabilities, which allows us to exercise complete control over the light applied to each ion. However, the AOM also deflects the beam depending on the applied rf frequency (in our case, vertically). To prevent these deflections from causing different frequencies to have different overlap with an ion, light from the AOM needs to be carefully reimaged onto the ion.
The output of the multichannel AOM consists of 32 parallel beams with an 80-
After the AOM, the beams immediately go through a pair of cylindrical lenses, designed to change the aspect ratio of the beam to the desired 10:1. These lenses were centered using an air-bearing/autocollimator alignment station [52], [53] to ensure that their optical axes were exactly aligned before being bonded into custom mounts. The cylindrical lens assembly was mounted to the breadboard using a Newport LP-1A for
The flexure stage is shown in Fig. 16. It is bolted directly onto a mounting ring on the re-entrant window, registering the lenses to the center of the chamber. Hidden from view in the photo is the relay lens itself, because it is entirely inside the re-entrant bore. The flexure design uses opposing micrometers to align the position in
Image of the five-axis flexure mounted onto the individual addressing re-entrant flange. The parts are 3-D printed from titanium and steel and then assembled before adding the lenses. The optics are aligned to the optical center of the lens (rather than the mechanical center) using external hardware and then bonded in place. By completing relative alignment of the optics, before mounting the flexure stage, we realize greater optical precision than we could achieve by hand. This lends to the achievement of the desired beam waist with few aberrations.
D. Beam Characterization
To determine the quality of our optical alignment, we characterize the beam profile at the ions. For the global beam, a beam profiling camera at the ion location can be used (before the chamber is sealed and baked for vacuum). We measured a beam waist of 10.9
Image of the individual addressing beams skimming across the trap surface. The horizontal features are where the reflected scatter is increased at the edge of trap electrodes. The bottom lines are at the edge of the slot on an HOA trap and the top is the edge of the rf rail. The vertical cones are the beams reflecting from the surface of the trap slightly after the beam waist. This shows beams 1, 8, 16, 24, and 32 (out of 32) from left to right. The imaging system is not designed to be fully diffraction limited at 355 nm and is limiting the resolution of this image, causing the beams to appear fuzzy and jagged, which is not a faithful representation of the beam profiles.
We can shuttle the ion through the beams and extract horizontal beam profiles by driving qubit rotations and averaging the number of detection counts per ion position (200 repetitions per point). The ion position is controlled by voltage solutions that are precisely calculated to a submicrometer scale, resulting in a more accurate measurement of the beam profiles along an ion chain, shown in Fig. 18. The beam profiles confirm that the beam waists and spacings are roughly consistent with the design and that there are no obvious aberrations.
Average number of counts seen on a detector during a 350-
1) Crosstalk
Linear chains of ions spaced closely together have stronger Coulomb interactions, which lead to larger frequency spacings of the motional modes and is advantageous for the practical implementation of fast two-qubit gates. However, having neighboring sites close together increases the probability of optical crosstalk. We measure the impact of the neighboring beams at our 4.5-
Optical crosstalk is determined by the relative Rabi frequency measured when an individual addressing beam is interrogating a neighboring site. By measuring the Rabi frequency versus ion position using counterpropagating Raman beams, we determine the optical crosstalk value to be 2.3(6)% at the neighboring beam location and 0.6(2)% at the next nearest neighbor site. We do not see any clear evidence of electric or acoustic crosstalk on neighboring AOM channels causing an increase in the crosstalk at the ion. The solid line is an empirical Lorentzian fit with a full-width half-max of 1.29
Ion Imaging and Detection
Another piece of hardware for our quantum system is the measurement and detection scheme. As described in Section III, detection is performed by illuminating ions on resonance with a cycling transition accessible to only one of the qubit states. The resulting ion florescence is collected, and depending on the number of photons captured in a particular time, we determine whether the ion is in the
The thresholding technique is very good for a single ion. However, when there are multiple ions, the histograms generated from repeated measurements of two bright ions and one bright ion overlap considerably. At larger numbers of ions, distinguishing between the numbers of bright ions becomes even more challenging. Additionally, for quantum algorithms, it is important to know which ions are bright and dark, instead of just the pure number of bright ions.
