Demonstration of a Multiplexing Trapped Ion Quantum Processing Unit

This paper demonstrates a scalable trapped-ion quantum processing unit that utilizes a time-multiplexed sample-and-hold technique to reduce control wiring complexity while maintaining high-fidelity operations with motional heating rates below one phonon per second and gate errors under $10^{-4}$.

The Gist

The Big Picture: The "Wiring Nightmare"

Imagine you are trying to build a massive quantum computer using trapped ions. Think of these ions as tiny, floating marbles that hold information. To control them, you need to apply precise electrical voltages to many different metal plates (electrodes) surrounding them.

The problem is that a useful quantum computer needs thousands of these marbles. If you tried to run a separate wire from every single metal plate to a control room outside the machine, you would need millions of wires.

This creates a "wiring nightmare."

1. The Hole Problem: You can't poke a million holes through the walls of the machine (the cryostat) because it would let heat in and ruin the experiment.
2. The Space Problem: Inside the machine, there isn't enough room to fit a million wires next to each other without them touching and causing short circuits.

The Solution: The "Multiplexer" (The Traffic Cop)

The researchers solved this by building a special electronic switch called a multiplexer.

Think of the control room as a bus station with only a few buses (DACs, or voltage controllers). In the old way, you needed a dedicated bus for every single passenger (electrode). With the multiplexer, you have one bus that can stop at many different bus stops, drop off a passenger, and move on.

However, there's a catch: The bus can only stop at one place at a time. So, how do you keep the voltage steady at a bus stop after the bus leaves?

The Trick: "Sample-and-Hold" (The Water Bucket)

The paper uses a technique called Sample-and-Hold.

Imagine you are filling a garden with water.

1. Sample: You connect a hose (the bus) to a specific flower bed (an electrode) and fill it up to the perfect level.
2. Hold: You disconnect the hose. The flower bed is now a "floating" bucket of water. As long as the bucket doesn't leak, the water stays at the right level for a while.
3. Repeat: You move the hose to the next flower bed, fill it, and disconnect.

The researchers built a chip that does exactly this. It charges up the electrodes and then disconnects them, letting them "float" while the computer does its work.

The Experiments: Testing the Bucket

The team built a prototype "Quantum Processing Unit" (QPU) that combines a special ion trap (the garden) with this multiplexer chip (the bus system). They tested it in three main ways:

1. The "Leak" Test (Voltage Decay)
When you disconnect the hose, the water level (voltage) slowly drops due to tiny leaks.

• The Finding: They measured how fast the voltage dropped. They found that if they refreshed the connection (re-filled the bucket) every 50 milliseconds, the voltage stayed stable enough to keep the "gate errors" (mistakes in the quantum math) extremely low. It was like checking the water level often enough that the plants never noticed it was dropping.

2. The "Spill" Test (Charge Injection)
When you unplug a hose, sometimes a little bit of water splashes out or the pressure changes suddenly. In electronics, this is called "charge injection."

• The Problem: In their first version, this "splash" was big enough to physically push the ion (the marble) out of its spot, ruining the experiment.
• The Fix: They added giant capacitors (think of them as huge, extra water tanks) to the circuit. These tanks absorbed the splash.
• The Result: After adding the tanks, the ion didn't move at all when they switched the wires. The "splash" was completely suppressed.

3. The "Noise" Test (Heating Rates)
Quantum computers are very sensitive to heat and vibration. If the electrodes are too noisy, the ions get jittery and lose their information.

• The Finding: They measured how much the ions "shook" (heated up) when the switches were closed (connected) versus open (floating).
• The Result: The shaking was incredibly low in both cases—less than one "jitter" per second. This proves that the multiplexer doesn't add any extra noise to the system.

The Hardware: Stacking the Layers

To make this fit in a tiny space, they didn't just glue things side-by-side. They built a stack.

• Bottom Layer: A silicon board.
• Middle Layer: The multiplexer chip (the traffic cop).
• Top Layer: The ion trap (the garden).

They glued these layers together using special industrial glue that works in extreme cold (near absolute zero) and high vacuum. They even tested different glues to make sure the stack wouldn't fall apart when it got cold.

The Conclusion

The paper demonstrates that you can control a complex quantum system using a "time-sharing" method (multiplexing) without losing precision.

• They proved that the "floating" electrodes stay stable long enough to do calculations.
• They proved that the "switching" doesn't jostle the ions.
• They proved that the system stays quiet (low heating).

Essentially, they showed a working blueprint for how to wire up a massive quantum computer without needing a million wires, solving one of the biggest bottlenecks in building these machines.

Technical Summary

Technical Summary: Demonstration of a Multiplexing Trapped Ion Quantum Processing Unit

Problem Statement
Scaling trapped-ion quantum computers to the thousands of qubits required for fault-tolerant operation faces a critical wiring bottleneck. In surface ion trap architectures, the number of control lines scales linearly with the number of potential wells (sub-registers). A processor with millions of qubits would theoretically require millions of separate control lines penetrating the cryostat. This presents two major challenges: (1) maintaining thermal isolation becomes unfeasible with such a high density of feedthroughs, and (2) the physical space required for interconnects on the chip exceeds the area available for other critical components like RF routing and optical waveguides. Existing strategies, such as co-wiring electrodes or integrating cryogenic Digital-to-Analog Converters (DACs), suffer from either a lack of flexibility (preventing arbitrary ion-crystal reconfigurations) or excessive heat dissipation and large footprints.

