Dynamically Generated Logical Qubits

Abstract

We present a quantum error correcting code with $\textit{dynamically generated logical qubits}$. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a $two$-qubit Pauli measurement.