Regensburg 2022 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 4: Poster: Quantum Information

QI 4.22: Poster

Montag, 5. September 2022, 18:00–20:00, P2

Solvable projected entangled pair states for ternary unitary quantum gates — •Richard Maximilian Milbradt¹, Christopher Aßmus¹, and Christian Bernhard Mendl^{1, 2} — ¹Technical University of Munich, Department of Informatics, Boltzmannstraße 3, 85748 Garching, Germany — ²Technical University of Munich, Institute for Advanced Study, Lichtenbergstraße 2a, 85748 Garching, Germany

Recently we introduced the so-called ternary unitary quantum gates. These are four-particle gates acting in 2+1-dimensions and are unitary in time and both spatial dimensions. Now we generalise the concept of solvable MPS[Phys. Rev. B 101, 094304 (2020)] to two spatial dimensions with cylindrical boundary conditions. We show that such solvable PEPS can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out, and we delineate and implement a numerical algorithm for computing such correlations.