Electron spin qubits on liquid helium

Short answer: Electrons held on the surface of liquid helium are a proposed qubit platform, because the spin of a free electron in vacuum should decohere slowly. A 2003 arXiv paper suggested coherence times exceeding 100 seconds, a 2009 paper (published in Physical Review Letters in 2010) proposed coupling a single electron to an on-chip superconducting cavity, and a 2023 Physical Review Applied paper presents a blueprint using ferromagnetic micropillars. All three are proposals and calculations. The abstracts report no working qubit.

2003: the original suggestion

The arXiv abstract (cond-mat/0301581, version 2 posted in 2006) notes that many physical systems have been proposed for quantum computers, but that building even modest systems of a few hundred qubits faces formidable obstacles. The author suggests that the spin of electrons floating on liquid helium would make excellent qubits. They can be held and manipulated electrostatically like electrons in semiconductor heterostructures, but because they sit in vacuum, their spins should suffer much less decoherence. In particular, spin-orbit interaction is reduced, so moving the qubits with gate voltages has little effect on coherence. After considering the remaining decoherence sources, the author reports that coherence times for electron spins on helium can be expected to exceed 100 seconds, and shows how to obtain a controlled-NOT between two qubits using the magnetic dipole-dipole interaction. These are estimates and not measurements.

2009 to 2010: coupling to a cavity

The arXiv paper 0912.1406 (journal reference Physical Review Letters 105, 040503, 2010) proposes coupling an on-chip high-finesse superconducting cavity to the lateral motion and spin state of a single electron trapped on the surface of superfluid helium. The authors estimate motional coherence times above 15 microseconds, with energy exchanged coherently with cavity photons in less than 10 nanoseconds for charge states and faster than 1 microsecond for spin states. They say this makes the system attractive for quantum information processing and cavity quantum electrodynamics, and that strong interaction with cavity photons would allow nondestructive readout and coupling of distant electrons. These are estimates from a proposal.

2023: a blueprint

The Physical Review Applied abstract presents a blueprint for a fault-tolerant quantum computer using electron spin states on liquid helium. The authors propose ferromagnetic micropillars to trap single electrons and to create a local magnetic field gradient. The gradient hybridizes charge and spin, which they say lets the design benefit from both the long spin coherence time and the long-range Coulomb interaction acting on charge. They present concrete schemes for single- and two-qubit gates and quantum nondemolition readout. They say the hybridization is large enough for fast gates and small enough not to degrade spin coherence significantly, which would lead to high-fidelity gates. This is a design claim that depends on an experiment that has not been reported here.

Limits

All three sources are theory. A fault-tolerant machine, as in the 2023 title of the proposal, is a goal and not a result. Coherence figures above are estimates by the authors, and no source in this set reports a measured qubit.

FAQ

Why helium?

Electrons on helium sit in vacuum, which the 2003 author argues reduces decoherence.

What coherence time was predicted?

More than 100 seconds for spin, in the 2003 paper.

Has a helium-electron qubit been built?

These abstracts do not report one.

What does the micropillar do?

It traps an electron and creates a magnetic field gradient, per the 2023 proposal.

Is this a fault-tolerant computer?

No. The 2023 paper is a blueprint.