Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits
Abstract
Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits.
Related
- QECirc: A Community-Driven, FAIR Library of Quantum Error Correction Circuits
- Sampling Noise and Optimized Measurement Distribution in Imaginary-Time Quantum Dynamics Simulations
- Norm-Aware Product Formulas for Hamiltonian Simulations
- Valency-bounding correction potential for coarse-grained molecular dynamics simulations
- Bosonic quantum error correction with microwave cavities for quantum repeaters
BibTeX
@misc{orioli2026optimized,
title = {{Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits}},
author = {Asier Piñeiro Orioli and Chen Zhao and Guido Masella and Tommaso Macrì and Hengyun Zhou and Shannon Whitlock},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03073},
eprint = {2609.03073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03073},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimized Matrix-Product State Simulations of Quantum Error Correction Circuits
AU - Asier Piñeiro Orioli
AU - Chen Zhao
AU - Guido Masella
AU - Tommaso Macrì
AU - Hengyun Zhou
AU - Shannon Whitlock
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03073
UR - https://arxiv.org/abs/2609.03073
AB - Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits.
ER -