Trapped-Electron Qubit

Figure

Description

The trapped-electron qubit encodes quantum information in the spin state of a single electron confined in an electromagnetic trap — either a radio-frequency Paul trap or a Penning trap. The electron spin-1/2 provides a natural two-level system: $|0⟩=|\uparrow ⟩$ and $|1⟩=|\downarrow ⟩$, split by the Zeeman energy $\hslash {\omega }_s=g_e{\mu }_{B}B$ in an applied magnetic field $B$.

The fundamental motivation is the electron’s extraordinarily low mass: at $9.1\times 10^{-31}$ kg, it is roughly 1,800× lighter than the lightest trapped-ion species (${}^9{\text{Be}}^{+}$) and over 250,000× lighter than ${}^{171}{\text{Yb}}^{+}$. Since motional (secular) frequencies in a Paul trap scale as ${\omega }_{\text{sec}}\propto 1/\sqrt{m}$, electrons have motional frequencies in the GHz range (vs. MHz for ions). This translates to potentially much faster two-qubit gate operations — the ion’s shared-motion entangling gate speed is limited by the motional frequency — and faster transport in QCCD-style architectures.

Unlike trapped ions, electrons have no internal level structure beyond spin, eliminating laser-based state preparation, manipulation, and readout entirely. All control would be electronic: microwave fields for spin rotations, dc/rf electric fields for trapping and transport, and image current or cavity-coupled detection for readout. This “all-electronic” approach avoids the laser system complexity that is a primary scaling bottleneck for trapped-ion systems.

However, the same light mass that enables fast operations also creates challenges: the electron is highly sensitive to electric field noise (anomalous heating rates scale as $\propto q^2/m$, so heating is severe), and the spin readout — trivial for ions via fluorescence — requires sophisticated detection schemes using magnetic gradients and motional coupling (Peng et al. 2017) or coupling to superconducting resonators.

Hamiltonian

A single electron in a linear Paul trap with an applied magnetic field:

$H=\frac{{\hat{p}}^2}{2m_e}+\frac{1}{2}{m}_e{\omega }_{\text{sec}}^2{\hat{x}}^2+\frac{\hslash {\omega }_s}{2}{\sigma }_z$

where $m_e$ is the electron mass, ${\omega }_{\text{sec}}$ is the secular trap frequency (GHz range), and ${\omega }_s=g_e{\mu }_{B}B/\hslash$ is the spin Larmor frequency.

For two-qubit gates, the spin-motion coupling is induced by a magnetic field gradient $\partial B/\partial x$:

$H_{\text{int}}=-g_e{\mu }_B\frac{\partial B}{\partial x}\hat{x}{\sigma }_z$

This couples the electron’s motional state to its spin, enabling Mølmer-Sørensen-type or geometric phase entangling gates via the shared motional mode, directly analogous to trapped-ion gates but at GHz motional frequencies.

The predicted two-qubit gate time scales as:

${\tau }_{\text{gate}}\sim \frac{1}{\eta {\omega }_{\text{sec}}}$

where $\eta$ is an effective Lamb-Dicke-like parameter for the spin-motion coupling, yielding predicted gate times of tens to hundreds of nanoseconds — comparable to superconducting qubits.

Motivation

Trapped-electron qubits aim to combine the best features of trapped ions (long spin coherence, identical qubits, motional-mode entangling gates) with the speed of superconducting circuits (ns-scale gates), while eliminating laser systems entirely. If the technical challenges of single-electron detection, ground-state cooling, and heating suppression can be overcome, trapped electrons could offer a uniquely scalable platform: all-electronic control, CMOS-compatible fabrication of surface traps, and gate speeds competitive with solid-state platforms while maintaining the isolation-from-material-defects advantage of trapped-particle approaches.

Experimental Status

Quantum information processing proposal — Daniilidis et al. (2013):

• Proposed interfacing trapped electrons with superconducting electronics via parametric frequency conversion.
• Designed a scheme for coherent quantum information transfer between electron motional states and superconducting resonators.
• Identified geometric nonlinearities in the trapping potential as a resource for coupling.

Feasibility study — Yu et al. (2022):

• Comprehensive theoretical analysis of trapped-electron quantum computing in a linear Paul trap.
• Proposed experimental sequence: trapping, resistive cooling to ~0.4 K, electronic detection, spin readout via magnetic gradients, and entangling gates.
• Simulated two-qubit Bell-state fidelities of ~99.99% under realistic parameters.
• Proposed QCCD architecture adapted for electrons, with transport times ~100× faster than ions.

Spin readout proposal — Peng et al. (2017):

• Proposed spin readout via oscillating magnetic field gradients in a surface Paul trap.
• Predicted readout fidelity of 99.7% in 25 μs.
• All-electronic scheme: no lasers or fluorescence required.

Electron trapping and detection — Taniguchi and Noguchi (2025):

• Demonstrated image current detection of electrons in a room-temperature Paul trap.
• Extracted electron signals via coupling to microwave cavity modes.
• Observed resistive cooling of trapped electron clouds.
• Key step toward single-electron ground-state cooling at cryogenic temperatures.

Electron dynamics simulations — Huang et al. (2025):

• Numerical studies of electron dynamics in linear Paul traps including Wigner crystal formation for multi-electron entangling operations.
• Analyzed cooling methods and stability under strong magnetic fields.

Status as of 2026:

• No trapped-electron spin qubit has been experimentally demonstrated. Electron trapping in Paul traps at room temperature and image current detection have been achieved, but single-electron isolation, ground-state cooling, and spin readout remain undemonstrated.

Key Metrics

Metric	Value	Notes	Fidelity reference
Motional frequency	~GHz	vs. ~MHz for ions; enables faster gates	Yu et al. 2022
2Q gate fidelity	~99.99% (predicted)	Simulated Bell-state fidelity	Yu et al. 2022
Spin readout fidelity	99.7% (predicted)	Via magnetic gradient + motional coupling	Peng et al. 2017
Gate time (2Q)	~10–100 ns (predicted)	Comparable to superconducting gates	Yu et al. 2022
Control mechanism	All-electronic	Microwave spin rotations, dc/rf trapping, image current readout	—
Operating temperature	~100 mK (target)	Cryogenic needed for ground-state cooling; trapping at room temperature demonstrated	—

Scaling Considerations

• Anomalous heating: the $q^2/m$ scaling of heating rates means electrons are ~10⁶× more susceptible to electric field noise than ions. Cryogenic operation and ultra-clean trap surfaces are essential, and the heating rate may ultimately limit gate fidelities.
• Single-electron detection: detecting and addressing individual electrons without fluorescence requires sensitive electronic readout (image currents, superconducting resonators). This has been demonstrated for electron clouds but not single electrons in Paul traps.
• Ground-state cooling: achieving motional ground state at GHz frequencies requires starting temperatures below ~50 mK. Resistive cooling followed by sideband cooling via spin-motion coupling is the proposed path.
• Magnetic field stability: the Zeeman splitting depends on magnetic field, requiring either shielding or clock-like transition schemes for long coherence.
• Fabrication compatibility: surface Paul traps for electrons can leverage CMOS fabrication technology, with electrode dimensions of ~10 μm, a potential advantage over ion traps requiring ~100 μm features.
• Comparison to ions: trapped electrons trade the proven, high-fidelity operations of trapped ions for theoretical speed advantages that remain unvalidated experimentally.

References

Proposals

• N. Daniilidis et al., “Quantum information processing with trapped electrons and superconducting electronics,” New J. Phys. 15, 073017 (2013) | arXiv:1304.4710
• P. Peng, C. Matthiesen, and H. Häffner, “Spin readout of trapped electron qubits,” Phys. Rev. A 95, 012312 (2017) | arXiv:1611.00130
• Q. Yu et al., “Feasibility study of quantum computing using trapped electrons,” Phys. Rev. A 105, 022420 (2022) | arXiv:2112.04034

Experimental progress

• A. Huang et al., “Numerical Investigations of Electron Dynamics in a Linear Paul Trap,” arXiv:2503.12379 (2025)

Linked Papers

• daniilidis-2013-trapped-electron-superconducting
• peng-2017-electron-spin-readout
• yu-2022-trapped-electron-feasibility

Related Entries

• trapped-ion-qubit — parent platform concept; electrons replace ions
• cirac-zoller-gate — entangling gate principle adapted for electron motional modes
• spin-qubit — broader spin qubit family