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.
Zhou \ and\ author A
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The arrow of time exhibits nonanalytic behavior at the critical point of measurement-induced phase transitions, with an identified critical exponent, in an exactly solved model of random quantum circuits with non-projective measurements.
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
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.
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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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Arrow of Time as an indicator of Measurement-Induced Phase Transitions
The arrow of time exhibits nonanalytic behavior at the critical point of measurement-induced phase transitions, with an identified critical exponent, in an exactly solved model of random quantum circuits with non-projective measurements.
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Geometry of Free Fermion Commutants
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
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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.