Sequentially generated states for the study of two dimensional systems

Abstract

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product States, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of Projected Entangled Pair States and investigate their suitability for approximating the ground states of local Hamiltonians.

10 pages, 4 figures

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Cited by in corpus (39)

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• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Sequential generation of projected entangled-pair states
• Sequential Quantum Circuits as Maps between Gapped Phases
• Non-classicality of temporal correlations
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
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• Continuum tensor network field states, path integral representations and the encoding of spatial symmetries
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• Isometric tensor network representations of two-dimensional thermal states
• Genuinely multi-point temporal quantum correlations and universal measurement-based quantum computing
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
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• String operators for Cheshire strings in topological phases
• Noise-robust exploration of many-body quantum states on near-term quantum devices
• Dual-isometric Projected Entangled Pair States
• Low-temperature Gibbs states with tensor networks
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Sequential Adiabatic Generation of Chiral Topological States
• Efficient certification and simulation of local quantum many-body Hamiltonians
• Adiabatic ground state preparation in an expanding lattice
• Reconfigurable dissipative entanglement between many spin ensembles: from robust quantum sensing to many-body state engineering
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• A Generalised Haldane Map from the Matrix Product State Path Integral to the Critical Theory of the $J_1$-$J_2$ Chain
• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Quantum many-body scarring from Kramers-Wannier duality
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes