Quantum non-demolition measurements as a practical primitive for fault-tolerant computation against biased noise

Leveraging noise bias, where phase-flip errors dominate over bit-flips, can drastically reduce the hardware overhead of fault-tolerant quantum computation, but existing approaches require bias-preserving CNOT gates whose implementation remains experimentally challenging and is provably impossible for strictly two-dimensional systems. We show that high-fidelity quantum non-demolition (QND) multi-qubit Pauli Z measurements provide an equally powerful yet more accessible primitive. We demonstrate that such measurements can fully replace bias-preserving CNOT gates for compiling all operations required by bias-tailored error correction, including stabilizer measurements for repetition codes, XZZX surface codes, and LDPC codes. We propose concrete physical implementations of this primitive for two platforms: solid-state nuclear spins coupled to electron spin ancillas, and dissipatively stabilized superconducting cat qubits. Through circuit-level numerical simulations, we show that an asymmetric XZZX surface code implemented with weight-four QND Z measurements achieves a phase-flip threshold of sim1.25\% and provides a qubit overhead reduction of up to 6times compared to a bias-unaware surface code at noise bias η= 10⁴. In the regime of very large bias, a repetition code with QND Z measurements attains a threshold of sim2.3\% and achieves overhead comparable to that of a bias-preserving CNOT scheme, without requiring such a gate. Our results establish QND multi-Z measurements as a practical and hardware-efficient route to fault-tolerant quantum computation for a broad class of biased-noise platforms.