Efficient fidelity simulation of high-rate magic distillation circuits
Abstract
Non-Clifford gates are essential for avoiding classical simulability under the Gottesman-Knill theorem. An error-corrected circuit with non-Clifford gates will therefore be an important element for realizing useful fault-tolerant quantum algorithms. However, accurately understanding the fault-tolerant performance of such circuits faces challenges due to the classical hardness of simulating these circuits. We avoid simulating logical measurements and develop exact and efficient classical methods for benchmarking circuits composed of X, CNOT, and diagonal gates in the Clifford hierarchy, including state and gate teleportation gadgets with feedforward. For circuits with third-level diagonal gates, our benchmarking algorithm efficiently samples syndrome statistics and estimates the output logical fidelity and expectation values of certain Clifford observables, including all Pauli observables. The evaluation of syndrome expectation values also extends to circuits with fourth-level diagonal gates. Our algorithm scales polynomially in the number of physical qubits n and circuit depth T, independent of the number of logical qubits. The benchmarking applications include IQP sampling and magic state preparation/cultivation. We demonstrate the practical utility of our simulation algorithms by using them to optimize high-rate magic state distillation factories based on three copies of a [[27,3,3]] tricycle code.
Related
- Efficient Fidelity Estimation of General Quantum Resource States via Clifford Circuits
- Exact efficient simulation of noisy logical magic states using Clifford stabilizers
- Efficient Simulation of Hybrid Continuous- and Discrete-Variable Quantum Circuits via Gaussian Decompositions
- Efficient Quantum Circuits for Electronic Hamiltonian Simulation without Pauli Expansion
- The limits of magic-state distillation
BibTeX
@misc{xiao2026efficient,
title = {{Efficient fidelity simulation of high-rate magic distillation circuits}},
author = {Xiao Xiao and Dominik Hangleiter and J. Pablo Bonilla Ataides and Rohan Mehta and Varun Menon and Mikhail D. Lukin and Michael J. Gullans},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03605},
eprint = {2610.03605},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03605},
}
RIS
TY - UNPB
TI - Efficient fidelity simulation of high-rate magic distillation circuits
AU - Xiao Xiao
AU - Dominik Hangleiter
AU - J. Pablo Bonilla Ataides
AU - Rohan Mehta
AU - Varun Menon
AU - Mikhail D. Lukin
AU - Michael J. Gullans
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03605
UR - https://arxiv.org/abs/2610.03605
AB - Non-Clifford gates are essential for avoiding classical simulability under the Gottesman-Knill theorem. An error-corrected circuit with non-Clifford gates will therefore be an important element for realizing useful fault-tolerant quantum algorithms. However, accurately understanding the fault-tolerant performance of such circuits faces challenges due to the classical hardness of simulating these circuits. We avoid simulating logical measurements and develop exact and efficient classical methods for benchmarking circuits composed of X, CNOT, and diagonal gates in the Clifford hierarchy, including state and gate teleportation gadgets with feedforward. For circuits with third-level diagonal gates, our benchmarking algorithm efficiently samples syndrome statistics and estimates the output logical fidelity and expectation values of certain Clifford observables, including all Pauli observables. The evaluation of syndrome expectation values also extends to circuits with fourth-level diagonal gates. Our algorithm scales polynomially in the number of physical qubits n and circuit depth T, independent of the number of logical qubits. The benchmarking applications include IQP sampling and magic state preparation/cultivation. We demonstrate the practical utility of our simulation algorithms by using them to optimize high-rate magic state distillation factories based on three copies of a [[27,3,3]] tricycle code.
ER -