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  • Open Access

Sequential Generation of Two-Dimensional Super-Area-Law States with Local Parent Hamiltonian

Wucheng Zhang*

  • *Contact author: wz8361@princeton.edu
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PRX Quantum 7, 010311 – Published 16 January, 2026

DOI: https://doi.org/10.1103/t7py-glgv

Abstract

We construct examples of highly entangled two-dimensional states by exploiting a correspondence between stochastic processes in d dimensions and quantum states in d+1 dimensions. The entanglement structure of these states, which we explicitly calculate, can be tuned between area law, sub-volume law, and volume law. This correspondence also enables a sequential generation protocol: the states can be prepared through a series of unitary transformations acting on an auxiliary system. We also discuss the conditions under which these states have local, frustration-free parent Hamiltonians.

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Preparing two-dimensional quantum states with entanglement beyond the usual area law is crucial but difficult: standard routes need fine-tuned or nonlocal interactions, and random circuits create uncontrollable entanglement. This shortage hinders our ability to test simulators, benchmark algorithms, and study entanglement transitions in higher-dimensional systems.

We show how to generate such highly entangled two-dimensional states by turning a familiar idea from classical physics, i.e., how a rough surface grows, into a blueprint for a quantum wave function. Think of stacking and removing tiny blocks to make a fluctuating landscape. By adjusting how often the surface “deposits” versus “evaporates” blocks, we can tune the state’s entanglement from area law to intermediate scaling to full volume law. The same recipe naturally yields a practical preparation scheme: a small auxiliary device (“emitter”) interacts with qubits in a fixed order, laying down the pattern row by row. Because each step is local and sequential, the method is compatible with near-term platforms that excel at streaming operations (for example, photonics). We also show how to encode the rules of the surface dynamics into a local, frustration-free Hamiltonian whose ground state is exactly the target state.

Together, these ideas provide a route to create and analyze two-dimensional quantum states with tunable and super-area-law entanglement, opening paths to benchmark quantum simulators, stress-test tensor-network methods, and apply them in quantum information processing.

Article Text

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PRX Quantum 7, 010311– Published 16 January, 2026
  • Received 3 July 2025
  • Accepted 23 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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