Methodology
The authors present a modular Quantum Processing Unit (QPU) that integrates a surface ion trap with a cryogenic analog multiplexer to address the wiring challenge via time-division multiplexing. The system employs a "sample-and-hold" technique where electrodes are charged to specific voltages via a DAC and then isolated by opening analog switches, allowing them to float while maintaining their potential via integrated capacitance.

Key hardware components include:

• Multiplexer: An Application-Specific Integrated Circuit (ASIC) developed by Infineon Technologies, based on 130 nm bipolar transistor technology. It distributes 22 DAC inputs across up to 199 DC electrodes. The chip features integrated capacitances (15 pF for dynamic electrodes, 50 pF for shim electrodes) and operates within a $\pm 10$ V range.
• Surface Ion Trap: Fabricated on fused silica substrates with a single aluminum metal layer. The initial design features an ion-surface distance of 170 $\mu$m to accommodate the $\pm 10$ V constraint, utilizing "zigzag" shaped DC electrodes to route signals on a single metal layer.
• Experimental Setup: The QPU (trap chip and multiplexer) is assembled on a Printed Circuit Board (PCB) using epoxy adhesives and wire bonding. The system operates in a closed-cycle pulse tube cryostat with a base temperature of $\sim 10$ K. To mitigate charge injection effects during switching, a second-generation design incorporates 39 nF capacitors between electrode lines and the ground plane.
• Characterization: The team utilized trapped $^{40}\text{Ca}^+$ ions to measure motional heating rates, voltage decay rates of floating electrodes, and the impact of charge injection on ion position. Measurements were performed at various metal temperatures (up to $\sim 300$ K) and axial frequencies.

Key Contributions

1. Integrated QPU Demonstration: The paper reports the first demonstration of a QPU combining a surface ion trap and a cryogenic analog multiplexer, validating the feasibility of time-multiplexed control for ion traps.
2. Charge Injection Suppression: The study quantifies the charge injection phenomenon inherent to analog switching, which causes ion displacement. By adding 39 nF shunt capacitors, the authors suppressed positional shifts to below measurable levels, enabling operations on floating electrodes.
3. Heating Rate Characterization: The authors measured motional heating rates for both closed and open switch configurations, demonstrating that the multiplexer introduces negligible noise.
4. Sample-and-Hold Validation: The work characterizes the voltage decay rates of floating electrodes, establishing the refresh rates necessary to maintain gate fidelity.
5. Stacked Architecture Proposal: The paper outlines a fully integrated, stacked QPU design where the multiplexer and trap are directly wire-bonded to minimize footprint, along with a study on adhesive compatibility for cryogenic assembly.

Results

• Heating Rates: At a metal temperature of 47(5) K and an axial frequency of $1.71 \times 2\pi$ MHz, the motional heating rate was measured at 0.55(21) phonons/s for closed switches and 0.43(17) phonons/s for open switches. These rates are well below the threshold for high-fidelity operations.
• Frequency and Temperature Scaling: The heating rate scales with axial frequency as $\dot{\bar{n}} \propto \omega^{-\alpha}$, with exponents $\alpha = 3.16(28)$ (closed) and $\alpha = 2.50(18)$ (open). The rate also scales with metal temperature, following a power law with exponents $\beta \approx 1.05$ (closed) and $\beta \approx 1.37$ (open) in the measured range.
• Voltage Decay and Gate Fidelity: Without additional capacitance, floating electrodes exhibited voltage decay rates of approximately 0.1 V/min. With 39 nF capacitors, the decay rate dropped to $< 2.5$ mV/min. The authors calculate that sampling voltages at frequencies above 20 Hz keeps the gate infidelity due to detuning errors below $10^{-4}$.
• Charge Injection: In the absence of shunt capacitors, opening a switch caused a potential drop of $\sim 0.3$ V, resulting in ion displacements of $\sim 3$ $\mu$m. With the 39 nF capacitors, no positional shifts were observed even when all switches were opened simultaneously.
• Thermal Management: The multiplexer exhibited switching transients below 70 K due to charge carrier freeze-out. The authors demonstrated that heating the ASIC to $>70$ K (via SMD resistors) restores signal integrity without compromising the trap's operation.

Significance
The paper claims that the multiplexing scheme, combined with the sample-and-hold technique, offers a balanced route toward scalability. It retains the ability to perform arbitrary ion-crystal reconfigurations (unlike static co-wiring) while avoiding the high heat load and large footprint of integrated DACs. The results indicate that the multiplexer introduces negligible noise to the system, with heating rates comparable to or better than standard setups. The authors conclude that the demonstrated architecture is compatible with high-fidelity operations, provided that voltage refresh cycles are performed frequently enough (>$20$ Hz) to mitigate voltage decay and that charge injection is managed via sufficient shunt capacitance. The work serves as a foundational step toward modular, large-scale trapped-ion quantum processors.