To address these issues, each ion has a dedicated PMT to determine if that particular ion is bright or dark. Dedicated PMTs provide increased sensitivity and readout speed compared to commonly available cameras and less crosstalk between channels as compared to a PMT array. To get light to individual PMTs, we image the ion light into a multicore multimode fiber (see Fig. 20). This fiber has 32 separate 50-
Multicore fiber allows us to reimage each ion onto its own fiber and PMT. The result is distinguishable detection with minimal loss and crosstalk. (a) View of the entire single multicore fiber fanning out to 32 individual fibers. These can be easily routed to separate PMTs. (b) View of the multicore fiber tip. The individual cores are indistinguishable in this photo, but the linear arrangement is apparent.
For additional diagnostics, we have a camera (Andor Luca DL-604M-
Schematic of imaging system layout. The motorized flip mirrors deflect the light (dashed arrows) when engaged and pass light straight to the multicore fiber when disengaged. This way, the most sensitive optic is not prone to misalignment by actuating the mirrors.
Since the fiber cores are spaced by 125
A. Detection Crosstalk
To determine the detection crosstalk of our system, we trap a single ion and measure the photons (or counts) on the PMTs connected to neighboring fiber cores. We Doppler cool the ion for 1 ms, optically pump for 10
Detection histogram displaying data from Table 3. Core 2 is centered on the ion, and the corresponding detected events per detected photons show a Poissonian distribution centered at 12 photons (or counts). Cores 1 and 3 are offset from the ion (imaging regions 4.5
Control Hardware
Low-level operation of the experiment, both in its quiescent state and when running experimental sequences, is predominantly controlled via custom field-programmable-gate-array-based circuits. Chief among these circuits are the following:
master control system;
voltage control system;
coherent control system.
The master control system's purpose is to orchestrate sequences involving signals that are used to control cw lasers, digital inputs and outputs, and analog inputs and outputs. It is responsible for processes such as loading ions, Doppler cooling, and state detection. Certain steps in experimental sequences require the master control system to lend operational controls a dedicated subsystem, such as the voltage control system used for shuttling ions or the coherent control system for applying gates. Only the coherent control system will be discussed in detail in order to elucidate the low-level pulse control needed to realize quantum gates. While it is not necessary to fully understand the details of the control hardware to run successful circuits on the QSCOUT, our reasons for providing these details to the interested user and scientific community are twofold. First, one of the goals of the QSCOUT is transparency and offering low-level access. Second, a deeper understanding of the inner workings of certain details of the control hardware will help elucidate specific pulse construction requirements [56], in particular global phase synchronization (see Section VI-A1) and frame rotations (see Section VI-A3).
A. Coherent Control System
The coherent control system uses a custom design, referred to as “Octet,” implemented on a Xilinx RFSoC. It is responsible for generating the rf tones that drive the multichannel AOM. Due to the nature of the pulsed laser system, the control electronics satisfy the following requirements:
radio frequencies ranging from 0 to 409.6 MHz;
two tones per output channel;
full waveform generation in the digital domain;
global phase synchronization;
gate sequencer, which does the following:
schedules pulse sequences used to realize gates;
provides simultaneous control over frequency, phase, amplitude, and virtual
-rotations for all tones and channels. All parameters support discrete and smooth modulation using an on-chip spline interpolator [57];Z
dynamic correction for certain imperfections in the experimental hardware including the following:
frequency feedback to account for pulsed-laser cavity drift;
crosstalk cancellation that adds output signals to nearest- and next-nearest-neighbor channels with tunable amplitude and delay.
The details of these features and how they are used for pulse-level control differ from other standard rf delivery systems. While many of these elements are separately optimized and are not exposed to the end user, several features are directly accessible. Knowledge of how they work is vital to understanding how to write custom gates at the pulse level. The latter features and how they are controlled are broken into separate categories.
1) Global Phase Synchronization
One of the main challenges of coherent control is the ability to have absolute control over the rf phase. However, in most systems, this is difficult; it either requires several independent frequency sources that are separately mixed or a lot of manual phase bookkeeping. Using multiple frequency sources and mixing them externally does not scale well, and undesired phase shifts from changes in amplitude and frequency complicate calibration routines. Manual phase bookkeeping allows one to repurpose synthesizers by changing their frequency output. However, this comes with additional challenges and can add computational and data overhead.
