Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models

Abstract

A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine closed boundary conditions and charge sectors, these can be implemented by unitary matrix product operators. In this manuscript, we explain how to turn such duality operators into unitary linear depth quantum circuits via the introduction of ancillary degrees of freedom that keep track of the various sectors. The linear depth is consistent with the fact that these dualities change the phase of the states on which they act. When supplemented with measurements, we show that dualities with respect to symmetries encoded into nilpotent fusion categories can be realised in constant depth. The resulting circuits can for instance be used to efficiently prepare short- and long-range entangled states or map between different gapped boundaries of (2+1)d topological models.

arXiv comment5 pages, 2 figures

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• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• Duality defect in a deformed transverse-field Ising model
• Dualities between 2+1d fusion surface models from braided fusion categories
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• From gauging to duality in one-dimensional quantum lattice models
• Symmetric entanglers for non-invertible SPT phases
• Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation
• Quantum Circuits for Matrix-Product Unitaries