The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion–based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation–based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error–threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects.

Keywords

With appropriate modifications, photonic interconnect regions can be added to this blueprint, therefore allowing our microwave trapped ion quantum computer modules to also be connected using photonic interconnects, making the modules useful for alternative architectures proposed so far ( 9 , 10 ).

Architectures based on photonic interconnects have great potential for scaling up quantum computing ( 9 , 10 ); however, the interaction rate between modules and therefore the speed of a computer based on these is typically slow ( 14 ) compared to the execution time of other quantum operations ( 2 , 4 , 15 ). We propose an alternative method of scaling to a large number of modules based on technology that aligns modules next to each other, enabling ion transport between adjacent modules. A universal two-dimensional architecture is then formed by fast transport ( 16 , 17 ) of qubits from one module to adjacent modules. A suitable high error–threshold error correction code that only relies on nearest-neighbor interactions was developed by Fowler et al. ( 18 ) and can be implemented using this architecture.

In previously proposed trapped ion quantum computing architectures, modules are powered by laser-driven single- and multiqubit gates. However, the vast amount of individually controlled and stabilized laser beams required in such architectures would make the required engineering to build a large-scale quantum computer challenging. Here, we propose an architecture that is based on a concept involving global long-wavelength radiation and locally applied magnetic fields ( 12 ). The gate interactions are based on a mechanism first proposed by Mintert and Wunderlich in 2001 ( 13 ), making use of magnetic field gradients within dedicated gate zones. Only global laser light fields are required for loading, Doppler cooling, and state preparation and readout of ions, whereas laser-driven quantum gates requiring careful alignment in each gate zone are not required in our approach. Large-scale quantum computers, which rely on laser gates and are capable of solving classically intractable problems, may require millions of individual laser beams that have to be precisely aligned with respect to individual entanglement regions and need to be individually controlled. In our microwave-based architecture, all laser fields do not have to be precisely aligned or individually controlled. However, one should note that our architecture still incorporates a number of technical challenges, such as the creation of strong magnetic field gradients and the requirement of calibration operations and well-controlled voltages, which are required to execute quantum gates. We present the blueprint for a scalable microwave trapped ion quantum computer module, which is based on today’s silicon semiconductor and ion trap technology. The modules, driven by global laser and microwave fields, perform ion loading and ion shuttling, generate locally addressable magnetic fields as well as magnetic field gradients to perform single- and multiqubit gates, and feature on-chip photo detectors for state readout. All gate, shuttling, and state readout operations are controlled by on-chip electronics, and a cooling system is integrated into the module to allow for efficient temperature management. Each module, when placed in an ultrahigh vacuum (UHV) system and powered by global laser and microwave fields, operates as a modular stand-alone quantum computer.

An important challenge toward building a large-scale trapped ion quantum computer still remains: the development of a detailed blueprint for the individual modules that need to be capable of performing all required fundamental quantum operations and ideally act as a stand-alone small-scale quantum processor. Each module must also offer efficient connections with additional modules to create a universal quantum computer architecture.

The concept of using ion transport on microfabricated trap arrays to realize an ion trap quantum computer was proposed by Kielpinski et al. ( 8 ). Developing a comprehensive quantum computing architecture with trapped ions has since attracted a lot of interest. Recently, an approach addressing this was developed by Monroe and Kim ( 9 ) and Monroe et al. ( 10 ), where ion trap modules, also called elementary logic units, are photonically interconnected using commercial fibers and optical cross-connect switches. This proposal demonstrates that going from one to many modules is within reach of current technology and thereby provides an interesting path to a large-scale ion trap quantum computer. Theoretical investigations of this approach have shown that it can be used for fault-tolerant quantum computing even in the presence of noisy and lossy links ( 10 ) when combined with entanglement purification ( 11 ).

RESULTS

Microwave-based quantum gates Single- and multiqubit gates, executed with high fidelity, are essential building blocks of a universal quantum computer. For trapped ion quantum computing, internal states of atomic ions serve as qubits, and the Coulomb interaction between closely spaced ions makes conditional quantum gates with two or more qubits possible (1). Precisely aligned laser beams have predominantly been used to couple the dynamics of internal qubit states and motional states and thus implement multiqubit gate operations. This has led to the experimental demonstrations of multiqubit gates with up to 14 ions (19) and the demonstration of a two-qubit gate in the fault-tolerant regime (15). Nevertheless, there are challenges with the abovementioned implementations when trying to scale them up to a large number of qubits and when trying to increase the gate fidelity further to reduce the overall system size. Technical challenges when operating the large number of laser beams required for a large-scale quantum computer system include intensity and phase fluctuations, frequency drifts of the laser output, micrometer-precise beam alignment, beam-pointing instabilities, and nonperfect beam quality. In addition to the technical challenges, off-resonant coupling to states outside of the qubit subspace when using Raman beams can pose an additional challenge. A promising solution to the stability and scalability challenges that come with using lasers to implement large-scale multiqubit gate operations was proposed by Mintert and Wunderlich in 2001 (13) and makes use of microwave radiation in conjunction with a static magnetic field gradient. Microwave radiation has since been used to perform single-qubit gates with unprecedented fidelity (2, 20), featuring an error per gate as low as 10−6 (2), and when combined with locally adjustable magnetic fields or magnetic field gradients, individual addressing of closely spaced ions has been demonstrated with cross-talk as low as 10−5 (21). Coupling between internal states of trapped ions and their motion, necessary for multiqubit gates, is induced by electromagnetic radiation. Because of the long wavelength (on the order of centimeters), this coupling is vanishingly small for free-running microwaves and is, thus, not useful on its own for multiqubit gate operations. However, when adding a static magnetic field gradient, which exerts a force due to the magnetic moment associated with the qubit states of the trapped ion, multiqubit gates can indeed be implemented (13). This magnetic field gradient–induced coupling was first used to implement a two-qubit gate between nearest and non-nearest neighbors by Khromova et al. (22). Besides using a static magnetic field gradient to implement multiqubit gates, one can also make use of microwave near-field gradients (23), which has been demonstrated in the pioneering work of Ospelkaus et al. (24). A challenge when using the static magnetic field gradient scheme stems from the requirement of the qubit to be made up of at least one magnetic field–sensitive state. This limits the achievable coherence time and gate fidelities because of uncontrolled magnetic field fluctuations (22), and measures have to be taken to shield or compensate these fluctuations. An efficient method of obtaining a qubit that is robust against magnetic field noise is by making use of microwave dressed states (7, 25). These dressed states have been shown to exhibit a coherence time three orders of magnitude longer compared to bare magnetic field–sensitive qubit states and have already been combined with a static magnetic field gradient to cool a single ion to the quantum ground state of motion using long-wavelength radiation (26). Using these dressed states that give rise to quantum-engineered clock states, a high-fidelity two-qubit gate has recently been demonstrated (12), with the method being capable of producing fault-tolerant quantum gates. We note that recent work has shown the possibility to cancel the carrier transition during two-qubit gate operations, which is expected to permit much faster gates (7, 27). For the design of a scalable quantum computer module, it is highly advantageous to be able to rely on the matured and commercially developed field of microwave engineering, allowing stable microwave and radio frequency (rf) fields to be generated at comparably low cost and, for a typical user, with a fraction of the complexity of laser systems. Furthermore, microwave radiation can naturally address a large spatial volume, making it very useful when scaling a given operation to many ions. Static magnetic field gradient–induced couplings based on the approach outlined by Weidt et al. (12) will therefore be used as a basis for two-qubit gate operations within individual modules described here.

