I definitely have a favorite way of implementing MZZ, and it's lattice surgery on surface codes.

Along with our recent experimental work demonstrating color codes embedded on a square lattice arxiv.org/abs/2412.14256 and our work proposing new circuits for adapting to dead qubits and couplers arxiv.org/abs/2410.14891, this shows that we have a huge space of circuit constructions to explore!

Each of these circuits present a new possibility to design an architecture around. That all three work well on a device not optimized for them proves we have what @craiggidney.bsky.social calls “circuit agility”, like cryptographic agility but for QEC implementation. Same QEC, different circuit!

It was also long assumed that you need to use CNOTs or CZ gates to do QEC. We demonstrate the surface code compiled to iSWAP gates, which is more natural for transmons and doesn’t couple to leakage states! Our device was optimized for CZs, the iSWAPS do suffer from a lot of stray CPHASE error…

We also demonstrate a walking circuit, switching which physical qubits we use to measure the syndromes. Physically, this lets us remove leakage on all qubits every 2 rounds. Logically, it moved the whole patch diagonally through space.

It’s long been assumed you need a square grid of nearest neighbour connections to do the surface code. Turns out three couplings is plenty! As in our recent work arxiv.org/abs/2408.13687, we show that scaling the distance for the hexagonal circuit from distance 3 to 5 halves the logical error.

These circuits are all based on the detecting region approach to QEC arxiv.org/abs/2302.02192 As long as these regions tile spacetime, the QEC works, which gives you huge freedom to modify the circuit. It's a treat to work on theory for something and then get to work on the experiment.