Measurement as a shortcut to long-range entangled quantum matter

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 four 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 four classes are inspired by distinct physical insights, including tensornetwork constructions, short-range entangled states with non-trivial braiding structures, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral and symmetry-enriched topological orders, 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. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

“…Though purely unitary circuits provide a natural framework for the preparation (and classification) of quantum phases of matter from a quantum many-body perspective [8], general quantum computational tasks leverage a broader toolbox consisting of local operations and classical communication (LOCC), and efforts to classify states under this paradigm are underway [21,22]. To that end, several recent theoretical proposals have shown that measurement, in addition to unitary evolution, can aid in the preparation of certain long-range entangled states including the GHZ state, toric code, and states with non-Abelian topological orders [23][24][25][26].…”

“…First, we propose and experimentally demonstrate the measurement-assisted, constant-time preparation of a specific, topologically nontrivial resource state, useful for applications ranging from quantum teleportation and MBQC [10][11][12][13] to blind quantum computation [29] and remote state preparation [30]. Second, and more broadly, this work serves as an experimental demonstration of the practical utility and readily available advantage that measurementassisted preparation schemes -a topic of rapidly advancing theoretical interest [23][24][25][26] -can provide over their purely unitary counterparts, even for relatively small system sizes.…”

Decoding Measurement-Prepared Quantum Phases and Transitions: from Ising model to gauge theory, and beyond

“…In the second branch, one focuses on systematic measurements in a static situation, preparing quantum states by performing measurements on a subsystem of a so-called resource state, which is related to the measurement-based quantum computation (MBQC). Remarkably, various families of quantum states with long range entanglement, such as Greenberger-Horne-Zeilinger (GHZ) state or those with certain topological and fracton orders among others [18][19][20][21][22][23][24][25][26][27][28] can be prepared through measurements on cluster states.…”

Dynamical entanglement transition in the probabilistic control of chaos

“…The dynamics of quantum many-body systems host a range of phenomena usually out of reach to the classical world. Of particular relevance is the ability to locally measure and control systems to enable quantum technological applications such as efficient state preparation [1][2][3], quantum error correction [4,5], and nondestructive measurements [6,7]. Allowing such nonunitary "hybrid" dynamics in the evolution of many-body states enriches the problem beyond simple, unitary evolution alone.…”

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