A direct digital synthesizer (DDS) can be represented as three main pieces: a phase accumulator,1 a separate summer for shifting the phase accumulator output by a fixed phase value, and a lookup table (LUT) to convert the phase to a sinusoidal amplitude, as shown in Fig. 23. In the case where manual bookkeeping is used, either the external phase input,
Diagram highlights the key elements for a simplified model of a DDS. The first component is a phase accumulator, which is represented as a summer that adds a frequency word,
In the QSCOUT Octet system, phase synchronization is handled using a separate paradigm, in which a global phase is constantly being calculated on chip, as shown in Fig. 24. In this case, a counter (represented as an accumulator with a unity frequency word) is multiplied by the DDS frequency word and updated on every clock cycle. This counter then tracks the global phase for any given frequency by calculating
Modified form of the simplified DDS. A free-running counter tracks the global time,
While each Octet board contains 16 custom DDS modules, resulting in eight output channels each comprising two tones, there is only a single global counter common to all DDSs. This counter is effectively nulled when the board is power cycled and initialized. Thus, no assumptions should be made about the absolute value of the global counter. Proper usage of the synchronization mechanism requires that every pulse for which the rf frequency and phase are reused should be applied with a synchronization operation. The absolute phase of the first pulse is effectively random in this case, as it depends on the value of the global counter. As long as the first pulse is synchronized, the phase of the Bloch vector will be set relative to the global phase. Subsequent pulses, for which phase synchronization is also applied, are guaranteed to be properly phase aligned not only to earlier pulses at the same frequency, but the phase alignment is identical across all tones and channels. This is particularly important for the two-qubit MS gates [see Fig. 25(a)], in which the red and blue sideband frequencies form a beat note.
Diagram of red (red arrows) and blue (blue arrows) sideband transitions used in a two-qubit Mølmer–Sørensen gate.
In this case, the global phase of the MS gate is set by the relationship between the phase of the beat note and the phase of the frequency resonant with the qubit transition. Because the QSCOUT system qubit laser drives Raman transitions, any single transition is driven via a beat note given by the difference frequency of the two legs of the Raman transition. This means the two-qubit gate picture is in reality a bit more complex, as shown in Fig. 25(b), and the phase of the beat note between the red and blue sidebands determines the global phase of the MS gate.
Fortunately, this imposes the requirement that the beat note formed by the sidebands needs to be phase aligned only to the relevant leg of the Raman transition. This alignment is easily achieved by using the built-in phase synchronization on the desired tones. However, one of the caveats when working with any type of digital hardware is discretization effects, which can lead to subtle rounding errors because the frequency is limited to a depth of 40 bits. The frequency word,
\begin{equation*}
F\left(\nu \right) = \text {round}(\nu /f_s\times 2^{40}) \tag{1}
\end{equation*}
These rounding errors can play a larger role when the secondary beat note is involved. For example, the beat frequency generated by the sideband tones is given by
\begin{equation*}
\begin{aligned} f(t) &= \sin (\omega _b t + \phi _b) \sin {(\omega _r t + \phi _r)} \\
&= \frac{1}{2}\left[\cos {\left((\omega _b-\omega _r\right)t + \phi _b-\phi _r)} \right.\\
&\qquad \left.\,- \cos {\left((\omega _b+\omega _r)t+\phi _b+\phi _r\right)}\right] \end{aligned} \tag{2}
\end{equation*}
\begin{equation*}
2\omega _{\text{carrier}} = \omega _b + \omega _r. \tag{3}
\end{equation*}
\begin{equation*}
\begin{aligned} \omega _{\text{carrier}} &= 2\pi \times 228 732 824.32571054 \text{s}^{-1} \\
\omega _{\text{SB}} &= 2\pi \times 2 235 174.1793751717 \text{s}^{-1}. \end{aligned} \tag{4}
\end{equation*}
\begin{align*}\begin{aligned} &F_{\text{carrier}} = \text {round} \left(\frac{\omega _{\text{carrier}}}{2\pi f_s}\times 2^{40}\right) &=307 000 000 000 \\
&F_{r} = \text {round}\left(\frac{(\omega _{\text{carrier}}-\omega _{\text{SB}})}{2\pi f_s}\times 2^{40}\right) &= 304 000 000 000\\
&F_{b} = \text {round} \left(\frac{(\omega _{\text{carrier}}+\omega _{\text{SB}})}{2\pi f_s}\times 2^{40}\right) &= 310 000 000 001.\\
\end{aligned}\end{align*}
2) Frequency Feedback
Drift in the cavity length of the pulsed laser that is used for driving quantum transitions is not actively corrected at the source. Instead, we use a scheme similar to [58] to correct for frequency errors by feeding forward frequency corrections due to variations in the laser's repetition rate. Variation in the repetition rate leads to a “breathing” of the frequency comb that is generated by the pulsed laser. In order to bridge the 12.642-GHz qubit transition, the frequency difference between the Raman beams is set such that the closest integer harmonic is shifted into resonance with the qubit transition. This means that the frequency error due to variations in the repetition rate must be amplified to account for the net frequency deviation at the target harmonic.