Description of individual quantum computer modules We propose a blueprint for a scalable quantum computer module, which makes use of the discussed microwave-based multiqubit gate scheme and is fabricated using silicon microfabrication technology. Each module is a unit cell for a large-scale quantum computer and features microfabricated ion trap X-junction arrays (28–30). In each X-junction, two or more ions are trapped and feature up to three different zones, as shown in Fig. 1A, including a microwave-based gate zone, a state readout zone, and a loading zone. Once an ion is trapped in the loading zone, high-fidelity ion shuttling operations (16, 31) transfer the ion to the gate zone. There, ions can be individually addressed using locally adjustable magnetic fields and entangled using static magnetic field gradients in conjunction with global microwave and rf fields. When the state of the qubit needs to be detected, the ion is transferred to the readout zone, where global laser fields and on-chip photo detectors are used for state readout. A second ion species is used to sympathetically cool the qubit ion without affecting its internal states (32). All coherent quantum operations are performed and controlled by on-chip electronics, relying only on global microwave and rf fields. In our microwave-based architecture, laser light is only required for state preparation and detection, photoionization, and sympathetic cooling. The required laser beams have much less stringent requirements than laser beams for quantum gate realization. The laser beams do not need to have high intensity, and do not need to be phase-stable; the mode profile only requires some overlap with the ion to scatter sufficient photons. Laser beams for sympathetic cooling can even be provided as sheets. Fig. 1 X-junction with multiple zones and corresponding layer structure. (A) X-junction featuring multiple zones, including a loading zone (marked red) in selected junction. Multiqubit gates are performed after bringing two or more ions (green balls) together in the gate zone (marked green). The gates are performed by applying a static magnetic field gradient produced by current wires placed underneath the electrodes. State readout is carried out in the readout zone (marked blue) using global laser fields and photodetectors placed underneath the electrodes. (B) Layer structure of the ion trap chip consisting of HR silicon substrate and copper current wires embedded in the silicon. Conductive and insulating layers form buried wires, VIAs, through-silicon VIAs (TSVs), and electrodes. (C) Left: Illustration of the rf pseudopotential at the ion height of the proposed optimized X-junction geometry. Right: Remaining rf barrier experienced by the ion when moving through the rf minimum along the z axis. The rf minimum becomes an rf null inside the entanglement region. This simulation was performed for a 171Yb+ ion for an ion height of 100 μm and using a drive frequency and voltage of 25 MHz and 200 V, respectively. The design of the X-junction, individual zones, control electronics, cooling, and alignment system of the modules will be described in detail in the next paragraphs. We start with the ion trap X-junction and its arms, which constitute the unit cell of the modules and are the core element of the proposed architecture. The gate, detection, and loading zones, which are placed in the arms of the junction, in combination with an optimized design of the junction electrode geometry, which allows for fast high-fidelity ion shuttling and separation, are essential for the operation of the modules. High-fidelity shuttling through junctions requires a highly optimized electrode geometry (31, 33). An example for this junction geometry including its arms is shown in Fig. 1A, featuring minimal rf barrier and barrier gradient shown in Fig. 1C. The optimized electrode geometry is combined with static voltage electrodes designed for fast and efficient ion shuttling and separation (34). The rf barrier of the highly optimized X-junction was simulated to be on the order of 0.15 meV for a trap depth of ~80 meV and an ion height of 100 μm. High-fidelity shuttling through X-junctions in a surface trap with a similar barrier has been successfully demonstrated (31). We propose the use of fast ion shuttling through the junction, similar to the work presented by Bowler et al. (16) and Walther et al. (17), and fast ion separation demonstrated by Bowler et al. (16) and Ruster et al. (35) to achieve a quantum computer cycle time on the order of 235 μs. Decoherence that would be caused by transferring ions through strong magnetic field gradients required for microwave-based quantum gates is avoided by globally turning off the gradient fields during shuttling operations. Remaining spatially varying magnetic fields are compensated for by mapping the magnetic fields in the junctions. Slow variations of the global magnetic field can be detected using dedicated ions at various positions across the module (36) and compensated using local magnetic field coils, which will be described in more detail later. Static voltage electrodes are connected using proven and developed vertical interconnect access (VIA) and buried wire technologies (30). In addition, a structured ground plane layer is used to avoid exposed dielectrics. The microfabricated conductive and insulating layers are placed on a high-resistivity (HR) silicon substrate exhibiting minimal rf losses (loss tangent, <0.004). The resulting layer structure is shown in Fig. 1B. Using TSV structures, connections to the static and rf electrodes are made from the back of the structure holding the X-junction. The electronic control systems generating the static and rf voltages will be described in more detail in the electronic control section below. Initial loading of ions and replacement of lost ions are performed using the loading zones placed in one arm of the X-junction close to the edge of each module. Backside loading zones require a global ionization laser beam in combination with an atomic flux originating from the back of the substrate, commonly known as backside loading (37). The atomic flux is generated by an atomic oven passing through slots fabricated into the silicon substrate and carefully designed center segmented electrodes, shown in Fig. 1A. The design of these electrodes and the exact shape of the slot were iteratively optimized to obtain an rf potential barrier of the same order or less as an X-junction center. When an ion is lost from a particular position within a module, a new ion is trapped, and all ions placed between the position of the lost ion and the loading zone are shifted by one position, requiring only single-shuttling sequences. A gate zone that features a strong magnetic field gradient and an adjustable local magnetic field offset is located in another arm of the optimized X-junction. The required magnetic field gradients and fields are generated using current-carrying wires and coils embedded in the silicon substrate, as shown in Fig. 2A. Large static magnetic field gradients of 150 T/m at the ions’ position (100 μm above the electrode surface) are used for fast, high-fidelity microwave gates. A current of ~10 A is passed through each copper wire to generate these gradients. Conductivity and cooling of the silicon substrate and copper wires will be discussed in detail in the cooling system description below. Fig. 2 Gradient wires placed underneath each gate zone and embedded silicon photodetector. (A) Illustration showing an isometric view of the two main gradient wires placed underneath each gate zone. Short wires are placed locally underneath each gate zone to form coils, which compensate for slowly varying magnetic fields and allow for individual addressing. The wire configuration in each zone can be seen in more detail in the inset. (B) Silicon photodetector (marked green) embedded in the silicon substrate, transparent center segmented electrodes, and the possible detection angle are shown. VIA structures are used to prevent optical cross-talk from neighboring readout zones. The strong magnetic field gradients work in combination with global long-wavelength radiation fields to perform multiqubit gates in parallel to the entire quantum computer architecture, following the method proposed by Weidt et al. (12). Here, the correlation between the number of ions and the number of required gate radiation fields vanishes, and only a fixed number of gate radiation fields are needed independent of the number of ions. Therefore, instead of requiring thousands or even millions of individually controllable laser or microwave fields, the method used here only requires a handful of global microwave fields originating from emitters periodically placed within the vacuum chambers to implement the required quantum logic on arbitrarily many ions. This scaling method can be implemented using two different approaches. The first involves making use of the already present static magnetic field gradient in the gate zone, where the ions can be shuttled along this gradient to change the ions offset magnetic field, utilizing voltages that are applied to the microfabricated ion trap chips, thereby bringing the qubit frequency into resonance with the global microwave fields of choice to perform the desired single- or multiqubit gate. The alternative approach involves using local B-field coils to bring the qubit into resonance. Because the proposed architecture already features local offset coils used to adjust the magnetic field in each gate zone and to compensate slow variations of the local magnetic field, we will focus on the latter approach to shift qubits in and out of resonance with global radiation fields. The local B-field coils are placed underneath each gate zone and are shown in Fig. 2A. To ensure that they can be used to shift ions in and out of resonance with multiple global microwave fields, we implemented a fast control system. The on-chip control electronics is based on digital-to-analog converters (DACs) that control the currents applied to the very low inductance coils (on the order of 25 nH), with 16-bit precision and an update rate of >1 MHz. Required microwave frequencies for the global fields are generated by commercial frequency generators, and amplifiers supply the signal with sufficient amplitude to emitters inside the system. The gate zones then perform all quantum operations controlled by in-vacuum electronics and powered by global long-wavelength radiation fields. Ions are precisely placed in the large static magnetic field gradient during the gate operations using highly stable (better than 50 μV) and precise voltages applied to the appropriate voltage electrodes in the gate zones. To perform shuttling operations, these voltages are overridden using the fast control system using a summing amplification circuit. During shuttling operations, the large