Multiplexed cryo-CMOS control of an isolated double quantum dot

This paper demonstrates that sample-and-hold multiplexed cryo-CMOS control can reliably bias and pulse an isolated silicon double quantum dot at 0.5K, confirming its compatibility with the stability and speed requirements necessary for scalable spin-qubit processors.

The Gist

The Big Picture: The "Wiring Nightmare" of Quantum Computers

Imagine you are trying to build a massive city of tiny, super-sensitive robots (these are quantum computers). To make them work, you need to give each robot a very specific instruction, like "turn left" or "spin faster."

In a traditional setup, every single robot needs its own dedicated wire running all the way from the control room (at room temperature) down to the robot (which lives in a freezer colder than outer space).

The Problem: If you want to build a computer with millions of robots, you would need millions of wires.

1. The Bundle: You can't fit millions of wires through the tiny hole of a freezer without blocking the cold air.
2. The Heat: Every wire acts like a tiny heater, bringing warmth into the freezer. If the freezer gets too warm, the robots stop working.
3. The Chaos: It's a tangled mess that is impossible to manage.

The Solution: The "Sample-and-Hold" Multiplexer

The researchers in this paper built a clever "traffic controller" (a cryo-CMOS chip) that lives inside the freezer with the robots.

Think of this chip like a smart water valve system for a garden with 64 sprinklers, but you only have two water hoses coming from the house.

• Old Way: You need 64 hoses to water 64 sprinklers.
• New Way (Sample-and-Hold): You have a bucket (a capacitor) next to every sprinkler.
  1. You quickly pour water into the first bucket to set the sprinkler to "high."
  2. You close the valve. The bucket holds the water (the voltage) even though the hose is disconnected.
  3. You move to the next bucket, fill it, and close it.
  4. You do this so fast that all 64 sprinklers are set, and then you disconnect the hoses entirely.

The buckets hold the water steady, so the sprinklers keep working without needing a constant hose connection. This is called Sample-and-Hold (SH) multiplexing.

The Experiment: Testing the "Bucket" System

The scientists wanted to know: Does this "bucket" system work well enough for the delicate quantum robots?

They built a Double Quantum Dot (a tiny trap for electrons) using silicon. They used their new "traffic controller" chip to set the voltage on the gates that trap the electrons.

Here is what they tested:

1. The "Leaky Bucket" Test (Voltage Drift)
In the real world, buckets have tiny holes. If you fill a bucket and walk away, it slowly leaks. In electronics, this is called voltage drift. If the voltage changes too much, the quantum robot gets confused and stops working.

• The Result: They measured the leak. It was incredibly slow (about 5.5 microvolts per second).
• The Analogy: Imagine filling a bucket and walking away. You wouldn't notice the water level drop for days. This is slow enough that they could theoretically control 10 million quantum dots with just one or two wires!

2. The "Electron Zoo" (Isolation)
They trapped four electrons inside their silicon trap and closed the doors so no new electrons could enter or leave.

• The Result: Even though the control chip was constantly "refreshing" the buckets (checking and refilling them) one by one, the electrons stayed perfectly still and stable. The system didn't get confused by the switching.

3. The "Fast Switch" Test (Pulsing)
Quantum computers need to do more than just sit still; they need to move fast. The researchers needed to flip the switches rapidly to make the electrons jump from one side of the trap to the other.

• The Result: They successfully made the electrons jump back and forth in milliseconds. They could even watch single electrons tunneling (jumping) in real-time.
• The Analogy: It's like a traffic light that can switch from Red to Green instantly, even though the person controlling it is only allowed to touch the button for a split second at a time.

Why This Matters

This paper is a milestone because it proves two things at once:

1. Stability: The "bucket" system is stable enough to hold the delicate quantum state without leaking too much.
2. Speed: The system is fast enough to perform the rapid calculations quantum computers need.

The Bottom Line:
Before this, scientists weren't sure if this "multiplexing" trick would work for real quantum computers. They worried the "buckets" would leak too much or switch too slowly. This experiment says: "Yes, it works!"

It paves the way for building quantum computers with millions of qubits without needing a room full of wires. Instead of a tangled mess of cables, we can have a clean, scalable system where a tiny chip inside the freezer manages the entire computer.

Technical Summary

1. Problem Statement

Scalable spin-based quantum computing using gate-defined semiconductor quantum dots (QDs) faces a critical bottleneck: wiring complexity and thermal load.

• The Challenge: Large-scale fault-tolerant architectures require millions of qubits, each needing individually tuned biasing voltages to compensate for device inhomogeneity. Connecting millions of wires from room temperature to the cryogenic environment creates an unmanageable heat load and physical crowding.
• The Proposed Solution: Cryogenic control circuits using Sample-and-Hold (SH) multiplexing. This architecture stores gate voltages in integrated capacitors and sequentially refreshes them, allowing a limited number of input lines to control a large array of gates.
• The Uncertainty: While SH multiplexing offers scalability, its compatibility with the stringent requirements of quantum dot operation (stability, low noise, and high-speed pulsing) remains unproven. Concerns include voltage drift, charge injection during switching, and the ability to perform fast dynamic operations (pulsing) required for qubit gates.