Details of how the repetition rate signal is monitored and converted into a useable signal for locking is described in Section IV-B. This signal is passed into the RFSoC via one of the fast ADC inputs integrated on the chip. The frequency lock involves a complex mixing stage between the ADC data and a dedicated DDS core in the firmware design. The mixed output is sent to a proportional-integral-derivative (PID) module that feeds the error back onto the dedicated DDS to create a phase-locked loop that tracks the repetition rate. The accumulated error is then optionally forwarded to the various output tones and subsequently multiplied by the appropriate harmonic, depending on the specific details of the coherent operation or gate being applied. Different locking configurations arise because the feedforward correction must add a relative shift to the tones that are used to realize the Raman transition. In other words, one tone must be shifted by an additional amount to keep the frequency offset of the desired harmonic fixed relative to the other Raman beam. The feedforward correction differs in sign, depending on which leg of the Raman transition the correction is being applied.
Since the correction depends on the integer harmonic and its sign, both of which are not dynamically configurable on a per-gate basis, the user need not worry about the specific details of the underlying lock settings. It is instead more important to consider when the feedforward correction should be applied and to which tones. There are two basic rules of thumb the user should follow.
Each Raman transition consists of two tones, where exactly one of those tones should have a feedforward correction applied.
The feedforward correction is applied to the higher frequency tone.
Following the above conventions, frequency feedback for single qubit rotations is straightforward. Whichever tone is higher in frequency receives the feedback, regardless of whether it is copropagating or counterpropagating. However, for the MS gate, red and blue sideband frequencies could be defined around
3) Frame Rotations
Virtual
Because the frame rotations are specific to the frame of the qubit itself, different configurations are required for how this phase is applied. For example, the phase of a single-qubit gate is determined by a phase difference between the two legs of the Raman transition. Applying a positive phase,
Copropagating gates must have the virtual
4) Gate Sequencer
The Octet design contains two separate modes of operation, which we refer to as static and dynamic. These modes are not mutually exclusive and are always running at the same time from the perspective of the DDS module. In other words, the DDS is always taking into account separate inputs corresponding to both modes and constantly combining the various input parameters based on their type. Static mode is meant for slow updates, where output channels can be set to a specific frequency, phase, and amplitude with an overall scale factor. Static mode also includes settings for the frequency feedforward target harmonic and crosstalk compensation settings (see Section VI-A5). These settings, which are not exposed to the end user, are primarily used for other experimental operations, such as to assist with ionization when loading ions or adding slow drift corrections.
Dynamic mode is designed for running time-critical sequences of pulses that are used to realize quantum gates. The final static and dynamic values for frequency, phase, and amplitude are simply added together, and the overall scale factor reduces the overall amplitude, each at the hardware level. However, the user should assume that the static mode settings are all zero, except for a unity overall amplitude scaling.
Dynamic mode uses a firmware module, referred to as the “Gate Sequencer,” that is fitted with fast LUTs for recycling pulse data and a set of spline interpolation modules (or “spline engines”) for carrying out parameter modulation. The spline interpolation scheme is based on a NIST design [57] which maps the spline coefficients such that the interpolator can be modeled as a chain of accumulators. This method uses third-order polynomial B-splines or 1-D cubic splines.
