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

Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. In this talk, we present 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 quantum phases. We illustrate this by constructing isoTNS paths with bond dimension D=2 interpolating between distinct symmetry-enriched topological (SET) phases. At the transition points, the wavefunctions are related to a gapless point in some classical statistical models. Furthermore, the critical wavefunctions support power-law correlation along certain spatial direction. We provide explicit parametrized local quantum circuits for the paths and show that the isoTNS can also be efficiently simulated by a holographic quantum algorithm requiring only a quantum hardware in one dimension lower than the isoTNS.