Abstract:Topological quantum phases emerge from correlated quantum many-body systems containing novel features such as nontrivial entanglement structure and mutual statistics. However, the co-emerged exponential computational complexity strongly hampers the research of these systems using classical computers. Present booming quantum computing techniques offer a new way to investigate these challenging systems: the quantum simulation approach. Combining current available noise intermediate-scale quantum (NISQ) devices with variational quantum eigensolver (VQE) algorithm to solve quantum many-body problems has attracted extensive attention. Although the NISQ devices have up to hundreds of qubits, treating a quantum many-body problem with a similar size on these devices is still impossible. One fundamental reason for this is the lack of scalability (i.e., the required quantum resources increase much faster than the increase of the problem size).

In this seminar talk, I will first introduce the current status of the quantum simulation on NISQ devices and then explain how to realize scalable VQE calculations for the ground states of a symmetry-protected topological (SPT) model [1] and a quantum spin model with intrinsic topological order [2] by designing problem-specified scalable parameterized quantum circuit (PQC) Ansätze. For the former, we construct a PQC with a two-layer structure to capture both the basic entanglement structure and finite correlations of an SPT Haldane phase in the nonexactly solvable alternating Heisenberg chain. For the latter, we construct a real-device-realizable PQC, representing a weight-adjustable quantum loop gas, to study the toric code model in an external magnetic field, which is also nonexactly solvable. 

 [1] Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki, Phys. Rev. B 108, 075127 (2023). 

[2] Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki, Phys. Rev. B 107, L041109 (2023).