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arXiv:2508.00437 · Physical Review A

Replacement-type quantum gates

Florian Ginzel, Javad Kazemi, Valentin Torggler, Wolfgang Lechner

Published Feb 5, 2026• 1 citation
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Abstract

We introduce the paradigm of replacement-type quantum gates. This type of gate introduces input qubits, candidate qubits, and output qubits. The candidate qubits are prepared such, that a displacement conditional on the input qubit results in the targeted output state. Finally, the circuit continues with the output qubits constructed from the candidate qubits instead of the input qubits, thus the name "replacement-type gate". We present examples of replacement-type $X$ and $\mathrm{CNOT}$ gates realized with spin qubits and with neutral atom qubits with error rates predicted near the threshold of the XZZX surface code. By making use of the extended Hilbert space, including the position of the particles, these gates approximately preserve the innate noise bias of the qubits. The gate preserves the noise bias which motivates advanced quantum computer architectures with quantum error correction.

DOI
10.1103/frwk-cb6n

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We introduce the paradigm of replacement-type quantum gates. This type of gate introduces input qubits, candidate qubits, and output qubits. The candidate qubits are prepared such, that a displacement conditional on the input qubit results in the targeted output state. Finally, the circuit continues with the output qubits constructed from the candidate qubits instead of the input qubits, thus the name "replacement-type gate". We present examples of replacement-type XXX and CNOT\mathrm{CNOT}CNOT gates realized with spin qubits and with neutral atom qubits with error rates predicted near the threshold of the XZZX surface code. By making use of the extended Hilbert space, including the position of the particles, these gates approximately preserve the innate noise bias of the qubits. The gate preserves the noise bias which motivates advanced quantum computer architectures with quantum error correction.
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The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware.In this work, we identify a new type of structured noise motivated by neutral-atom qubits, biased erasure errors, which arises when qubit errors are dominated by detectable leakage from only one of the computational states of the qubit.We study the performance of this model using gate-level simulations of the XZZX surface code.Using the predicted erasure fraction and bias of metastable 171 Yb qubits, we find a threshold of 8.2% for two-qubit gate errors, which is 1.9 times higher than the threshold for unbiased erasures and 7.5 times higher than the threshold for depolarizing errors.Surprisingly, the improved threshold is achieved without bias-preserving controlled-NOT gates and, instead, results from the lower noise entropy in this model.We also introduce an XZZX cluster state construction for measurement-based error correction, hybrid fusion, that is optimized for this noise model.By combining fusion operations and deterministic entangling gates, this construction preserves the intrinsic symmetry of the XZZX code, leading to a higher threshold of 10.3% and enabling the use of rectangular codes with fewer qubits.We discuss a potential physical implementation using a single plane of atoms and movable tweezers.
Biased-noise qubits, in which one type of error (e.g. XXX- and YYY-type errors) is significantly suppressed relative to the other (e.g. ZZZ-type errors), can significantly reduce the overhead of quantum error correction. Codes such as the rectangular surface code or XZZX code substantially reduce the qubit overhead under biased noise, but they still face challenges. The rectangular surface code suffers from a relatively low threshold, while the XZZX code requires twice as many physical qubits to maintain the same code distance as the surface code. In this work, we introduce a 2D local code construction that outperforms these codes for noise biases η≥7×104η\ge 7\times10^{4}η≥7×104, reducing the qubit overhead by over 50% at pZ=10−3p_Z=10^{-3}pZ​=10−3 and η=2×106η= 2 \times 10^6η=2×106 to achieve a logical error rate of 10−1210^{-12}10−12. Our construction relies on the concatenation of two classical codes. The inner codes are repetition phase-flip codes while the outer codes are high-rate bit-flip codes enabled by their implementation at the logical level, which circumvents device connectivity constraints. These results indicate that under sufficiently biased noise, it is advantageous to address phase-flip and bit-flip errors at different layers of the coding scheme. The inner code should prioritize a high threshold for phase-flip errors, while the bit-flip outer code should optimize for encoding rate efficiency. In the strong biased-noise regime, high-rate outer codes keep the overhead for correcting residual bit-flip errors comparable to that of the repetition code itself, meaningfully lower than that required by earlier approaches.