Symmetry-preserving quantum compilation
Abstract
Fault-tolerant quantum simulation requires compiling symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous symmetries even when the target evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a fault-tolerant compilation framework that preserves SU(2) symmetry exactly. We characterize the number-theoretic obstruction preventing symmetry-preserving unitary Clifford+T circuits from approximating arbitrary SU(2)-symmetric evolutions and circumvent it using measurement and feed-forward. The resulting synthesis confines compilation errors to the symmetry-preserving operator algebra rather than introducing symmetry-breaking perturbations. We demonstrate the algorithm by simulating transport in the one-dimensional Heisenberg model. At a lower matched T-count, for instance, 54 T gates per two-site Trotter step, standard synthesis yields an incorrect transport exponent, whereas our symmetry-preserving compilation reproduces the expected exponent for the same expected T-count. If instead each approach is allocated whatever resources are necessary to estimate this exponent to the same accuracy, our construction reduces the T-count by approximately a factor of five. We further extend the framework to gauge symmetries in lattice gauge theories and to particle-number and spin symmetries in fermionic models relevant to quantum chemistry and the Fermi-Hubbard model. These results show that symmetry-preserving fault-tolerant compilation can qualitatively change the effects of synthesis error while substantially reducing the resources required for quantum simulation.
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BibTeX
@misc{mudassar2026symmetrypreserving,
title = {{Symmetry-preserving quantum compilation}},
author = {Maryam Mudassar and Zhi-Yuan Wei and Alexander Schuckert and Michael J. Lawler and Michael J. Gullans and Daniel Gottesman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03624},
eprint = {2610.03624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03624},
}
RIS
TY - UNPB
TI - Symmetry-preserving quantum compilation
AU - Maryam Mudassar
AU - Zhi-Yuan Wei
AU - Alexander Schuckert
AU - Michael J. Lawler
AU - Michael J. Gullans
AU - Daniel Gottesman
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03624
UR - https://arxiv.org/abs/2610.03624
AB - Fault-tolerant quantum simulation requires compiling symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous symmetries even when the target evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a fault-tolerant compilation framework that preserves SU(2) symmetry exactly. We characterize the number-theoretic obstruction preventing symmetry-preserving unitary Clifford+T circuits from approximating arbitrary SU(2)-symmetric evolutions and circumvent it using measurement and feed-forward. The resulting synthesis confines compilation errors to the symmetry-preserving operator algebra rather than introducing symmetry-breaking perturbations. We demonstrate the algorithm by simulating transport in the one-dimensional Heisenberg model. At a lower matched T-count, for instance, 54 T gates per two-site Trotter step, standard synthesis yields an incorrect transport exponent, whereas our symmetry-preserving compilation reproduces the expected exponent for the same expected T-count. If instead each approach is allocated whatever resources are necessary to estimate this exponent to the same accuracy, our construction reduces the T-count by approximately a factor of five. We further extend the framework to gauge symmetries in lattice gauge theories and to particle-number and spin symmetries in fermionic models relevant to quantum chemistry and the Fermi-Hubbard model. These results show that symmetry-preserving fault-tolerant compilation can qualitatively change the effects of synthesis error while substantially reducing the resources required for quantum simulation.
ER -