The ability to perform quantum error correction is a fundamental requirement for fault tolerant quantum computing. Standard error correction protocols rely on fast mid- circuit measurements and feedback on physical qubits is applied depending on measurement outcomes. A promising alternative is measurement-free error correction, where the feedback is performed using quantum logic and no mid-circuit measurements are required. However, so far measurement-free protocols have been suggested only for small error correcting codes and the goal to scale these approaches up to large code distances remained a seemingly impossible task. In a collaboration with Markus Müller, Friederike Butt, and David Locher, we solved this problem and demonstrated the efficient scaling of measurement-free error correction to arbitrary code distances.
The main idea is based on the measurement-free and fault-tolerant implementation of a universal logical gate set. The problem is challenging as no quantum code can transversally implement a universal gate set. Here, transversal quantum gates are gates on logical qubits where operations are only applied bit wise on the physical qubits. We circumvent this problem by demonstrating measurement-free code switching between two codes with complementary transversal gates sets. Then, the scaling to higher code distances can be achieved by replacing the physical qubits by logical qubits — a process called concatenation. This process can be scaled up to arbitrary code distance and in combination with the universal quantum gate set on logical qubits enables measurement-free, scalable and fault-tolerant universal quantum computing.