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arXiv · 1905.08821

Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions

Freek Witteveen·Volkher Scholz·Brian Swingle·Michael Walter
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Abstract

The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories.

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Freek Witteveen, Volkher Scholz, Brian Swingle, Michael Walter. 2021-11-30. Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions. https://doi.org/10.1007/s00220-021-04274-w

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