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.

Key Findings

• Clock-state encoding provides first-order insensitivity to magnetic field fluctuations, with coherence times $T_2>10$ minutes demonstrated using dynamical decoupling (Wang et al. 2021).
• Two-qubit gate fidelities of 99.9(1)% achieved via light-shift gates (Ballance et al. 2016) and amplitude-modulated Mølmer-Sørensen gates (Gaebler et al. 2016).
• Quantinuum H2 processor achieves system-level 2Q gate fidelities of 99.8% across a fully connected 56-qubit register.
• State preparation and measurement (SPAM) fidelity exceeds 99.9% using electron shelving to the ${}^2{D}_{3/2}$ state.
• Mid-circuit measurement and qubit reuse demonstrated, enabling real-time quantum error correction protocols.

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	—

Linked Papers

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

Related Entries

• trapped-ion-qubit
• cirac-zoller-gate
• motional-mode-coupling-in-ion-traps
• coherence-time-hierarchy