⚛️ quantum physics

Beyond-Ten-Hour Coherence in a Decoherence-Free Trapped-Ion Clock Qubit

By combining clock-state qubits with decoherence-free subspace encoding in a trapped-ion system, researchers achieved a record-breaking coherence time exceeding ten hours (approximately 3.77 × 10⁴ seconds) without magnetic shielding, effectively unlocking the million-year coherence potential of atomic ions for scalable quantum information processing.

Original authors: Jiahao Pi, Xiangjia Liu, Junle Cao, Pengfei Wang, Lingfeng Ou, Erfu Gao, Hengchao Tu, Menglin Zou, Xiang Zhang, Junhua Zhang, Kihwan Kim

Published 2026-03-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jiahao Pi, Xiangjia Liu, Junle Cao, Pengfei Wang, Lingfeng Ou, Erfu Gao, Hengchao Tu, Menglin Zou, Xiang Zhang, Junhua Zhang, Kihwan Kim

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

Imagine you are trying to keep a delicate secret safe in a noisy, chaotic room. The secret is a piece of information, and the room is filled with people shouting, magnets wobbling, and lights flickering. In the world of quantum computing, this "secret" is called quantum coherence, and the "room" is the environment surrounding our tiny quantum computers.

For a long time, scientists have been trying to keep these secrets safe for as long as possible. The best they could do was keep the secret for about an hour before the noise of the room scrambled it. But a team of researchers from Tsinghua University and other institutions has just pulled off a magic trick: they kept the secret safe for over 10 hours (specifically, about 10.5 hours).

Here is how they did it, explained through simple analogies.

1. The Problem: The "Shaky Table" and the "Noisy Radio"

Think of a trapped ion (a single atom) as a tiny, spinning top. To store information, we make this top spin in a specific way.

The Shaky Table: The table the top sits on vibrates because of magnetic fields in the room. This makes the top wobble and lose its balance (decoherence).
The Noisy Radio: To talk to the top, we use a radio signal (microwaves). If the radio signal itself is crackly or unstable, it confuses the top.

Previously, scientists tried to fix this by building a soundproof room (magnetic shielding) or buying a super-expensive, perfect radio. But even with the best equipment, the tops only stayed balanced for about an hour.

2. The Solution: The "Twin Dance" (Decoherence-Free Subspace)

Instead of trying to stop the noise or build a better room, these scientists changed the dance they taught the tops.

They didn't use just one top; they used two tops (two atoms) dancing together, while a third, heavier friend (a Barium ion) acted as a "cooling fan" to keep them from getting too hot and jittery.

Here is the clever part:

The Old Way: You tell Top A to spin "Up" and Top B to spin "Down." If the room shakes, Top A might get confused, and the secret is lost.
The New Way (DFS): They teach the tops a special synchronized dance.
- State 1: Top A is Up, Top B is Down.
- State 2: Top A is Down, Top B is Up.

The magic is that if the whole room shakes (a "common" noise), both tops get pushed in the exact same way at the exact same time. Because they are dancing in a pair, the difference between them stays exactly the same. It's like two people walking side-by-side in a strong wind; if the wind pushes both of them equally, they don't fall over relative to each other. They stay in sync.

This special dance is called a Decoherence-Free Subspace (DFS). It makes the information immune to the "shaky table" and the "crackly radio" because the noise affects both partners equally, canceling itself out.

3. The "Swap" Problem: When Dancers Switch Places

Even with this perfect dance, there was one tiny problem. Sometimes, the two tops would accidentally swap places on the stage.

Imagine Top A and Top B are holding hands. If they swap places, the "Up-Down" pattern flips to "Down-Up."
In a perfect world, this wouldn't matter. But in their lab, the magnetic field wasn't perfectly smooth; it was slightly stronger on one side of the room than the other.
When the tops swapped, the "Up-Down" pattern suddenly felt a different magnetic pull, causing the dance to get confused.

The Fix: The scientists realized they didn't need to stop the swapping (which is hard); they just needed to make the room's magnetic field so smooth that swapping didn't matter. They used special magnets to "iron out" the wrinkles in the magnetic field, making the room perfectly flat. Now, even if the tops swap places, the dance remains perfect.

4. The Result: A Super-Stable Memory

By combining this "Twin Dance" with a "Smooth Room" and a "Cooling Fan," they achieved something incredible:

The Test: They let the atoms dance for 1,600 seconds (about 26 minutes) and watched them.
The Outcome: The dance barely slowed down at all.
The Prediction: Based on their math, if they could eliminate the tiny remaining issues (like the tops swapping places), this system could theoretically keep the secret safe for millions of years.

Why Does This Matter?

Think of quantum computers as the next generation of super-computers. But right now, they are like a house of cards in a hurricane; they fall apart too fast to do anything useful.

This research is like building a fortress for those cards. By proving that we can keep quantum information safe for over 10 hours without needing expensive, bulky shielding, they have opened the door to:

Unbreakable Encryption: Keeping secrets safe for centuries.
Global Quantum Internet: Sending quantum messages across the world without them getting lost.
Super-Precise Clocks: Measuring time so accurately we could detect changes in gravity or the expansion of the universe.

In short, they found a way to make the quantum world "quiet" not by silencing the noise, but by teaching the atoms to dance in a way that the noise simply cannot touch.

1. Problem Statement

Quantum information processing relies fundamentally on the preservation of quantum coherence. While trapped atomic ions (specifically $^{171}\text{Yb}^+$ ) theoretically possess coherence times extending to millions of years due to the stability of their hyperfine ground states, experimental demonstrations have been severely limited by technical noise.

