2024/12/18 by Hugo Lóio, Lóio, Hugo, Guillaume Cecile +7 · 2 citations
Chemistry · Computer Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2412.14261
openalex publication_date 2024/12/18 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/31
We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension χ. Specifically, we consider ensembles produced by: (i) random sequential unitary circuits, (ii) random brickwork unitary circuits, and (iii) circuits involving both unitaries and projective measurements. In all cases, we analyze the spectra of the MPS transfer matrices and relate them to the spreading of mutual information in the MPS state. We demonstrate how different features of the spectral density correspond to distinct types of circuits, revealing that these MPS ensembles retain crucial physical information about the underlying microscopic dynamics. Notably, in the presence of quantum monitoring, we show the existence of a measurement-induced entanglement transition (MIPT) in MPS ensembles, with the averaged dimension of the transfer matrix's null space serving as the effective order parameter.