🔬 mesoscale physics

Robust spin-qubit control in a natural Si-MOS quantum dot using phase modulation

This paper demonstrates that applying a concatenated continuous drive (CCD) with phase-modulated microwave signals to a natural silicon metal-oxide-semiconductor quantum dot significantly extends spin coherence times and improves single-qubit gate fidelity from 95% to 99%, thereby overcoming environmental noise limitations in isotopically natural silicon.

Original authors: Takuma Kuno, Takeru Utsugi, Andrew J. Ramsay, Normann Mertig, Noriyuki Lee, Itaru Yanagi, Toshiyuki Mine, Nobuhiro Kusuno, Raisei Mizokuchi, Takashi Nakajima, Shinichi Saito, Digh Hisamoto, Ryuta Tsuc

Published 2026-01-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Takuma Kuno, Takeru Utsugi, Andrew J. Ramsay, Normann Mertig, Noriyuki Lee, Itaru Yanagi, Toshiyuki Mine, Nobuhiro Kusuno, Raisei Mizokuchi, Takashi Nakajima, Shinichi Saito, Digh Hisamoto, Ryuta Tsuchiya, Jun Yoneda, Tetsuo Kodera, Hiroyuki Mizuno

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Keeping a Quantum Spin Stable in a Noisy Room

Imagine you are trying to balance a spinning top on a table. In a perfect, silent room, the top spins for a long time. But in a real-world room, there are drafts, vibrations, and people walking by. These disturbances knock the top over quickly.

In the world of quantum computing, Silicon Quantum Dots are like those spinning tops. They are promising because they are small and can be made using the same factories that make our current computer chips. However, the "room" they live in (natural silicon) is very noisy. Specifically, tiny magnetic atoms called $^{29}$ Si isotopes act like invisible drafts, causing the quantum information (the spin) to lose its balance and fade away almost instantly.

The researchers from Hitachi and their partners found a clever way to keep this spinning top stable, even in that noisy room, without needing to constantly adjust the table or the top manually.

The Problem: The "Idle" Problem

Usually, when a quantum computer isn't doing a specific calculation, the qubit (the spinning top) just sits there waiting. This is called the "idle" state.

The Issue: In natural silicon, while waiting, the noise from the environment knocks the spin out of sync very quickly. It's like trying to balance a spinning top while someone is shaking the table. The top falls over in about 1.2 microseconds (a millionth of a second).
The Consequence: Because the spin falls over so fast, the computer can't perform many calculations before the information is lost.

The Solution: The "Phase-Modulated" Dance

The researchers developed a technique called Concatenated Continuous Drive (CCD). Instead of letting the spin sit still, they keep it moving in a very specific, rhythmic dance using microwave signals.

Think of it like this:

The Standard Spin: Imagine a dancer standing still. If the floor shakes (noise), they stumble.
The Microwave Drive: Now, imagine the dancer is spinning rapidly in place. The rapid spinning averages out the small shakes of the floor, keeping them stable. This is good, but not perfect.
The CCD Method (The "Phase-Modulated" Dance): The researchers added a second layer of movement. They didn't just spin the dancer; they made the dancer wobble in a precise, rhythmic pattern while spinning.

By using phase modulation (changing the timing of the microwave signal rather than its strength), they created a "double protection" system:

Layer 1: The main spin protects against one type of noise.
Layer 2: The rhythmic wobble protects against a second type of noise.

This is like a dancer who is spinning so fast that the floor shaking doesn't matter, and they are also bobbing their head in a pattern that cancels out any remaining vibrations.

The Results: A Massive Improvement

The paper reports some impressive numbers showing how well this "dance" works:

Staying Power: Without the special dance, the spin lasted 1.2 microseconds. With the CCD method, the spin stayed stable for over 200 microseconds. That is more than 100 times longer.
Coherence (The "Memory"): When they tested how long the spin could remember a specific state (using a test called a Ramsey sequence), it improved from 143 nanoseconds to 40.7 microseconds.
Accuracy (The "Fidelity"): The most important test was how accurately they could perform a single "move" (a gate operation).
- Before: The move was correct 95% of the time.
- After: The move was correct 99.1% of the time.

This 99.1% accuracy is a huge deal because it crosses a critical threshold needed for advanced error correction in quantum computers.

Why This Matters

The paper highlights three key benefits of this method:

No Constant Adjustments: Usually, to keep these spins stable, scientists have to constantly measure and re-calibrate the system (like constantly re-tuning a guitar). This new method is "intrinsically robust," meaning it works well on its own without needing constant human or computer feedback.
Global Control: Because the method is so robust, it could allow scientists to control many qubits at once with a single signal, rather than needing a unique, perfectly tuned signal for every single qubit.
Working with "Natural" Silicon: Most high-performance silicon quantum computers require expensive, purified silicon to remove the noisy atoms. This experiment worked with natural silicon (the kind found in the ground), proving that you don't necessarily need expensive purification if you have the right control technique.

