GKP cluster-state concatenated code[1]
Description
Multi-mode code encoding logical qubits into a cluster-state stabilizer code concatenated with a single-mode GKP code. Provides a way to perform a continuous-variable (CV) analogue of fault-tolerant measurement-based qubit computation.
A cluster state of GKP qubits on a graph is made by applying two-mode \(C_Z\)-type gates \(e^{\pm i \hat{x}\otimes\hat{x}}\) to a tensor product of \(|\overline{+}\rangle\) logical GKP states on each vertex. Logical Clifford gates are performed on the cluster state using CV measurement-based computation [2][3], i.e., via a combination of linear-optical gates and homodyne measurements on subsets of vertices. Magic-state distillation is required for universal computation. GKP error correction can be naturally combined with CV measurement-based protocols since the performance of both is quantified by a squeezing parameter.
Gates
Fault Tolerance
Parents
- Qudit-into-oscillator code
- Multi-mode GKP code — A GKP-based cluster state is a multimode GKP codeword, although other codewords are not utilized in CV measurement-based computation.
Cousin
Zoo code information
References
- [1]
- N. C. Menicucci, “Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States”, Physical Review Letters 112, (2014). DOI; 1310.7596
- [2]
- N. C. Menicucci et al., “Universal Quantum Computation with Continuous-Variable Cluster States”, Physical Review Letters 97, (2006). DOI; quant-ph/0605198
- [3]
- M. Gu et al., “Quantum computing with continuous-variable clusters”, Physical Review A 79, (2009). DOI; 0903.3233
Cite as:
“GKP cluster-state concatenated code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/gkp-cluster-state