Universal quantum computation via scalable measurement-free error correction

Understand

We show that universal quantum computation can be concretely made fault-tolerant without mid-circuit measurements.

• To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $\mathit{CCZ}$ gate.
• Combined with a fold-transversal logical Hadamard gate, this enables a universal set of fault-tolerant operations using only transversal gates and qubit permutations.
• For the purpose of benchmarking under circuit-level noise, we develop an efficient method to simulate non-Clifford circuits with a small number of Hadamard gates.