Journal
PHYSICAL REVIEW X
Volume 8, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.8.011003
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Funding
- European Commission (EC) via ERC Grant [ERQUAF (715861)]
- Simons Foundation as part of the It From Qubit Collaboration, through a Simons Investigator Award
- MURI Grant from ARO [W911NF-14-1-0003]
- Simons Foundation
- AFOSR [FA9550-16-1-0082]
- NWO Veni Grant [680-47-459]
- Fannie and John Hertz Foundation
- Stanford Graduate Fellowship program
- EC through grant QUTE
- EC through grant SIQS
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We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a half-shift: translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.
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