Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate

• URL: http://arxiv.org/abs/2506.14688v1
• Date: Tue, 17 Jun 2025 16:23:47 GMT
• Title: Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate
• Authors: Shival Dasu, Simon Burton, Karl Mayer, David Amaro, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Davide DelVento, Andrew C. Potter, David Hayes,
• Abstract summary: We propose a magic-state preparation protocol to fault-tolerantly prepare a pair of logical magic states in a quantum error-detecting code using only eight physical qubits.<n>We show that this protocol can be self-concatenated to produce extremely high-fidelity magic states with low space-time overhead.
• Score: 1.6986469299341722
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing this overhead is key for the practical development of large-scale fault-tolerant quantum computers. We propose and experimentally implement a magic-state preparation protocol to fault-tolerantly prepare a pair of logical magic states in a [[6,2,2]] quantum error-detecting code using only eight physical qubits. Implementing this protocol on H1-1, a 20 qubit trapped-ion quantum processor, we prepare magic states with experimental infidelity $7^{+3}_{-1}\times 10^{-5}$ with a $14.8^{+1}_{-1}\%$ discard rate and use these to perform a fault-tolerant non-Clifford gate, the controlled-Hadamard (CH), with logical infidelity $\leq 2.3^{+9}_{-9}\times 10^{-4}$. Notably, this significantly outperforms the unencoded physical CH infidelity of $10^{-3}$. Through circuit-level stabilizer simulations, we show that this protocol can be self-concatenated to produce extremely high-fidelity magic states with low space-time overhead in a [[36,4,4]] quantum error correcting code, with logical error rates of $6\times 10^{-10}$ ($5\times 10^{-14}$) at two-qubit error rate of $10^{-3}$ ($10^{-4}$) respectively.

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