There's still work to do for full fault-tolerant *computation*, especially logical gate implementations. But this lays an important foundation.
Comments welcome! 🙂 (4/4)

This bridges a long-standing gap: while Lloyd & Braunstein showed that universal CV gates are theoretically sufficient for quantum computing, it wasn't clear if or how they could support fault tolerance. Our results strongly suggest they can—at least for memory. (3/4)

TL;DR:
If you
1. Start from vacuum
2. Use continuous-variable gates from a Lloyd-Braunstein universal set
3. Optimize gate parameters to prepare GKP qubits
→ you can achieve error rates below the threshold for GKP-surface-code quantum memory ✅ (2/4)

8/ If you're into quantum computing, quantum optics, or fundamental questions about bosonic systems, check it out! 📄👇

🔗 arxiv.org/abs/2501.13857

Would love to hear your thoughts! #QuantumComputing #QuantumOptics #Physics

7/ Takeaway: Even though bosonic systems live in infinite dimensions, the effective descriptions we use are actually sufficient to capture their physics! 🎯

6/ Why does this matter? 🤔

✔️ Validates common modeling approaches in quantum optics & computing.

✔️ Provides a general way to engineer bosonic quantum states & gates.

✔️ Leads to an infinite-dimensional Solovay–Kitaev theorem.

5/ We tackle this question & prove two key results:

1️⃣ Any physical bosonic unitary evolution can be approximated by a finite-dimensional one.

2️⃣ Any finite-dimensional unitary evolution can be exactly generated by a Hamiltonian that's a polynomial of canonical operators.

4/ To simplify their description, we often use Hilbert space truncations or polynomial Hamiltonians. But do these approximations really capture the physics❓

3/ Bosonic systems are key to many quantum phenomena—think Hong-Ou-Mandel interference or Bose-Einstein condensation.

They also involve some continuous quantities (position, momentum etc), which require infinite dimensional spaces, making some calculations more involved.

2/ TL;DR: We consider common effective models for bosonic systems & show that such simplified approaches actually produce the correct results. ✅