Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
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In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.
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On the Complexity of Quantum States and Circuits from the Orthogonal and Symplectic Groups
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.