Fock, the rules (... or how to ZX-calculus for continuous variable quantum computation)
summary
Graphical ZX-calculus extends to infinite-dimensional CVQC by adding a Fock spider (discrete photon-number basis) and a W node and gives diagrammatic encodings of the universal gate set: Gaussian generators (shifts, squeezers, rotations, beamsplitters, CZ/CX variants) plus a non‑Gaussian resource such as the cubic phase. The calculus is provably complete for the Gaussian fragment via an invertible translation to the graphical symplectic algebra, represents GKP finite‑squeezing as injected Gaussian noise and derives syndrome correction, and yields a hafnian normal form for Gaussian boson sampling.
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chapters (8)
- 0:00Fock ZX calculus intro
- 1:26Generators of Fock ZX
- 4:53Rules and notation
- 8:27Gates in CV QC
- 10:17Completeness for Gaussian
- 12:29Quantum error correction with GKP
- 15:44Boson sampling advantage
- 17:12Q&A on GKP distance
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