Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes

• DOI: 10.22331/q-2024-11-26-1539
• Publication Date: 2024-11-26T16:38:36Z
• Authors: Florian Hopfmueller; Maxime Tremblay; Philippe St-Jean; Baptiste Royer; Marc-Antoine Lemonde
• Keywords: Pauli exclusion principle; Pauli matrices

A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with qubit code. Development such concatenated codes requires simulation tools which realistically model noise, while being able to simulate dynamics many modes. However, so far, large-scale for GKP have been limited idealized noise models and implementations. Here, we introduce Bosonic Pauli+ (BP+), can be simulated efficiently large number modes, capturing rich in bosonic multi-mode Hilbert space. We demonstrate method by simulating hybrid surface code, where data qubits are finite-energy stabilized using small-Big-small (sBs) protocol, syndrome standard two-level systems. Using BP+, present logical rates an implementation. Confidence accuracy gained comparing its predictions full time evolution simulations several relevant circuits. While developed specifically sBs mathematical structure BP+ generic may applicable also concatenations other codes.