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QI: Fachverband Quanteninformation

QI 33: Quantum Materials and Many-Body Systems

QI 33.1: Talk

Friday, March 22, 2024, 09:30–09:45, HFT-TA 441

Classification of Phases of Matrix Product States with Symmetric Quantum Circuits, and Symmetric Measurements with Feedforward — •David Gunn¹, Tristan Kraft¹, Georgios Styliaris², and Barbara Kraus^{1, 3} — ¹University of Innsbruck — ²Max-Planck-Institut für Quantenoptik — ³Technical University of Munich

We consider how symmetry-preserving measurements with feedforward alter the phase classification of matrix product states (MPS) in the presence of global on-site symmetries. We demonstrate that, for all finite abelian symmetries, by including symmetry-preserving measurements, any two symmetric MPS belong to the same phase. We give an explicit protocol to achieve a transformation between any two phases that uses only a depth-two circuit, two rounds of symmetric measurements, and a constant number of auxiliary systems per site. In the case of non-abelian symmetries, symmetry protection prevents one from deterministically transforming states to product states directly via measurements. Nonetheless, we provide an asymptotically deterministic, symmetry-preserving protocol, using a log-depth circuit and measurements, that demonstrates certain non-abelian, symmetry-protected topological (SPT) phases also trivialize.

Keywords: Phases; Matrix Product States; Symmetry Protected Topological Order; Local Operations Classical Communication; Short-depth Circuits