Single ion qubit with estimated coherence time exceeding one hour

Quantum coherence underpins scalable quantum computation, quantum metrology, and quantum communication, but practical systems suffer decoherence from environmental coupling and control fluctuations, degrading information processing, sensing sensitivity, and communication protocols. Stable, long-coherence quantum memories are therefore of high practical importance. Prior work achieved long coherence times in ensembles (up to minutes at room temperature and hours at cryogenic temperatures) and, for single-qubit memories—crucial building blocks for quantum computers and repeaters—records at the minute scale in trapped ions. The previous single-ion record (171Yb+) reached 660 s using sympathetic cooling and dynamical decoupling to mitigate heating-induced detection infidelity and magnetic-field fluctuations. Despite the expectation that fundamental limits lie well beyond one hour, technological barriers remained. This work targets those barriers—ambient magnetic-field fluctuations, local oscillator phase noise, and microwave leakage—to realize a single-ion quantum memory with an estimated coherence time exceeding one hour, and further characterizes the decoherence dynamics via quantum process tomography and resource-theoretic benchmarks.

The paper situates its contribution within efforts to extend quantum memory coherence across various platforms. Ensembles of trapped ions and solid-state nuclear spins have reached 10 minutes and 40 minutes at room temperature, and several hours at 4 K. For single qubits in trapped ions, coherence times up to minutes have been reported, with key limiting factors including qubit-detection infidelity due to laser-cooling-induced heating and magnetic-field noise. Sympathetic cooling combined with dynamical decoupling enabled coherence beyond 1 minute, culminating in a 660 s record for a single 171Yb+ ion qubit. These advances suggested longer times are technically limited rather than fundamental. The present study identifies and mitigates residual magnetic noise, local oscillator phase noise, and microwave leakage, and adopts advanced dynamical decoupling to push coherence into the hour scale, while employing quantum process tomography and resource-theoretic measures (robustness of quantum memory and relative entropy of coherence) to benchmark performance.

Experimental platform: A single 171Yb+ ion (memory qubit) and a 138Ba+ ion (sympathetic coolant) are co-trapped in a four-rod Paul trap. The 171Yb+ qubit is encoded in the S1/2 hyperfine clock states |0⟩ = |F=0,mf=0⟩ and |1⟩ = |F=1,mf=0⟩ separated by ~12.642 GHz (reported as 26421811.9 ± 3.10 kHz with magnetic field along Z). Continuous Doppler cooling is applied to 138Ba+ to sympathetically cool the two-ion crystal throughout experiments, enabling high-fidelity state preparation and readout of 171Yb+ without detection infidelity from heating.

Suppression of ambient magnetic-field noise: The vacuum chamber containing the trap is enclosed within a two-layer yoke-laminated magnetic shield. A fluxgate meter shows >40 dB attenuation at 50 Hz (dominant lab AC line noise). The bias magnetic field (~5.8 G) is provided by a Sm2Co17 permanent magnet (temperature coefficient ~0.03%/K) with adjustable positioning to tune field strength. After shielding and permanent magnet installation, the coherence time of a field-sensitive Zeeman qubit increases to >30 ms. Noise spectroscopy via dynamical decoupling indicates that 50 Hz and 150 Hz noise components are suppressed below 16 dB and 32 dB, respectively; further CPMG diagnostics show 50 Hz and 150 Hz field noise below ~16 μG and ~32 μG.

Microwave frequency stability: Qubit control uses resonant microwaves near 12.6 GHz. Ramsey measurements are sensitive to local oscillator phase noise. A low-noise crystal oscillator reference (order-of-magnitude smaller Allan variance than a regular generator) is used to reduce low-frequency phase noise.

Suppression of microwave and laser leakage: A microwave switch chain is inserted after amplification to reduce leakage by >70 dB; overall microwave output is suppressed by an additional ~16 dB when all switches are off. With 175 μs control pulses and 0.4 s interpulse intervals, leakage effects are negligible and further mitigated by dynamical decoupling. Leakage of 171Yb+ laser light is reduced using AOMs, an electro-optic pulse picker, mechanical shutters, and single-mode fiber delivery.

Control sequence and dynamical decoupling: The protocol initializes 171Yb+ to |0⟩ via optical pumping, applies a Ramsey sequence with π/2 pulses bracketing storage, and reads out via state-dependent fluorescence. Continuous 138Ba+ cooling is maintained. Basic Ramsey yields a short T2* (~1.6 μs in a specific measurement), improved to ~11.5 μs with a single spin-echo. To achieve long storage, Knill dynamical decoupling (KDDn) sequences comprising equally spaced π pulses with phase-cycling (first five as σ− rotations, second five as σ+ with 90° phase shift) are interleaved between Ramsey π/2 pulses. The filter function of KDDn exhibits a peak determined by pulse spacing, enabling optimization against the measured noise spectrum. Pulse intervals are chosen to place the filter peak around 2π × 1.25/T to suppress ambient noise effectively. Mechanical shutters and the EOPP are closed during storage and opened before readout (≈10 ms delays).