The Octet uses spline engines for frequency, phase, amplitude, and frame rotations for both tones on all channels. Because each set of coefficients is calculated for a precise number of time steps or clock cycles, each set of coefficients, as well as the number of clock cycles, is sent as a single word to the hardware. Each word contains four 40-bit coefficients,2 a 40-bit duration, and various other metadata bits used for controlling extra operations, such as phase synchronization, internal routing, and programming information. For uniformity, and to match natural bus widths in the design, the total word size is 256 bits. It has the same format for all spline engines.
Each output channel has a dedicated gate sequencer module, each of which contains a data arbitration module, fast LUTs, and eight spline engines with first-in first-out (FIFO) buffers, as shown in Fig. 26.
Gate sequencer spline engine layout. Each parameter has a dedicated spline engine, each of which is fed by a 256 deep FIFO. Incoming data for the particular channel are routed through a data arbitration module and a series of LUTs for recycling data.
Incoming data fill the FIFOs until the gate sequence is either exhausted or the FIFOs are completely filled and present a blocking condition. An external trigger simultaneously enables all spline engines, which will consume data until the FIFOs are empty or a wait for trigger flag is encountered in the metadata, at which point the spline engines will wait for another external trigger.
Because each data word carries its own timing information, each spline engine can consume data at different rates and runs independently from other spline engines. As a result, the number of spline knots per parameter for a given pulse need not match. Rather the total sum of the duration arguments for each parameter should match at the gate level or, in the most extreme case, match the total elapsed timing between wait for trigger flags. Asymmetry between the numbers of spline points mainly imposes additional requirements on the order in which the data are sent. This is done in such a way that FIFO blocking for one parameter does not starve another FIFO. This situation is avoided by properly interleaving data based on parameter type and time-sorting data. Each output channel has a dedicated gate sequencer, where each gate sequencer is fed from a common arbiter. It has a structure almost identical to Fig. 26, except that the spline engines would be replaced with gate sequencers, and each gate sequencer feeds a separate DDS. Ultimately, eight channels, each with eight parameters, have to be run simultaneously. They are, however, fed serially. Thus, blocking conditions can arise from parameter FIFOs and channel FIFOs. The data sorting must also take into account ordering of all 64 parameter FIFOs across channels.
The overall model requires that all spline engines are consuming data during a circuit, even if the data are equivalent to a NOP (no operation), so that data are properly aligned at a later time when the value is potentially nonzero. Specific channels and parameters can, in fact, be disabled to reduce overall data for smaller circuits and calibration routines, but this is generally not needed or used. Ignoring potential optimizations, at least one word for each parameter must be provided to describe a gate, which is a minimum of 2 kb of data per gate. This amount of data can add up for long datasets, where latency between circuits needs to be minimal. For an exhaustive protocol such as gate set tomography (GST) [60], the total number of gates used can easily be on the order of
Gate sequencer LUT layout. Incoming words are, depending on metadata, optionally routed through a cascade of LUTs for reading out the associated pulse data on all parameters and subsequently routed to the correct spline engine input FIFO. Gate IDs can be densely packed in single words to improve overall throughput. These IDs are passed through an initial table to determine the memory bounds that need to be iterated over in a secondary LUT, which provides the final address associated with the final raw pulse data LUT.
