Razin A. Shaikh

We develop graphical tools for continuous-variable (CV) fault-tolerant quantum computation using the Focked-up ZX-calculus, an infinite-dimensional generalisation of the ZX-calculus. Our main contribution is a CV theory of Pauli webs and fault-equivalence. This allows us to construct and transform protocols, circuit representations, and computational models while preserving their behaviour under noise. We apply this framework to multimode Gottesman–Kitaev–Preskill (GKP) codes. First, we construct recursive fault-tolerant preparations of GKP analogues of the multimode GHZ states, and use them to obtain Shor-style syndrome-extraction circuits for multimode GKP codes. Second, we use fault-equivalent rewrites to move between circuit-based, measurement-based, and fusion-based descriptions of CV stabilizer computation. Starting from the single-mode square-lattice GKP code, we derive a fault-equivalent four-mode dynamic CV stabilizer code. Together, these results provide a graphical foundation for reasoning about fault tolerance in CV quantum codes.