Quantum process tomography and metrics: Full process tomography is performed at multiple storage times to reconstruct the process matrix ρexp and quantify process fidelity Fp to the ideal identity channel. A phenomenological model combining depolarization (time constant T1) and dephasing (time constant T2) is fit to the evolution, yielding T1 and T2. Mean output fidelity Fmean is estimated via Monte Carlo over 105 random input states (Haar-distributed). Resource-theoretic benchmarks include the relative entropy of coherence (REC) calculated as ratios between output and input states averaged over 105 states (with REC<1), and robustness of quantum memory (RQM) as a channel-level measure of information preservation. Additional diagnostics include CPMG-based magnetic noise spectroscopy and alternative Ramsey/spin-echo measurements without DD for special-case applications.

• By suppressing dominant error sources—ambient magnetic-field fluctuations (two-layer magnetic shielding and permanent magnet bias), local oscillator phase noise (low-Allan-variance crystal reference), and microwave leakage (>70 dB reduction with additional 16 dB output suppression)—the 171Yb+ single-ion qubit exhibits an estimated coherence time of about 5500 s. This estimate is the time constant from an exponential fit to Ramsey-contrast data acquired with KDD dynamical decoupling, with direct measurements performed up to 960 s.
• Process tomography analyzed with a combined depolarization and dephasing model yields T1 = 2200 ± 230 s and T2 = 4200 ± 580 s. The process fidelity decays consistently with this noise model.
• The mean output fidelity Fmean decays with a time constant of 5200 ± 500 s (Monte Carlo over 105 input states), consistent within error bars with a simple estimate Fmean ≈ (2F1 + 1)3/4 giving 5600 ± 650 s.
• Magnetic noise at 50 Hz and 150 Hz (line noise and harmonic) is strongly suppressed; CPMG diagnostics show fringe contrasts of 0.97–0.98 at t = 10 ms and 3.3 ms with 190 pulses, corresponding to residual magnetic noise levels below ~16 μG (50 Hz) and ~32 μG (150 Hz).
• Detection efficiency is 96.8% (corrected for correlated error magnitude under uncorrelated error assumption per cited method).
• Baseline Ramsey T2* without DD is short (∼1.6 μs in one measurement), improved to ∼11.5 μs with a single spin-echo; alternative measurements show T2* ≈ 0.38 s and coherence time 16 ± 0.22 s in specific detuned Ramsey protocols, underscoring the critical role of optimized DD.
• Resource-theoretic metrics: The mean REC ratio exhibits exponential decay with a characteristic time of ~3500 ± 150 s, reflecting sensitivity to small process-matrix errors and stringent averaging conditions. RQM analysis supports that the memory significantly preserves quantum information relative to classical measure-and-prepare limits over extended durations.

The study directly addresses the technological impediments that limited single-ion quantum memory coherence to minutes, demonstrating that ambient magnetic-field fluctuations, local oscillator phase noise, and microwave leakage were the dominant, surmountable sources. Through targeted engineering—magnetic shielding with a stable permanent magnet bias, low-noise clock referencing, and rigorous suppression of microwave and optical leakage—combined with robust Knill dynamical decoupling, the authors extend the effective coherence to the hour scale. Process tomography reveals that both dephasing and depolarization contribute, with multi-thousand-second T2 and T1 times, respectively, and the mean output fidelity confirms long-lived information retention. Resource-theoretic benchmarks (REC and RQM) contextualize the performance in a channel-agnostic framework, showing substantial resilience of quantum information compared to classical memory channels. These results validate that practical, long-coherence quantum memories are achievable with careful noise engineering and control, impacting scalable quantum computing architectures (where memory idling is frequent), quantum repeaters and networks (where storage bridges probabilistic steps), and precision metrology (where long interrogation times boost sensitivity).

This work demonstrates a trapped-ion single-qubit quantum memory (171Yb+) with an estimated coherence time exceeding one hour (~5.5 × 10^3 s), surpassing previous records by an order of magnitude. By identifying and mitigating magnetic-field noise, local oscillator phase noise, and microwave leakage, and by deploying optimized KDD dynamical decoupling, the system maintains high process and mean fidelities over extended storage times. Quantum process tomography and resource-theoretic analyses (REC, RQM) provide comprehensive characterization of decoherence channels and memory robustness. Future directions include scaling to multi-qubit memories with independently addressable, long-lived storage and retrieval, further improving oscillator stability and magnetic-field control to push coherence beyond 10^5 s, and ultimately approaching the fundamental hyperfine-state lifetime limits (estimated to be extremely long). These advances will support near-term NISQ-era applications lacking full quantum error correction and pave the way for robust quantum communication and metrology.

• The hour-scale coherence relies on dynamical decoupling; applications unable to deploy DD may experience significantly shorter T2* (e.g., μs–s range in baseline/spin-echo measurements).
• Current coherence appears primarily limited by local oscillator phase noise and residual magnetic-field fluctuations; further improvements require better clock references and magnetic stability.
• Microwave and optical leakage, while strongly suppressed (>70 dB for microwaves), remain potential decoherence channels if not rigorously controlled.
• Process tomography exhibits discrepancies (e.g., dephasing time inference) due to quantum projection noise and finite sampling across multiple measurement bases; increased statistics would reduce these errors.
• Measurement data directly acquired up to 960 s necessitate extrapolation (exponential fits) to estimate multi-thousand-second coherence constants.
• Additional limiting mechanisms include ion hopping, scattering from 138Ba+ cooling light during continuous sympathetic cooling, and background gas collisions, which may impose practical ceilings without further engineering.