The “Pulse LUT” (PLUT) contains raw data words, such as those used in the streaming case, that need to be forwarded to a particular spline engine FIFO. However, a particular gate may contain a large number of PLUT entries, which all need to be sent out to their respective FIFOs. Moreover, two gates might have common PLUT entries, and to reduce overall memory usage, all PLUT entries are generally unique. For example, a simple square pulse X-gate will contain eight data words, but the equivalent type of Y-gate will be identical with the exception of a single phase word; thus, a total of nine PLUT entries are needed to describe both gates. Because PLUT entries are unique and often shared among different gates, a secondary “Memory Map LUT” (MLUT) is used to create dense arrays of pointers in a linear address space. In other words, stepping through a particular set of MLUT addresses will return a series of address words of the PLUT entries needed to describe a particular gate. Gates are then encoded using a set of MLUT address boundaries, packed into a single data word and stored in the “Gate LUT” (GLUT), the output of which is connected to an iterator module for reading out a sequence of MLUT addresses. The GLUT address size is currently set to 6 bits, but it can easily be reconfigured in firmware, and sets the ultimate compression ratio for the data and an upper bound on the number of unique gates that can be stored locally. Data still must be sent in 256-bit words and, because of metadata constraints, the number of 6-bit GLUT address words, or “gate IDs,” which can be packed into a 256-bit word is 36. This gives a compression ratio of
While it may seem that the additional overhead for programming the LUTs may, in some cases, encumber the data flow because of additional words needed to program the LUTs, the LUT approach can artificially increase FIFO depths and offers more flexibility. Because programming data and sequence data can be packed into single 256-bit transfers, the total number of data words to program and stream a simple square pulse gate is
The maximum LUT size is determined by constraints in the fabric and is dominated by the PLUT, which contains
5) Crosstalk Compensation
Crosstalk effects induce undesirable rotations on nearest or next-nearest-neighbor qubits, and they can arise as a result of several possible sources. Optical crosstalk can arise from larger individual addressing beam waists in which a small proportion of stray light is incident on the ions. Other sources of crosstalk are due to unintended driving of neighboring AOM channels, either from electrical crosstalk between transducers or from sympathetic vibrations between crystals. Compensating for these effects requires applying cancellation tones on nearest- and next-nearest-neighbor channels. Cancellation tones need to match the waveforms applied to the neighboring channels, but with a reduced amplitude and, for electrical or acoustic crosstalk, a delay.
To prevent frequency- and amplitude-dependent phase shifts associated with external rf components, crosstalk signals are added digitally in firmware. Coarse delays are, thus, resolution limited by the 409.6-MHz clock used to transfer data. However, fine-tuning the delay can be approximated by applying an overall phase shift to the neighboring output before it is added onto the target channel's waveform. Multiplying the waveform data in the complex domain gives full control over relative phase and amplitude.
Crosstalk compensation could be implemented to support infinite feedback, where the output of one DDS channel is added to its neighbor, and the modified output from the neighbor is added back into the original channel ad infinitum. This implementation has some advantages, in the sense that it can be used to compensate crosstalk compensation signals themselves. In other words, the compensation signal applied to channel 5 that accounts for the output on channel 7 can be further echoed to channel 3, which is compensating for the output on channel 5. The downside of this approach is that the implicit delay is bounded by the latency of the digital signal processing (DSP) elements in the design that are used to scale and add signals from neighboring channels. Instead, the initial version of the Octet design only applies signals from the uncompensated outputs onto neighboring channels. The uncompensated signals are passed into a delay line to match the latency of the DSP elements that are used to scale and add the compensation signals coming from neighboring channels. This allows for optical crosstalk compensation, where the compensation signals must be perfectly synchronous with the original signal.
Performance
The previous sections outlined the hardware and design decisions that went into the QSCOUT. Here, we discuss some of the experiments where we tested the performance of the overall system. These experiments were performed on either one or two ions.
A. Coherence Times
Ions are generally known for their long coherence times, and the QSCOUT system is no exception. Coherence times are typically limited by such factors as the reference clock, external magnetic fields, and noise (from vibrations and power supplies). Fortunately, since we are using a hyperfine qubit and Raman transitions, we are less sensitive to overall phase noise than an ion that has qubit states separated by an optical transition [61]. To reduce the impacts of these factors, this experiment uses an ultrastable Cesium clock CsIII Model 4310B from Microchip with a TSC 4145C OP01 quartz ultra clean-up oscillator to provide a reference 10 MHz to all of our hardware. The specified drift is 3e-13 from 1 to 100 s [62], [63], which allows our microwave coherence times to be long enough that they are limited by ion heating on our current trap devices. Permanent SmCo magnets in a 3-D printed ring mounted to the chamber produce the external magnetic field. These produce a field strength of approximately 4.37 G at the ions that is fairly insensitive to changes in temperature at
To characterize the coherence time, for each configuration, we performed a Hahn echo experiment [65] to estimate the T
(a)
The second method for characterizing the coherence times is a pulse sequence of
1) Microwaves
Coherent microwaves can be used to drive the qubit frequency directly. To deliver the microwaves to the ion, we use a microwave horn (Pasternack PE9855/SF-10). This horn is mounted externally to the chamber, and the alignment is optimized to achieve the highest Rabi frequency. Typical microwave Rabi oscillations are shown in Fig. 29(a).
