If you've ever tried to keep a room full of toddlers focused on a single task, you'll appreciate the challenge of maintaining electron spin coherence in quantum dots. These microscopic arenas, where electrons pirouette to the tune of quantum mechanics, hold the key to fault-tolerant quantum computing - if only we can keep them dancing long enough.
In the quantum dot spin circus, two performers dominate the show:
The surface code threshold theorem tells us that error correction is possible if physical error rates are below ~1%. For spin qubits in quantum dots, this translates to demanding coherence time requirements:
| Operation | Typical Duration | Required T1/T2 |
|---|---|---|
| Single-qubit gate | 10-100 ns | T2 > 1 μs |
| Two-qubit gate | 50-500 ns | T2 > 10 μs |
| Measurement | 1-10 μs | T1 > 100 μs |
Several mechanisms conspire to ruin our quantum spin party:
The spin-orbit interaction couples the electron's spin to its orbital motion, allowing energy to leak into the environment. In GaAs quantum dots, this typically limits T1 to milliseconds at low temperatures, while silicon offers better performance with T1 extending to seconds.
The electron spin interacts with the nuclear spins of the host material, creating a fluctuating magnetic field. This is particularly problematic in materials like GaAs with nonzero nuclear spins, where T2* (the inhomogeneous dephasing time) can be as short as 10 ns.
Fluctuating electric fields from trapped charges or defects modulate the spin energy levels through spin-orbit coupling or g-factor variations. This typically manifests as slow T2 decay on timescales of microseconds.
The choice of quantum dot host material dramatically impacts spin coherence:
In silicon, removing the 4.7% 29Si isotopes (which have nuclear spin I=1/2) can dramatically improve coherence. Studies have shown:
Characterizing these timescales requires sophisticated measurement techniques:
Using carefully timed microwave pulses to measure T1 via inversion recovery and T2 via Hahn echo or more complex pulse sequences.
For quantum dots integrated with charge sensors, spin-to-charge conversion enables measurement without bulky microwave setups.
High-fidelity single-shot spin measurement is crucial for error correction, with recent demonstrations achieving >98% fidelity in Si/SiGe quantum dots.
The surface code threshold of ~1% physical error rate translates to specific requirements:
Operating at "sweet spots" where the qubit is first-order insensitive to dominant noise sources can dramatically improve coherence:
Emerging techniques promise further improvements:
Hole spins in strained Ge/SiGe quantum dots have shown promising properties:
Combining different qubit types may offer advantages:
Squeezing every last microsecond from spin coherence:
The state of play in spin qubit coherence (as of 2023):
| Material System | T1 (ms) | T2* (μs) | T2 echo (μs) | Suitability for FTQC |
|---|---|---|---|---|
| GaAs (natural) | >1 | ~0.01 | ~1 | Marginal |
| Natural Si/SiGe | >10 | ~0.1 | >10 | Promising |
| Isotopic Si/SiGe | >1000 | >1 | >1000 | Excellent |
| Ge/SiGe holes | >1 | >0.1 | >100 | Promising |