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arXiv · 2603.04584

Fault-tolerant execution of error-corrected quantum algorithms

Michael A. Perlin·Zichang He·Anthony Alexiades Armenakas·Pablo Andres-Martinez·Tianyi Hao·Dylan Herman·Yuwei Jin·Karl Mayer·Chris Self·David Amaro·Ciaran Ryan-Anderson·Ruslan Shaydulin
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Abstract

Scaling up quantum algorithms to tackle high-impact problems in science and industry requires quantum error correction and fault tolerance. While progress has been made in experimentally realizing error-corrected primitives, the end-to-end execution of logical quantum algorithms using only fault-tolerant (FT) components has remained out of reach. We demonstrate the FT and error-corrected execution of two quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA) and the Harrow-Hassidim-Lloyd (HHL) algorithm applied to the Poisson equation, on Quantinuum H2 and Helios trapped-ion quantum processors using the $[[7,1,3]]$ Steane code. For QAOA circuits on 5 and 6 logical qubits, we show performance improvements from increasing the number of QAOA layers and the number of $T$ gates used to approximate logical rotations, despite increased physical circuit complexity. We further show that QAOA circuits with up to 8 logical qubits and 9 logical $T$ gates perform similarly to unencoded circuits. For the largest QAOA circuits we run, with 12 logical (97 physical) qubits and 2132 physical two-qubit gates, we still observe better-than-random performance. Finally, we show that adding active QEC cycles and increasing the repeat-until-success limit of state preparation subroutines can improve the performance of a quantum algorithm, thereby demonstrating critical capabilities of scalable FT quantum computation. Our results are enabled by an FT logical $T$ gate implementation with an infidelity of $\sim 2.6(4)\times10^{-3}$ and dynamic circuits with measurement-dependent feedback. Our work demonstrates near-break-even performance of complex, error-corrected algorithmic quantum circuits using only FT components.

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Michael A. Perlin, Zichang He, Anthony Alexiades Armenakas, Pablo Andres-Martinez, Tianyi Hao, Dylan Herman, Yuwei Jin, Karl Mayer, Chris Self, David Amaro, Ciaran Ryan-Anderson, Ruslan Shaydulin. 2026-03-04. Fault-tolerant execution of error-corrected quantum algorithms. https://arxiv.org/abs/2603.04584

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