Bosonic entanglement renormalization circuits from wavelet theory
| Autor: | Michael Walter, Freek Witteveen |
|---|---|
| Přispěvatelé: | Algebra, Geometry & Mathematical Physics (KDV, FNWI), KdV Other Research (FNWI), Logic and Computation (ILLC, FNWI/FGw), String Theory (ITFA, IoP, FNWI), ILLC (FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
QC1-999 Gaussian FOS: Physical sciences General Physics and Astronomy Quantum entanglement 01 natural sciences Renormalization symbols.namesake Theoretical physics Wavelet 0103 physical sciences Tensor Quantum field theory 010306 general physics Quantum Condensed Matter - Statistical Mechanics Mathematical Physics Physics Quantum Physics Statistical Mechanics (cond-mat.stat-mech) 010308 nuclear & particles physics Mathematical Physics (math-ph) High Energy Physics - Theory (hep-th) symbols Quantum Physics (quant-ph) Hamiltonian (quantum mechanics) |
| Zdroj: | SciPost Physics, 10(6), 143.1-143.30 SciPost Physics, 10(6):143. SciPost Foundation SciPost Physics, Vol 10, Iss 6, p 143 (2021) |
| ISSN: | 2542-4653 |
| Popis: | Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this design problem and provide an approximation theory that relates the properties of the filters to the accuracy of the corresponding quantum circuits. Finally, we explain how the continuum limit (a free bosonic quantum field) emerges naturally from the wavelet construction. 22 pages, 7 figures |
| Databáze: | OpenAIRE |
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