static magnetic field gradient could be turned off, removing the requirements on shuttling through large magnetic fields. The wires creating the large static magnetic field gradients will have an impedance on the order of 10 μH, allowing a gradient ramp-up and ramp-down time on the order of 5 μs. Readout zones are incorporated into the other arm of the X-junction to detect the quantum state of the ions after performing single- and multiqubit gates, as shown in Fig. 1A. In the readout zone, multiple center segmented electrodes are made of indium tin oxide (ITO) instead of gold. ITO is ultraviolet (UV)–transparent (~80% transmission) and allows the light emitted from an ion placed above the zone to pass through the electrodes. Photodetectors are fabricated onto the silicon substrate and separated from the electrodes by a highly UV-transparent dielectric layer, similar to the concept presented in a study by Eltony et al. (38) and shown in Fig. 2B. VIA wall structures are used to prevent optical cross-talk from neighboring readout zones. Commercial silicon-based microfabricated photon counters (Hamamatsu S12571-100, multi-pixel photon counters) reach quantum efficiencies of ~30% and are compatible with the proposed silicon substrate. When cooled to 77 K, they also show a reduction of dark count rate on the order of 105 to ~1 Hz (39). The total photon detection efficiency of this detection setup will be on the order of 2%, considering an 80% transmission rate of the ITO and dielectric layer and a collection efficiency of ~10%. The detection efficiency and dark count rate are comparable to the values given in the study by Noek et al. (4), and a similar state readout fidelity on the order of 99.9% for a detection window of 25 μs can therefore be expected for this setup. State readout operations will have to be performed many times during error-corrected logical qubit operations. To preserve the state of physical qubits performing these operations, only ions placed inside the readout zones are illuminated, whereas ions placed in the gate zones are not. Readout and gate zones are placed in perpendicular arms of junctions, as shown in Fig. 1A. Global laser beams are steered parallel to and between the gate zone arms, which are separated by 2.5 mm, only addressing the ions in the readout zones shown in Fig. 2B. The required accuracy of the beam steering is readily achieved using in-vacuum optics. The X-junction structures, equipped with the zones discussed, occupy an area of 2.5 × 2.5 mm2 and can be fabricated in large numbers on a silicon wafer to form the scalable quantum computer module. A total of 1296 individual X-junctions can be monolithically fabricated onto a 90 × 90–mm2 silicon wafer piece, compatible with standard 150-mm wafer sizes. If all of these X-junctions are electrically connected together, the capacitance and power dissipation will become too large to be driven with a standard helical resonator of high-quality factor (40). Simulations performed using the Advanced Design System software tool (Keysight Technologies) show that by connecting 6 × 6 junctions together to form an electrical submodule, the capacitance can be kept below 80 pF, and a quality factor of Q > 200 is achievable using a compact helical resonator of ~15 mm in diameter. An additional requirement to achieve a high-quality factor is to use a substrate with low rf loss. Therefore, an HR silicon substrate with a bulk resistivity of 50 kΩ·cm was assumed for these simulations. Compact resonators are placed inside the system underneath the module and connected with shielded cables to the electrical submodules. All resonators are attached to the same frequency source, and the resonant circuits are tuned into resonance with the frequency source using variable capacitors. The close proximity of the electrical sections will lead to capacitive coupling between the resonators and, as a result, lead to phase matching of the resonators and neighboring rf electrodes. Careful design of the connection paths on the ion chips is used to avoid non-negligible phase differences between relevant rf electrodes. Each electrical submodule features 1224 static voltage electrodes and 108 individual local gradient current wires. The required static voltages and currents are supplied by DACs inside the vacuum system similar to the concept presented by Guise et al. (41). DACs are fabricated on separate silicon substrates, which are attached to the ion trap substrate using TSV and wafer-stacking (42) technology. Each wafer layer features four DACs with 160 analog outputs in total (the DAC AD5370 has sufficient outputs and was used as an example, but a modified version will be required that operates at higher update rates) and, combined with the required TSV and RC filters, occupies an area of no more than 15 × 15 mm2. Generating enough analog outputs requires a total of nine wafer layers that will be stacked together. An additional layer is used to house an electronic control unit, which controls the in-vacuum DACs and detection system. Each scalable quantum computer module is made up of 6 × 6 electrical submodules, fabricated onto a 90 × 90–mm2 HR silicon wafer piece. The module is controlled by on-chip electronics and performs the required quantum operations using magnetic field gradients, local magnetic fields, and global laser and microwave fields. Embedded copper wires generating the magnetic field gradients, shown in Fig. 2A, are routed in