Alkaline-Earth Neutral-Atom Clock Qubit

Figure

Description

The alkaline-earth neutral-atom clock qubit is a family of neutral-atom architectures that exploits the clock-compatible $J=0$ manifolds of alkaline-earth-like atoms such as ${}^{87}$Sr and ${}^{171}$Yb. The central idea is not usually to store the logical qubit directly in the bare electronic ${}^1{S}_0\leftrightarrow {}^3{P}_0$ optical transition. Instead, in the clearest computing demonstrations, logical information is stored in long-lived nuclear-spin states within the ${}^1{S}_0$ ground manifold, while the ultra-narrow clock transition and metastable manifolds are used for shelving, transport, ancilla roles, or access to Rydberg interactions.

This architecture therefore sits between pure nuclear-spin storage and literal optical-clock qubits. In ${}^{171}$Yb, for example, the data qubit can live in the two $m_I=\pm 1/2$ nuclear-spin states of ${}^1{S}_0$, while optical-clock and Rydberg-accessible states provide the control stack. Recent hybrid schemes go one step further by pairing nuclear-spin data qubits with separate optical-clock ancilla qubits in dual-isotope arrays.

Because both ${}^1{S}_0$ and ${}^3{P}_0$ have $J=0$, electronic magnetic sensitivity is strongly suppressed. The residual field sensitivity is set by the chosen hyperfine or nuclear-spin pair and operating bias field, so the relevant protection is a clock-like encoding condition, not a generic multi-branch Zeeman manifold of the bare electronic states.

Hamiltonian

A representative effective model treats the logical qubit as two long-lived nuclear-spin states $|0⟩,|1⟩$ in the ${}^1{S}_0$ manifold, with an auxiliary Rydberg state $|r⟩$ used for entangling gates:

$H={\sum }_i\left[\frac{{\omega }_q}{2}{\sigma }_z^{(i)}+\frac{{\Omega }_q^{(i)}(t)}{2}{\sigma }_x^{(i)}-{\Delta }_r^{(i)}{n}_r^{(i)}+\frac{{\Omega }_r^{(i)}(t)}{2}\left(|1_i⟩⟨r_i|+|r_i⟩⟨1_i|\right)\right]+{\sum }_{i<j}{V}_{ij}{n}_r^{(i)}{n}_r^{(j)}$

where ${\omega }_q$ is the nuclear-spin qubit splitting, ${\Omega }_q$ is the single-qubit drive, ${\Omega }_r$ and ${\Delta }_r$ control the temporary excitation into a strongly interacting Rydberg manifold, and $V_{ij}$ is the Rydberg blockade interaction.

The narrow ${}^1{S}_0\leftrightarrow {}^3{P}_0$ clock transition is then best viewed as part of the control and ancilla toolbox, not as the only possible logical basis. Hybrid architectures can also assign optical-clock qubits to dedicated ancilla atoms while retaining nuclear-spin data qubits.

Motivation

• Combines clock-grade internal-state stability with neutral-atom array scalability
• Separates long-lived data storage from fast interaction channels, reducing control crosstalk
• Naturally supports hybrid data/ancilla architectures for mid-circuit readout and QEC primitives
• Offers a clean route to erasure-biased neutral-atom computing because metastable-state structure makes loss and leakage easier to identify

Experimental Status

Original proposal — Daley et al. (2008):

• Proposed quantum computing with alkaline-earth atoms using nuclear-spin storage plus metastable-state transport and control
• Established the basic clock-compatible neutral-atom architecture

Detailed control architecture — Daley, Ye, and Zoller (2011):

• Developed state-dependent lattice schemes that separate storage and gate operations
• Clarified how ${}^1{S}_0$ and ${}^3{P}_0$ can play distinct architectural roles

Alkaline-earth Rydberg entanglement — Madjarov et al. (2020):

• Demonstrated high-fidelity entanglement and detection in ${}^{88}$Sr Rydberg atoms
• Validated the alkaline-earth-specific entangling path needed for clock-compatible architectures

