Symmetry-Accelerated Classical Simulation of Clifford-Dominated Circuits
Year: 2026
Type: article
Abstract: Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which quantifies the overhead of representing non-Clifford operations as linear combinations of Clifford unitaries. However, finding optimal decompositions rapidly becomes intractable as it constitutes a superexponentially large optimization problem. In this work, we exploit symmetries in the computation of the stabilizer extent, proving that for real, diagonal, and real-diagonal unitaries, the optimization can be restricted to the corresponding subgroups of the Clifford group without loss of optimality. This “strong symmetry reduction” drastically reduces computational cost, enabling optimal decompositions of unitaries on up to seven qubits using a standard laptop—far beyond previous two-qubit limits. Additionally, we employ a “weak symmetry reduction” method that leverages additional invariances to shrink the search space further. Applying these results, we demonstrate exponential runtime improvements in classical simulations of quantum Fourier transform circuits and measurement-based quantum computations on the Union Jack lattice, as well as insights into the nonstabilizer properties of multicontrolled phase gates and unitaries generating hypergraph states. Our findings establish symmetry exploitation as a powerful route to scale classical simulation techniques and deepen the resource-theoretic understanding of quantum advantage.
Source: PRX Quantum
DOI: 10.1103/nnzz-481j
Authors: Giulio Camillo, Filipa C.R. Peres, Markus Heinrich, Juani Bermejo-Vega
Institutions: Universidad de Granada, University of Cologne
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,450
Awards: G1175115578, G1224172124, G2262748287, G2371472412, G294895050, G300979063, G3356704239, G3480869486, G410571670, G425668148, G451917667, G4595741807, G5080475149, G523076202, G5539308778, G5967599077, G6033112984, G6218905885, G675437911, G7084143925, G7127239378, G7167251299, G7549035430, EXC 2004: Materie und Licht für Quanteninformation (ML4Q), G8888022036, G8991510593
OpenAlex ID: W4416245781