Typical Rabi oscillations using (a) the microwave horn with a typical
The microwave frequency is generated by single-sideband modulation of a 12.6-GHz oscillator by an approximately 42.8-MHz signal from the RFSoC (see Section VI), which allows for full frequency, phase, and amplitude control. The detailed description of the microwave frequency generation can be found in [67].
2) Laser Gates
Our method for using a pulsed laser to drive Raman transitions for qubit manipulation is described in Section IV. Just as in the case of the microwaves, the phase, frequency, and amplitude of an rf tone applied to an AOM are controlled by the RFSoC. Examples of Rabi oscillations from the 355 laser are shown in Fig. 29. Typical
B. Gate Fidelities
Gate fidelities are determined by using GST. This is a characterization method developed at Sandia, which gives a full tomographic description of gates, by performing pulse sequences to efficiently determine errors. For a full explanation of GST, see [67]. For a single ion, GST probes
Additionally, we implemented GST using BB1 gates for our
The results from our gates are compared to an overcomplete basis set from a “black box” model to determine the gate errors. As a result, we get a wealth of information, including gate decompositions, gate error generators, and other traditional fidelity metrics, which can be used to determine the sources of some gate infidelity. A summary of our typical GST result showing gate fidelity and rotations is in Table 4.
C. RF Stability
To achieve consecutive high-fidelity gates, the motional modes of the ion need to be consistent from one gate to the next. The two-qubit gate, in particular, is sensitive to the motional mode frequencies and can suffer fidelity loss if the modes at run time are different from those when the gate was calibrated. Mode drift during the gate will also result in errors, but for now we assume that drift is slower than the timescale of the gates. We track the stability of our radial modes over time to determine the stability of the system (see Fig. 30). Short-term variation (
Measurements of radial secular frequencies for a single ion over the course of 10+ h. Both the red and blue sideband of the horizontal and vertical radial modes are tracked. The bandwidth suggests a short-term stability of 200–300 Hz, and a long-term drift of a few kilohertz. These drifts are small enough to achieve our gate fidelity goals.
D. Crosstalk Compensation
As discussed in Sections IV-D1 and VI-A5, we have the ability to compensate optical crosstalk from a gate being driven on one ion onto its nearest neighbor and next nearest neighbor ion. As a demonstration, we apply a counterpropagating pulse of varying duration on one ion, qubit 0, and measure its effect on its nearest neighbor, qubit 1, sitting 4.5
(a) Rabi oscillations driven on qubit 0 (red) and corresponding natural crosstalk-driven Rabi oscillations seen on qubit 1 (green). Before any crosstalk compensation, Rabi oscillations seen on qubit 1 are about 4.1% of the original signal on qubit 0. (b) After compensation through the Octet hardware (original signal with an amplitude of 0.034 and a phase shift of 68
E. Two-Qubit Gate
Two-qubit entangling gates are performed using MS gates [46] and shown in Fig. 32. After performing an MS gate, to verify the resultant state is a Bell state, we apply a
Mølmer–Sørensen two-qubit gate is performed between two ions. (a) For a pulse duration of 200
F. Micromotion Compensation and Recalibration
Excess micromotion in this system is compensated using a variety standard techniques, for instance, the “resolved sideband measurement” technique [71], as well as a custom “chirped tickle” (see Section VII-F1) technique. This calibration is done daily and before any user code is run on the system. Since the system is not yet fully automated, recalibration is performed when the operator notices a decrease in gate fidelity. This occurs on the order of a few hours4 and seems to stem mostly from drifting electric fields moving the ions, so they are no longer centered in the tightly focused laser beams. The recalibration procedure may consist of simply using the voltage on the trap to recenter the ions in the beams. Sometimes, a full recalibration is required, which includes micromotion compensation, measuring the secular frequencies and measuring the Rabi rates. The procedure can take between 5 and 20 min.
1) Chirped Tickle Compensation
Resolved-sideband micromotion minimization is limited to compensating along directions that overlap with the interrogation lasers. Alternative techniques exist [72], [73], where Doppler-enhanced fluorescence is amplified by parametrically heating motional modes of the ions. This approach requires rotating the principal axes of the confining potential such that they overlap both the axis of the laser used for detection and the micromotion axis to be adjusted, allowing compensation along directions orthogonal to laser beam axes. This technique, however, requires many scans and can be slow. We use a variation of this technique, which we refer to as “chirped tickle,” which can yield a substantial speedup and calibration times comparable to resolved-sideband micromotion minimization.