such a way that only four high-current connections are required per module. Passing large currents of 10 A through wires with a small cross section (~30 × 60 μm2) makes it essential that the resultant heat is efficiently distributed and transported away from the modules. In addition, the power dissipated by the ion trap structure and the in-vacuum electronics needs to also be transported away from the modules. Melting of the wire structures can be avoided by cooling the silicon substrates to below 100 K, which results in an extremely high thermal conductivity [k >1000 W/(m·K)] of silicon (43) and an increase of the copper conductivity by a factor of 10 (44). To estimate the temperature of the copper wires in this design, the total heat output per module has to be calculated. Considering the heat generated by the copper wires, rf dissipation in the trap structure, and power dissipation of the on-chip electronics, a maximum heat output per module is estimated to be on the order of 1000 W, which is equal to 0.12 W/mm2 and less than that of a modern computer processer unit (Intel Ivy Bridge 4C has a power dissipation of ~0.5 W/mm2). A detailed calculation will be given in Materials and Methods. The assumed heat output is likely to be significantly lower because the power dissipation of on-chip electronics and ion trap structures is estimated for room temperature. A liquid nitrogen microchannel cooler is integrated into the back wafer of the modules to efficiently remove the heat from the modules. Deep trenches are etched into the backside of the last wafer, forming channels through which liquid nitrogen is passed. The channels are covered using an additional silicon wafer. Fabricating the entire module including the liquid cooler out of silicon prevents additional stress and wafer bow arising from different thermal expansion coefficients. A similar microchannel cooler has been shown to achieve a heat transfer coefficient of >0.1 W/(mm2·K) (45), which is sufficient for this system. On the basis of the total heat dissipation and the thermal conductivity of silicon wafers and copper interconnects, the thermal gradient between the copper wires and the coolant through the multiwafer package and microchannel cooler will only be ~2 K, preventing the copper wires from melting. Liquid nitrogen, which is cooled from 77 to 65 K to prevent boiling inside the microchannel cooler, will be used as a coolant and is supplied to the modules using multiple UHV-compatible flexible steel tubes. Continuous flow liquid nitrogen coolers are commonly used for detectors and, if designed correctly, introduce minimal vibrations to the system (much less than 100-nm amplitude) (46). Each of these modules can work as a stand-alone small-scale quantum processer module featuring 1296 X-junctions. If one wants to perform a computationally hard problem, such as Shor factorizing a 2048-bit number, a much larger architecture consisting of many modules will be required. Each module will have to be interfaced with each other to create a universal quantum computer architecture. The approach presented by Monroe et al. (9) makes use of photonic interconnects and commercial fibers to interface arbitrarily many modules. Fiber switches can then be used to connect any module with any other module in the architecture. This approach has great potential, but the performance of this system is currently limited by the interaction rate between modules (14), which is typically much slower than other quantum operations (2, 4, 15) performed by the modules.

Scaling modules to a universal quantum computer architecture We propose an alternative scheme that does not rely on photonic interconnects and is therefore not limited by their interaction rate. In our approach, modules are designed in such a way that ions can be directly shuttled from one module to another. Rf and static voltage electrodes thus need to be fabricated all the way to the edge of the modules so that the electric fields confining the ions reach beyond the edges. The modules must also be accurately aligned so that two neighboring modules create an overlapping electric field. If such an electric field can be created, ions can be shuttled from one module to another. The resulting two-dimensional module array will feature fast interaction rates between nearest-neighbor modules, without the need of a special photonic interconnect system. The challenging part of this scheme is to accurately align all modules to each other to prevent large barriers or interruptions of the overlapping electric fields from occurring. We have performed boundary element method electric field simulations of three-dimensional trap structures to investigate the feasibility of shuttling ions from one module to another, taking into account the possible misalignments between adjacent modules. We have analyzed the electric potential and rf barrier caused by rf rails misaligned in different directions and magnitudes. Results of the simulations show that an rf barrier occurs, similar to that found in the center of an X-junction. In the case of a misalignment in all three axes by ≤10 μm, the simulated rf barrier was found to be ≤0.2 meV, as shown in Fig. 3, for a trap depth of ~100 meV and an ion height of 100 μm. The barrier of 0.2 meV is of similar height to the one found in our optimized X-junction center and the one presented in a study by Wright et al. (31), where high-fidelity shuttling was successfully