Noise Transfer Approach to GKP Quantum Circuits

The choice between the Schrödinger and Heisenberg pictures can significantly impact the computational resources needed to solve a problem, even though they are equivalent formulations of quantum mechanics. Here, we present a method for analysing Bosonic quantum circuits based on the Heisenberg picture which allows, under certain conditions, a useful factoring of the evolution into signal and noise contributions, similar way to what can be achieved with classical communication systems. We provide examples which suggest that this approach may be particularly useful in analysing quantum computing systems based on the Gottesman-Kitaev-Preskill (GKP) qubits.