Universal logic in tweezers — Ma et al. (2022):

• Demonstrated universal gate operations on ${}^{171}$Yb nuclear-spin qubits in an optical tweezer array
• Reported single-qubit gate fidelity of 99.96% and spin-echo coherence beyond 10 s

Hybrid data/ancilla array — Nakamura et al. (2024):

• Demonstrated a dual-isotope Yb array with ${}^{171}$Yb nuclear-spin data qubits and ${}^{174}$Yb optical-clock ancilla qubits
• Showed low-crosstalk ancilla readout compatible with mid-circuit-QEC-style operation

Key Metrics

Metric	Value	Notes	Fidelity reference
1Q gate fidelity	99.96%	${}^{171}$Yb nuclear-spin qubit in optical tweezers	Ma et al. 2022
Coherence time	$T_2>10\text{s}$	Spin-echo coherence for ${}^{171}$Yb nuclear-spin clock qubit	Ma et al. 2022
Ancilla discrimination fidelity	0.9992	${}^{174}$Yb optical-clock ancilla readout in hybrid array	Nakamura et al. 2024
Ancilla survival probability	0.988	Post-readout atom survival in hybrid array	Nakamura et al. 2024
Erasure-conversion efficiency	$>97\%$ (proposed)	Converts loss / Rydberg-decay events into detectable erasures	Wu et al. 2022

References

Foundational architecture

• A. J. Daley, M. M. Boyd, J. Ye, and P. Zoller, “Quantum Computing with Alkaline-Earth-Metal Atoms,” Phys. Rev. Lett. 101, 170504 (2008), arXiv:0808.1940
• A. J. Daley, J. Ye, and P. Zoller, “State-dependent lattices for quantum computing with alkaline-earth-metal atoms,” Eur. Phys. J. D 65, 207 (2011), arXiv:1102.1463

Experimental milestones

• I. S. Madjarov et al., “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857 (2020), arXiv:2001.04455
• S. Ma, A. P. Burgers, G. Liu, J. Wilson, B. Zhang, and J. D. Thompson, “Universal Gate Operations on Nuclear Spin Qubits in an Optical Tweezer Array of ${}^{171}$Yb Atoms,” Phys. Rev. X 12, 021028 (2022), arXiv:2112.13487
• Y. Nakamura, T. Kusano, R. Yokoyama, K. Saito, K. Higashi, N. Ozawa, T. Takano, Y. Takasu, and Y. Takahashi, “Hybrid Atom Tweezer Array of Nuclear Spin and Optical Clock Qubits,” Phys. Rev. X 14, 041062 (2024)

Error-correction direction

• Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, “Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays,” Nat. Commun. 13, 4656 (2022), arXiv:2201.03540

Linked Papers

• daley-2008-quantum-computing-with-alkaline-earth-atoms
• daley-2011-state-dependent-lattices-for-quantum-computing-with-alkaline-earth-metal-atoms
• madjarov-2020-high-fidelity-entanglement-and-detection-of-alkaline-earth-rydberg-atoms
• ma-2022-nuclear-spin-atom
• nakamura-2024-hybrid-atom-tweezer-array
• wu-2022-erasure-neutral-atoms

Evergreen context

• coherence-time-hierarchy — the whole point is to keep the storage manifold much quieter than the interaction manifold
• rydberg-blockade-mechanism — fast entangling power still comes from temporary access to strongly interacting excited states
• erasure-error-vs-pauli-error — alkaline-earth platforms are unusually well placed to convert loss and leakage into decoder-friendly erasure information

Related Entries

• nuclear-spin-neutral-atom-qubit — the most direct subset focused on ground-manifold nuclear-spin storage
• rydberg-neutral-atom-qubit — broader neutral-atom entangling-gate ecosystem
• erasure-qubit — error-model perspective strongly aligned with alkaline-earth proposals
• qubit-readout — hybrid ancilla-readout schemes are a major recent differentiator