demonstrated. Shuttling fidelities comparable or higher than those through the X-junction centers can therefore be expected if the rf voltages applied to both modules show no significant phase or frequency difference, and the neighboring modules can be aligned with an accuracy of ≤10 μm. Fig. 3 Misaligned modules. Illustration of two modules misaligned in the xyz axes by 10 μm each (A) and the corresponding rf pseudopotential at the ion height (B). (C) The resulting rf barrier when moving along the rf minimum in the z direction is given in millielectron volt . This simulation was performed for a 171Yb+ ion for an ion height of 100 μm and using a drive frequency and voltage of 25 MHz and 200 V, respectively. As discussed in the previous section, all resonators providing the rf voltages to the modules are connected to the same frequency source. In addition, all modules feature the same path length and impedance of the coaxial connections from the resonators to the rf electrodes. This will result in a negligible rf phase difference of the electric fields generated by adjacent modules, which could otherwise weaken the trap depth at the intersection between modules. Precision machined steel frames are mounted inside the vacuum chambers to achieve an alignment of the modules with an accuracy of ≤10 μm in three dimensions. The planarized top surface of the steel frames is characterized using an interferometric measurement system, and the modules are mounted on the surface using a high-precision die bonder tool. To increase the alignment accuracy and to allow for drift compensation, multiple UHV- and cryogenic-compatible XYZ piezo actuators are placed between the bottom of each module and the top of the steel frames. The illustration in Fig. 4 shows a pictorial representation of a single module of the scalable architecture including required connections and attached piezos on the top of a steel frame. Fig. 4 Scalable module illustration. One module consisting of 36 × 36 junctions placed on the supporting steel frame structure: Nine wafers containing the required DACs and control electronics are placed between the wafer holding 36 × 36 junctions and the microchannel cooler (red layer) providing the cooling. X-Y-Z piezo actuators are placed in the four corners on top of the steel frame, allowing for accurate alignment of the module. Flexible electric wires supply voltages, currents, and control signals to the DACs and control electronics, such as field-programmable gate arrays (FPGAs). Coolant is supplied to the microchannel cooler layer via two flexible steel tubes placed in the center of the modules. The exact positions of the modules are determined using microfabricated diffraction gratings on the front of the modules in combination with a laser measurement system. The alignment system determines the position of neighboring modules and corrects for misalignment using the piezo actuators and, if required, the die bonder tool. The requirements for the high-precision position measurement system and the module placement are technically very challenging but, on a smaller scale, have been implemented with much higher precision using lithography stepper systems where 3- to 5-nm alignment precision of large-wafer stages in vacuum is routinely achieved (ASML TWINSCAN NXE:3300B). The discussed alignment capability would be severely hindered if the modules are strongly warped in random directions or the edges of the modules are not precisely fabricated. Because of the large thickness of the silicon wafer modules (on the order of 10 mm), negligible wafer bow is expected, and the bow will also be characterized for all modules before assembly. The edges of the modules are created using high-resolution photolithography and anisotropic dry etching (Bosch process). These process steps, which are commonly used in the microfabrication of microchips and microelectromechanical system devices, reach submicrometer precision and will not limit the alignment capabilities. In addition, only the top wafer carrying the ion trap structures will feature the full footprint size of the module, and all other wafers, containing control and detection electronics and cooler, will have a slightly smaller footprint. The discussed steel frames are accurately placed inside large octagon-shaped UHV chambers (~4.5 × 4.5 m2 large), which feature viewports on the sides and top to allow for optical access, as shown in Fig. 5. Imaging, beam shaping, and guiding the laser light fields above the trap surfaces are achieved using in-vacuum optics. Each chamber also incorporates all required feedthroughs for currents, static voltages, rf and microwave signals, coolant, and digital control signals. In addition, the chambers are equipped with liquid nitrogen–cooled heat shields and a variety of vacuum pumps to create an UHV environment. Multiple chambers can be directly bolted and welded together with a monolithic steel frame passing through all the vacuum chambers, creating a modular universal quantum computer of large size. Each chamber shown in Fig. 5 can hold ≥2.2 million individual junctions. Although the technical feasibility of our approach has been demonstrated above, it should be noted that the required engineering is certainly not simple. Fig. 5 Illustration of vacuum chambers. Schematic of octagonal UHV chambers connected together; each chamber is 4.5 × 4.5 m2 large and can hold >2.2 million individual X-junctions placed on steel frames.