Measurement as a shortcut to long-range entangled quantum matter
- URL: http://arxiv.org/abs/2206.13527v3
- Date: Wed, 12 Apr 2023 19:19:59 GMT
- Title: Measurement as a shortcut to long-range entangled quantum matter
- Authors: Tsung-Cheng Lu, Leonardo A. Lessa, Isaac H. Kim, Timothy H. Hsieh
- Abstract summary: We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter.
A large class of topological orders, including chiral topological order, can be prepared in constant depth or time.
A large class of CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The preparation of long-range entangled states using unitary circuits is
limited by Lieb-Robinson bounds, but circuits with projective measurements and
feedback (``adaptive circuits'') can evade such restrictions. We introduce
three classes of local adaptive circuits that enable low-depth preparation of
long-range entangled quantum matter characterized by gapped topological orders
and conformal field theories (CFTs). The three classes are inspired by distinct
physical insights, including tensor-network constructions, multiscale
entanglement renormalization ansatz (MERA), and parton constructions. A large
class of topological orders, including chiral topological order, can be
prepared in constant depth or time, and one-dimensional CFT states and
non-abelian topological orders with both solvable and non-solvable groups can
be prepared in depth scaling logarithmically with system size. We also build on
a recently discovered correspondence between symmetry-protected topological
phases and long-range entanglement to derive efficient protocols for preparing
symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane)
codes. Our work illustrates the practical and conceptual versatility of
measurement for state preparation.
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