Simulating 2D topological quantum phase transitions on a digital quantum computer

Abstract

Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. In this work, we propose a simple method to design exact linear-depth parameterized quantum circuits which prepare a family of ground states across topological quantum phase transitions in 2D. We achieve this by constructing ground states represented by isometric tensor networks (isoTNS), which form a subclass of tensor network states that are efficiently preparable. By continuously tuning a parameter in the wavefunction, the many-body ground state undergoes quantum phase transitions, exhibiting distinct 2D quantum phases. We illustrate this by constructing an isoTNS path with bond dimension $D=2$ interpolating between distinct symmetry-enriched topological (SET) phases. At the transition point, the wavefunction is related to a gapless point in the classical six-vertex model. Furthermore, the critical wavefunction supports a power-law correlation along one spatial direction while remaining long-range ordered in the other spatial direction. We provide an explicit parametrized local quantum circuit for the path and show that the 2D isoTNS can also be efficiently simulated by a holographic quantum algorithm requiring only an 1D array of qubits.

15 pages, 12 figures. Extended version with a modified title

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• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Sequential Adiabatic Generation of Chiral Topological States
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Holographic duality between bulk topological order and boundary mixed-state order
• Skeleton of isometric Tensor Network States for Abelian String-Net Models