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Explore optimal algorithms for sampling unitary Fermionic Linear Optics (FLO) circuits in this 22-minute conference talk from QTML 2025. Learn about fundamental quantum information tools including matchgate circuits and their applications in randomized benchmarking of continuous gate sets and fermionic classical shadows. Discover new methods for sampling over both non-particle-preserving (active) and particle-preserving (passive) FLO Haar measures through appropriate gate distributions for n-qubit parametrized circuits. Understand how these novel approaches overcome limitations of previous methods that either required classical O(n³) compilation costs or had suboptimal depths. Examine the simultaneous achievement of optimal Θ(n) depth and Θ(n²) gate count with only Θ(n²) classical overhead, and explore quantum circuits for sampling Clifford FLO with optimal Θ(n²) gate count. Gain insights into advanced quantum circuit optimization techniques and their theoretical foundations from research presented by Paolo Braccia, N. L. Diaz, Martin Larocca, M. Cerezo, and Diego García-Martín at the Centre for Quantum Technologies.