Summary

The researchers took a quantum spin that was falling over quickly in a noisy environment and taught it a complex, rhythmic dance using microwave signals. This dance protected the spin from the noise, making it last over 100 times longer and perform calculations with 99% accuracy, all without needing constant adjustments or expensive purified materials.

Technical Summary: Robust spin-qubit control in a natural Si-MOS quantum dot using phase modulation

Problem Statement
Silicon quantum dots are leading candidates for scalable quantum computing due to their compatibility with CMOS technology and operation at kelvin-scale temperatures. However, achieving fault-tolerant quantum computation requires high operational fidelity and long coherence times, which are currently limited in industry-standard natural silicon. The primary sources of noise are the non-zero nuclear spins of $^{29}$ Si isotopes and charge noise acting via spin-orbit interaction. While isotopic purification and interface optimization have improved gate fidelities, many approaches rely on frequent feedback and calibration. As systems scale, the overhead of such calibration becomes a bottleneck. Furthermore, the "idle" state (waiting without microwave drive) is particularly susceptible to low-frequency phase noise, limiting coherence times during qubit idling.

Methodology
The authors present a control protocol for a single spin qubit in a natural silicon metal-oxide-semiconductor (Si-MOS) quantum dot fabricated on a fully depleted silicon-on-insulator (FD-SOI) substrate. The device operates at 10 mK with an external magnetic field of 825 mT (resonance frequency 22.567 GHz).

To address noise, the team employs a Concatenated Continuous Drive (CCD) protocol using phase-modulated microwaves (MW). Unlike amplitude modulation, which can introduce nonlinearity and heating issues, phase modulation avoids these pitfalls. The method involves:

Dressed States: Applying an always-on MW drive to define a "dressed" or protected rotating qubit basis.
Phase Modulation: Modulating the phase of the MW drive to create a "double dressed" state. This dynamically decouples the spin from both detuning errors (low-frequency noise) and Rabi frequency errors.
Hamiltonian Engineering: The system Hamiltonian is analyzed in two rotating frames. In the second rotating frame, the qubit is protected by energy gaps ( $\hbar\Omega$ and $\hbar\epsilon_m$ ) against detuning and Rabi frequency fluctuations, respectively.
Control and Readout: The authors define a protected qubit basis and implement a readout matching condition where the total pulse duration is an integer multiple of $2\pi/\omega_m$ . This ensures the protected basis aligns with the laboratory basis for energy-selective readout.
Gate Design: To mitigate errors from counter-rotating terms (often neglected in the Rotating Wave Approximation), gate times are designed to be integer multiples of $\pi/\omega_m$ , allowing these terms to integrate to zero. The modulation strength $\epsilon_m$ is set to $\omega_m/4$ to enable $\pi/4$ increments for constructing Clifford gates (including T gates).

Key Contributions and Results

Extended Coherence: The CCD method extends the Rabi oscillation decay time from 1.2 $\mu$ s (bare qubit) to over 200 $\mu$ s. Specifically, the CCD-protected Rabi decay time ( $T_{\text{CCD-Rabi}}$ ) is measured at 54.9 $\mu$ s, and the Ramsey coherence time ( $T_{\text{CCD-Ramsey}}$ ) improves from 143 ns to 40.7 $\mu$ s.
Quality Factor: The quality factor of spin rotations ( $Q = \pi \text{ rotation time} / \text{decay time}$ ) improves from 2.2 to 25.0.
Gate Fidelity: Using randomized benchmarking on Clifford gates, the average single-qubit gate fidelity is improved from 95% (bare qubit) to 99.1 $\pm$ 0.1% (CCD-protected qubit). This result approaches the threshold required for surface code error correction.
Robustness without Feedback: The high fidelity is achieved without active feedback or continual calibration, demonstrating intrinsic robustness against environmental noise and qubit variability.
Two-Axis Control: The authors successfully demonstrate two-axis control of the protected qubit by varying the microwave phase, confirming the ability to perform arbitrary rotations in the protected basis.

Significance
The paper demonstrates that phase-modulated continuous drive (CCD) is an effective strategy for protecting spin qubits in natural silicon, a material abundant in industrial settings but typically plagued by nuclear spin noise. The method significantly improves gate fidelity and coherence times, reaching the critical threshold for error correction despite the use of natural silicon.

The authors emphasize that this approach is particularly valuable for global control schemes in large-scale arrays, as the robustness against detuning errors reduces the need for precise phase tracking of individual qubits. Additionally, the protocol is effective for "idling" operations, a critical requirement for quantum algorithms where qubits spend significant time waiting. The study validates the CCD protocol's utility in silicon spin qubits, offering a pathway to high-fidelity control that simplifies system architecture by removing the need for complex feedback loops.