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arXiv:1904.11220 · Nature Nanotechnology

Quantum non-demolition measurement of an electron spin qubit

Takashi Nakajima, Akito Noiri, Jun Yoneda, Matthieu R. Delbecq, Peter Stano, Tomohiro Otsuka, Kenta Takeda, Shinichi Amaha, Giles Allison, Kento Kawasaki, Arne Ludwig, Andreas Dirk Wieck, Daniel Loss, Seigo Tarucha

Published Apr 15, 2019• 75 citations
arXivHTMLPDF
DOI
10.1038/s41565-019-0426-x

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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 $\sim\!1.25\%$ and provides a qubit overhead reduction of up to $6\times$ compared to a bias-unaware surface code at noise bias $η= 10^4$. In the regime of very large bias, a repetition code with QND $Z$ measurements attains a threshold of $\sim\!2.3\%$ 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.

quant-pharXiv:2605.24262•May 26, 2026•0 citations
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 ZZZ 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 ZZZ measurements achieves a phase-flip threshold of ∼ ⁣1.25%\sim\!1.25\%∼1.25% and provides a qubit overhead reduction of up to 6×6\times6× compared to a bias-unaware surface code at noise bias η=104η= 10^4η=104. In the regime of very large bias, a repetition code with QND ZZZ measurements attains a threshold of ∼ ⁣2.3%\sim\!2.3\%∼2.3% and achieves overhead comparable to that of a bias-preserving CNOT scheme, without requiring such a gate. Our results establish QND multi-ZZZ measurements as a practical and hardware-efficient route to fault-tolerant quantum computation for a broad class of biased-noise platforms.