MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
Random Quantum Circuits
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Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.
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.
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.
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
Review of universality principles and examples in driven open quantum matter via Lindblad-Keldysh field theory, organized into three classes of nonequilibrium phenomena.
citing papers explorer
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Absence of poor local minima in matrix product states
MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
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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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Entanglement and circuit complexity in finite-depth random linear optical networks
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.
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Lecture Notes on Replica Tensor Networks for Random Quantum Circuits
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.