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This breakthrough simplifies the extraction of permutation-invariant data from quantum systems by replacing complex circuit implementations with efficient random SWAP tests. The new protocol reduces computational complexity to O(n³) while preserving relevant quantum information through pairwise qudit checks, offering a significant step forward for analyzing many-body quantum states. This advancement directly enhances the practical utility of unitary Schur sampling in quantum computation and information science.

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Duke University Cuts SWAP Tests for Schur Sampling to O(n³)

Quantum ZeitgeistOctober 2, 20265 min read

Unitary Schur sampling now bypasses complex calculations previously needed to unlock permutation-invariant data from quantum systems. This is achieved through random SWAP tests, simple pairwise checks between qudits, rather than circuit implementations reliant on transforms or phase estimation. The protocol uses O(n minn,d³log²(n/ε)) such tests to achieve an error rate of ε in diamond distance.

Unitary Schur sampling now utilises only pairwise checks between pairs of qudits rather than complex operations previously required. The protocol repeatedly identifies and extracts the largest possible antisymmetric subsystem within the quantum system to achieve this simplified process. Relevant quantum information is preserved while symmetry structures resolve with complexity scaling favourably with both the number of qudits and their local dimension. A streamlined method has been devised for obtaining key information from complex quantum systems, avoiding computationally intensive procedures previously considered essential. This new technique simplifies unitary Schur sampling, a…

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