Modulating the rf confinement by the secular frequency of one of the off-axis modes will induce a large motional excitation. This excitation can be measured by an increase in ion fluorescence induced by a laser that is sufficiently red-detuned from resonance.5 Because the motional sideband excitation is proportional to the strength of the rf field at the ion, the amplitude of the micromotion, and thus the measured fluorescence, decreases as the ion approaches the rf null.
In surface-ion traps, anharmonic components of the confining potential are greatest in higher order
Instead, we use a variation on the 2-D tickle scan, in which we modulate the rf confinement using a frequency chirp. The chirp is implemented via a continuous linear piecewise (triangle wave) frequency modulation, where the bounds are determined by the overall range in secular frequencies we expect to observe while sweeping the
The experimental step is now reduced to a single 1-D scan of the shim field with only a Doppler cooling stage, during which the ion fluorescence serves as the measurement for each value of the shim field. Each shim field point generally takes 300 ms. In practice, the ramp and acquisition times are generally fixed, and the upper and lower frequency bounds for the chirp as well as the overall amplitude of the modulation are varied to sufficiently excite the mode. For wider scans, parametric heating occurs over a proportionally smaller range of the chirp, which may require increasing drive amplitude to maintain a favorable signal-to-noise ratio (SNR). If the drive amplitude is too large, the frequency range of the chirp is too small, or the ramp times are too long, the ion can be excited so strongly that it is lost from the trap.
Once a reasonable set of parameters are determined, these “chirped tickle” scans can be performed over wide shim field ranges (several kV/m) for preliminary6 calibration without ion loss, as well as narrow ranges (1–100 V/m) with larger SNR for final calibration. In each case, the total time for a scan generally takes 1–2 min depending on the number of points. Because the acquisition times are an even multiple of the chirp period, the experimental process is greatly simplified, and the initial phase of the chirp has no impact on the measurement. We use a Tektronix AFG3102 function generator and simply enable the output for the entire duration of the scan. Moreover, initial tuning of parameters and even rough calibrations can be done by manually adjusting the shim fields and simply observing fluorescence, while the chirp is enabled. An example of one of the scan outputs is shown in Fig. 33. Depending on the scan parameters, the resolution of this technique can be
Ion fluorescence per shim field in the
Some special considerations must be taken into account when doing a chirped tickle. Insufficient bounds on the chirp can lead to a sharp drop off in the fluorescence signal if the motional mode frequency moves out of this range. Intensity variations of the cooling beam can lead to a background signal that has some curvature, in which case steps may need to be taken to account for background subtraction. Finally, if the range of chirp frequencies is large enough to span the fundamental mode frequency and its harmonics, there can be interference effects depending on the relative phase of the drive frequencies during the chirp. However, using a chirp span that is roughly matched to the expected range of secular frequencies, and keeping the range of shim fields small enough to neglect background curvature associated with the beam profile, this method can easily provide quick calibrations with clean signals.
Summary
In summary, this document has outlined the major decisions and implementations to build a quantum processor of up to 32 qubits based on trapped ions. It has created a blueprint for the current QSCOUT machine, with an emphasis on new technologies that enables expanding from one or two qubits to many. In particular, the major new technology introduced in this article is the Octet system for providing frequency feedback, frame rotations, and gate sequencing, which is described in Section VI. Other new technologies include engineering chamber internals to eliminate all organics in the chamber, optical design of 355 laser paths, custom mechanical mounts for sensitive optics, and the chirped tickle micromotion compensation technique. The details included are to assist QSCOUT users and potential users in evaluating the system for their algorithms, help them tailor programs for best chance of success, and help outside experimental trapped ion groups build their own systems.
QSCOUT Specifications Summary
Tables 5–8 are included as a reference for the user. They are the QSCOUT specifications, including general settings and parameters, infidelities and errors, and approximate gate durations.
ACKNOWLEDGMENT
The authors would like to thank Marko Cetina, Alan Bell, Ken Brown, Jungsang Kim, and Bert Tise for many useful discussions. This article describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the U. S. Government. SAND2021-3837O.