Sampling hard circuits with verifiably high fidelity
Abstract
Sampling-based proposals are prominent candidates for demonstrating quantum computations beyond the reach of classical supercomputers. However, it has been difficult to combine their complexity-theoretic hardness with two capabilities needed for scalable quantum computing more generally: suppressing hardware errors, and verifying the quantum computation itself. Here we address both issues by introducing structured circuits, which, in addition to provable hardness guarantees, admit an encoding in a quantum code. This allows us to simultaneously reach high fidelities at high circuit depths, and to certify an experimental fidelity via the circuit structure and measurement of code syndromes. The resulting certificate is device dependent, but requires substantially weaker noise assumptions than existing fidelity proxy benchmarks. We demonstrate our proposal with a $64$-qubit, depth-$73$ Clifford circuit, doped with $314$ T gates. We use a total of $76$ physical qubits to encode this computation in spacetime codes, effectively suppressing gate error rates by 10× after syndrome post-selection, and yielding a state with a fidelity lower bound of $0.349$ with 95% confidence. Our construction is a systematic method for promoting a stabilizer state to a magic state while keeping an error-detected fidelity certificate.
Related
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BibTeX
@misc{martiel2026sampling,
title = {{Sampling hard circuits with verifiably high fidelity}},
author = {Simon Martiel and Jay-U Chung and Alireza Seif and Soumik Ghosh and Ian Hincks and Abhinav Deshpande and Hidetaka Manabe and Hanfeng Gu and Feng Pan and Bill Fefferman and Jay M. Gambetta and Ali Javadi-Abhari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.25941},
eprint = {2607.25941},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25941},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sampling hard circuits with verifiably high fidelity
AU - Simon Martiel
AU - Jay-U Chung
AU - Alireza Seif
AU - Soumik Ghosh
AU - Ian Hincks
AU - Abhinav Deshpande
AU - Hidetaka Manabe
AU - Hanfeng Gu
AU - Feng Pan
AU - Bill Fefferman
AU - Jay M. Gambetta
AU - Ali Javadi-Abhari
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2607.25941
UR - https://arxiv.org/abs/2607.25941
AB - Sampling-based proposals are prominent candidates for demonstrating quantum computations beyond the reach of classical supercomputers. However, it has been difficult to combine their complexity-theoretic hardness with two capabilities needed for scalable quantum computing more generally: suppressing hardware errors, and verifying the quantum computation itself. Here we address both issues by introducing structured circuits, which, in addition to provable hardness guarantees, admit an encoding in a quantum code. This allows us to simultaneously reach high fidelities at high circuit depths, and to certify an experimental fidelity via the circuit structure and measurement of code syndromes. The resulting certificate is device dependent, but requires substantially weaker noise assumptions than existing fidelity proxy benchmarks. We demonstrate our proposal with a $64$-qubit, depth-$73$ Clifford circuit, doped with $314$ T gates. We use a total of $76$ physical qubits to encode this computation in spacetime codes, effectively suppressing gate error rates by 10× after syndrome post-selection, and yielding a state with a fidelity lower bound of $0.349$ with 95% confidence. Our construction is a systematic method for promoting a stabilizer state to a magic state while keeping an error-detected fidelity certificate.
ER -