Ytterbium-171 Hyperfine Qubit

Figure

Description

The ytterbium-171 hyperfine qubit encodes quantum information in the two hyperfine clock states of the ${}^{171}{\text{Yb}}^{+}$ ion’s ${}^2{S}_{1/2}$ ground-state manifold: $|0⟩\equiv |F=0,m_F=0⟩$ and $|1⟩\equiv |F=1,m_F=0⟩$, separated by 12.642812 GHz. Both states have $m_F=0$, making the qubit first-order insensitive to magnetic field fluctuations — the transition frequency shifts only quadratically with field, enabling exceptionally long coherence times.

The ${}^{171}{\text{Yb}}^{+}$ ion has nuclear spin $I=1/2$ and no electronic angular momentum in the ground state ($J=1/2$), yielding the simplest possible hyperfine structure: just four ground states. This simplicity, combined with convenient photoionization loading and state-dependent fluorescence detection on the ${}^2{S}_{1/2}\leftrightarrow {}^2{P}_{1/2}$ cycling transition at 369.5 nm, makes it the workhorse qubit for multiple trapped-ion quantum computing platforms including Quantinuum (H-series processors) and IonQ.

Two-qubit entangling gates are performed via the Coulomb-mediated motional bus using either Raman transitions (stimulated Raman with 355 nm pulsed laser) or microwave-driven schemes. Gate fidelities exceeding 99.9% have been demonstrated (Ballance et al. 2016, Gaebler et al. 2016).

Hamiltonian

The ground-state hyperfine Hamiltonian is:

$H_{\text{hfs}}=A_{\text{hfs}}\mathbf{I}\cdot \mathbf{J}$

where $A_{\text{hfs}}$ is the magnetic dipole hyperfine constant, $\mathbf{I}$ is the nuclear spin, and $\mathbf{J}$ is the electronic angular momentum. For ${}^{171}{\text{Yb}}^{+}$ with $I=J=1/2$, this gives a splitting:

$\Delta E_{\text{hfs}}=A_{\text{hfs}}=h\times 12.642812\text{GHz}$

In an external magnetic field $B$, the clock-state transition frequency has only a second-order Zeeman shift:

${\omega }_{01}(B)={\omega }_{01}(0)+\beta B^2$

where $\beta /2\pi \approx 310.8{\text{Hz/mT}}^2$, providing excellent field insensitivity.

Motivation

Trapped-ion qubits require long coherence times and high-fidelity operations to serve as building blocks for fault-tolerant quantum computing. Hyperfine clock states in ${}^{171}{\text{Yb}}^{+}$ provide first-order magnetic field insensitivity without active stabilization, coherence times exceeding 10 minutes, and a microwave-frequency splitting compatible with high-stability oscillators. The simple level structure and efficient state detection make ${}^{171}{\text{Yb}}^{+}$ the most widely deployed trapped-ion qubit platform.

Experimental Status

First characterization — Olmschenk et al. (2007):

• Demonstrated manipulation and detection of a trapped ${\text{Yb}}^{+}$ hyperfine qubit
• Characterized state preparation, single-qubit gates, and state-dependent fluorescence readout
• Established the ${}^{171}{\text{Yb}}^{+}$ system as a viable qubit platform

High-fidelity two-qubit gates — Ballance et al. (2016):

• Achieved 99.9(1)% two-qubit gate fidelity using light-shift gates on ${}^{171}{\text{Yb}}^{+}$ hyperfine qubits
• Oxford group demonstration using geometric phase gates

High-fidelity gate set — Gaebler et al. (2016):

• Demonstrated a high-fidelity universal gate set for ${}^9{\text{Be}}^{+}$ with amplitude-modulated Mølmer-Sørensen gates
• Methods directly applicable and transferred to ${\text{Yb}}^{+}$ platforms

Long coherence — Wang et al. (2021):

• Single ion qubit with estimated coherence time exceeding one hour using dynamical decoupling sequences
• Demonstrated the extraordinary coherence potential of clock-state encodings

System-level deployment — Quantinuum H2 (2024):

• 56-qubit fully connected ${}^{171}{\text{Yb}}^{+}$ register
• System-level two-qubit gate fidelities of 99.8%
• Mid-circuit measurement and qubit reuse demonstrated, enabling real-time quantum error correction

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_1$	>10 s	Radiative lifetime of ground state; effectively infinite	—
$T_2$ (echo)	>10 min	With dynamical decoupling sequences	Wang et al. 2021
$T_2^{\ast }$	1–10 s	Limited by magnetic field fluctuations	Olmschenk et al. 2007
Hyperfine splitting	12.642812 GHz	Clock transition, first-order field insensitive	Olmschenk et al. 2007
1Q gate fidelity	99.99%+	Randomized benchmarking	Gaebler et al. 2016
2Q gate fidelity	99.9%	Light-shift and MS gates	Ballance et al. 2016
SPAM fidelity	99.93%	Electron shelving detection	Noek et al. 2013
Gate time (1Q)	1–10 μs	Microwave or Raman driven	Olmschenk et al. 2007
Gate time (2Q)	30–600 μs	Depends on gate scheme and ion number	Gaebler et al. 2016
Operating temperature	~4 K (trap)	Room-temperature vacuum; ions laser-cooled to ~mK	—

References

Original characterization

• S. Olmschenk et al., “Manipulation and detection of a trapped Yb⁺ hyperfine qubit,” Phys. Rev. A 76, 052314 (2007)

High-fidelity gates

• C. J. Ballance et al., “High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits,” Phys. Rev. Lett. 117, 060504 (2016)
• J. P. Gaebler et al., “High-Fidelity Universal Gate Set for ⁹Be⁺ Ion Qubits,” Phys. Rev. Lett. 117, 060505 (2016)

Coherence

• P. Wang et al., “Single ion qubit with estimated coherence time exceeding one hour,” Nat. Commun. 12, 233 (2021)

SPAM

• R. Noek et al., “High speed, high fidelity detection of an atomic hyperfine qubit,” Opt. Express 21, 21449 (2013)

Linked Papers

• olmschenk-2007-yb171-qubit
• ballance-2016-ion-gate-fidelity
• gaebler-2016-ms-gate

Related Entries

• trapped-ion-qubit — parent platform
• cirac-zoller-gate — foundational trapped-ion gate proposal
• motional-mode-coupling-in-ion-traps — physics of the Coulomb-mediated bus
• coherence-time-hierarchy — context for coherence comparison
• barium-137-ion-qubit — Ba-137 hyperfine qubit; Yb-171 serves as sympathetic coolant in Helios
• calcium-43-ion-qubit — Ca-43 hyperfine qubit; alternative hyperfine species with microwave-driven gates
• strontium-88-ion-qubit — Sr-88 optical qubit; no hyperfine structure, visible wavelengths
• beryllium-9-ion-qubit — Be-9 hyperfine qubit; lightest ion, UV transitions