Current Limitations: Previous records reached approximately 90 minutes. The primary bottlenecks were:
- Microwave Phase Noise: Instability in the oscillators driving qubit transitions.
- Magnetic Field Fluctuations: Ambient environmental noise affecting Zeeman shifts.
- Motional Heating: Degradation of state discrimination during interrogation.
The Gap: There was a need to bridge the gap between experimental coherence times (hours) and the theoretical limits (millions of years) without relying on complex, resource-heavy active quantum error correction (QEC) or extreme magnetic shielding.

2. Methodology

The authors employed a hybrid approach combining Clock-State Qubits with Decoherence-Free Subspace (DFS) encoding and Sympathetic Cooling.

System Architecture:
- Qubits: Two $^{171}\text{Yb}^+$ ions encoded in the hyperfine "clock" states ( $|F=0, m_F=0\rangle$ and $|F=1, m_F=0\rangle$ ), which are naturally insensitive to first-order magnetic field fluctuations.
- Coolant: A single $^{138}\text{Ba}^+$ ion placed centrally between the two Yb ions (Yb-Ba-Yb configuration) to provide sympathetic cooling. This maintains the ions' motional state without disturbing the Yb quantum states via laser scattering.
- Encoding (DFS): The logical qubit is encoded in the antisymmetric subspace spanned by $\{|0\rangle_L \equiv |0\rangle|1\rangle, |1\rangle_L \equiv |1\rangle|0\rangle\}$ . This encoding makes the logical qubit phase dependent on the energy difference between the two ions rather than their absolute energy, rendering it immune to common-mode magnetic field fluctuations and global microwave phase noise.
Experimental Sequence:
1. Initialization: Preparation of the $|0\rangle|0\rangle$ state.
2. Superposition: A global microwave pulse creates the initial superposition.
3. Evolution & Decoupling: The system evolves for extended periods (up to 1600s). To counteract low-frequency noise and phase accumulation, a reverse-style spin-echo dynamical decoupling sequence is applied. This involves pairs of $\pi$ -pulses ( $R_0(\pi), R_\pi(\pi)$ ) with waiting intervals ( $\tau$ ).
4. Readout: State-dependent fluorescence is used to measure the two-qubit parity ( $P = \langle \sigma_{z1}\sigma_{z2} \rangle$ ), which serves as the metric for coherence.
Noise Mitigation Strategies:
- Gradient Suppression: The primary remaining decoherence source was identified as stochastic ion exchange hopping (ions swapping positions) in the presence of a residual magnetic field gradient. The team actively suppressed this gradient using compensation magnets, extending the phase evolution period from 1.8s to ~900–7000s.
- Leakage Control: High-extinction-ratio shutters and multi-stage switching networks were used to eliminate laser and microwave leakage.

3. Key Contributions

Passive Error Correction: Demonstrated that DFS encoding acts as a form of passive error correction, eliminating the need for active syndrome measurements or complex QEC circuits to reject dominant technical noise (magnetic and microwave).
Record-Breaking Coherence: Achieved a coherence time exceeding 10 hours (specifically $3.77 \times 10^4$ seconds) without magnetic shielding or enhanced microwave references.
Sympathetic Cooling Integration: Successfully integrated sympathetic cooling with DFS encoding to maintain long-term coherence while preserving the quantum state of the clock qubits.
Identification of New Limits: Systematically characterized the hierarchy of decoherence sources, identifying stochastic ion hopping in residual magnetic gradients as the current primary bottleneck, rather than fundamental atomic limits.

4. Key Results

Coherence Time: The logical DFS qubit exhibited a coherence time of $T_{DFS} = (3.77 \pm 1.09) \times 10^4$ seconds (approx. 10.5 hours).
Contrast Stability: Over 1600 seconds of measurement, the parity contrast decayed by only ~4%, remaining stable near the theoretical maximum of 0.5.
Physical Qubit Comparison: In contrast, the individual physical qubits (single ions) decohered rapidly with a time constant of $T_{single} \approx 8.1$ seconds, confirming that the observed long-term coherence is a property of the DFS encoding, not the individual ions.
$T_1$ Lifetime: The lifetime of the computational basis states ( $|0\rangle|0\rangle$ and $|1\rangle|1\rangle$ ) was measured to be $T_1 = (1.01 \pm 0.71) \times 10^5$ seconds, confirming that coherence is not limited by energy relaxation ( $T_1$ ) on this timescale.
Simulation vs. Experiment: Numerical simulations accounting for ion hopping rates and magnetic gradients predicted a coherence time of $3.95 \times 10^4$ s, which aligns closely with the experimental results.

5. Significance and Future Outlook

Scalable Quantum Memory: This work establishes that long-term quantum memory is achievable through strategic noise suppression and encoding rather than fundamental atomic limitations. This is crucial for scalable architectures (like QCCD) where qubits must idle in memory zones for extended periods.
Quantum Networks: Coherence times exceeding 10 hours allow for the preservation of entanglement over timescales longer than classical communication latencies and satellite orbital periods, paving the way for global quantum networks.
Fundamental Physics: Such stable systems offer unprecedented platforms for high-precision metrology and the search for variations in fundamental physical constants.
Path to "Million-Year" Coherence: The paper outlines a roadmap to reach the theoretical million-year limit:
1. Cryogenic Environments: To suppress stochastic ion hopping (currently the main bottleneck).
2. Magnetic Shielding: To further reduce residual field noise.
3. Individual Addressing: To minimize off-resonant photon scattering from cooling lasers.

In conclusion, this study demonstrates that by combining clock-state insensitivity with DFS encoding and advanced noise control, trapped-ion systems can achieve coherence times orders of magnitude beyond previous records, effectively unlocking the potential of atomic ions as persistent quantum memories.