Fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm
Year: 2026
Type: article
Abstract: Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum “magic”) plays a central role in enabling universal quantum computation. However, the deterministic evaluation of the second-order stabilizer Rényi entropy for generic many-body quantum states remains computationally challenging, with brute-force methods scaling as O ( 8 N ) = O ( d 3 ) for an N -qubit state with d = 2 N . Here, we develop an exact algebraic reformulation and a deterministic numerical algorithm, numerically exact up to floating-point roundoff, that reduces this cost to O ( N 4 N ) = O ( d 2 log 2 d ) while retaining natural parallelism. This is an exponential speedup, although the scaling remains exponential in the number of qubits. This advance enables high-precision calculations for generic state vectors at medium system sizes and provides a practical tool for investigating the scaling and nonequilibrium dynamics of quantum magic in many-body systems.
Source: Physical Review Research
DOI: 10.1103/f7ss-6tl1
Institutions: Shanghai University, National University of Singapore
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
Funders: Ministry of Education - Singapore, National Natural Science Foundation of China, China Scholarship Council, National Key Research and Development Program of China, Science and Technology Innovation Plan Of Shanghai Science and Technology Commission, Program for Changjiang Scholars and Innovative Research Team in University
OpenAlex ID: W7117980241