2. Methodology

The authors experimentally validated the compatibility of SH-based multiplexing with a silicon double quantum dot (DQD) system.

• Experimental Setup:

  • Device: A Silicon-on-Insulator (FDSOI) double quantum dot fabricated at CEA-Leti. The device features two parallel rows of top gates ($T1-T4$, $B1-B4$) and coupling gates.
  • Cryo-CMOS Controller: A demultiplexer circuit operating at 0.5 K. It uses an SH architecture to control up to 64 gates using only two analog voltage inputs ($V_A$ and $V_B$).
  • Isolation Regime: The DQD (formed by gates $B2$ and $B3$) was isolated from electron reservoirs by applying strong negative voltages to barrier gates ($B1, B4$). This fixed the total electron number ($N=4$), simplifying the charge stability diagram and reducing noise.
  • Readout: A sensing dot (under gates $T2, T3$) monitored the charge state of the DQD via RF-SET reflectometry using a 500 nH superconducting Nb inductor.

• Operational Protocol:

  • Sequential Refreshing: For every measurement point, the controller sequentially updated the voltages on the relevant gates ($T2, B2, T3, B3, J12, J23, J34$) using the SH circuit.
  • Disconnect: After the refresh sequence (lasting 6.4 µs), the gates were disconnected from room-temperature electronics to ensure measurements were taken solely under the influence of the stored cryo-CMOS voltages.
  • Pulsing: The system was tested for its ability to apply fast detuning pulses across inter-dot transitions to observe single-electron tunneling events.

3. Key Contributions

1. First Demonstration of Isolated DQD Control: The paper provides the first experimental validation that a multiplexed cryo-CMOS circuit can stably bias an isolated quantum system (where electron number is fixed) while performing rapid dynamic operations.
2. Quantification of Voltage Drift: The authors characterized the leakage of the analog SH cells in the presence of the quantum device's parasitic capacitance, establishing a drift rate suitable for large-scale scaling.
3. Dynamic Operation Validation: They demonstrated that the SH architecture supports not just static DC biasing but also fast voltage pulsing (sub-millisecond response), resolving single-electron tunneling events and stochastic switching.

4. Key Results

• Voltage Stability and Drift:

  • Using Coulomb peaks as a reference, the voltage drift of the analog cells was measured at ~5.5 µV/s (specifically 10 µV/s at 1.5 V, extrapolated to 5.5 µV/s in the text).
  • This drift is comparable to state-of-the-art results. The authors estimate that with this drift rate, a single input voltage and a 1 MHz clock could bias 10 million independent outputs while keeping voltage error below 100 µV.
  • Note: The connection to the quantum device increased parasitic capacitance, which improved voltage retention (by a factor of 5) but reduced the SH cell bandwidth (from 320 MHz to ~20 MHz).

• Charge Stability and Isolation:

  • The system successfully loaded and isolated four electrons in the DQD.
  • A charge stability diagram was successfully mapped, showing clear transitions between all five charge configurations: $(4,0), (3,1), (2,2), (1,3),$ and $(0,4)$.
  • The stability of these configurations confirmed that the sequential refreshing scheme did not introduce significant noise or instability to the quantum state.

• Fast Pulsing and Tunneling Dynamics:

  • The circuit successfully applied detuning pulses across the $(1,3) \leftrightarrow (0,4)$ inter-dot transition.
  • Single-shot readout resolved three distinct regimes:
    1. No tunneling (system remains in initial state).
    2. Single tunneling event (system switches state once).
    3. Stochastic switching (fluctuations between states near the transition).
  • The response time of the pulsing was shorter than the inter-dot tunnel coupling time (~1 ms), proving the system can perform the fast operations required for qubit gates.

5. Significance

This work represents a critical milestone toward scalable quantum processors:

• Scalability: It validates the "Sample-and-Hold" multiplexing approach as a viable solution for the massive wiring challenges of million-qubit architectures. It proves that the trade-off between wiring reduction and control fidelity is manageable.
• Operational Versatility: The demonstration that SH circuits can handle both static biasing (for defining the qubit) and fast pulsing (for gate operations and readout) is essential. Previous works were often limited to either static biasing or lacked pulsing capabilities.
• Path Forward: While this study focused on charge stability, it lays the groundwork for future integration of these control circuits with spin coherence and gate fidelity studies. It suggests that monolithic or 3D-integrated cryo-CMOS and quantum circuits are a feasible path to practical, large-scale silicon quantum processors.