Nonpublic Projects - Code Switching

Here is an introduction of my contribution to the project “Smallest Weakly Fault-tolerant Universal Quantum Computer with Code-Switching”. This paper is under preparation.

I. Abstract of the project

Code-switching offers a path to universal fault-tolerant quantum computation by circumventing the Eastin-Knill theorem, which prohibits universal transversal gate sets within a single quantum code. We present a fault-tolerant code-switching protocol between two versions of the $[[8, 3, 2]]$ quantum error detecting code. One version implements the logical $\rm CCZ$ gate with transversal $T/T^{\dagger}$ gates and the $\rm CNOT$ gate with the $\rm SWAP$ gate, while the other version implements the Hadamard and phase gate with weakly fault-tolerant circuits comprised of Mølmer–Sørensen–like gates. These operations are naturally suited to trapped-ion platforms. Both the code-switching protocol and the weakly fault-tolerant circuits detect all weight-1 errors, enabling universal, post-selective fault-tolerant computation.

II. Summary of my contribution

In this project, I performed numerical simulation based on the theory proposed by my collaborators. In particular, I computed the logical error rate and the acceptance rate of our code switching protocol with fault-tolerant and non-fault-tolerant syndrome measurement. I also computed the logical error rate of preparing all-plus state using both version of $[[8,3,2]]$ code. The numerical experiment shows that the code switching protocol can be done fault-tolerantly.

III. Numerical results

Here are logical error rate and acceptance rate of code switching.

Here are logical error rate and acceptance rate of preparing all-plus state using both version of $[[8,3,2]]$ code.