Scalable Quantum Simulation for Topological Phases on NISQ Devices

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 in current quantum algorithms (i.e., the required quantum resources for realizing a quantum algorithm increase much faster than the increase of the problem size). In this poster, we introduce how to realize scalable VQE calculation in the topological quantum phases by designing problem-specified scalable parameterized quantum circuits (PQC). We construct a PQC with a two-layer structure to capture both the basic entanglement structure of the target topological phase and finite correlations governed by the details of the many-body Hamiltonian. Utilizing such a PQC, we numerically simulate both symmetry-protected topological (SPT) Haldane phase and trivial dimmer phase in the non-exactly solvable alternating Heisenberg chain using the VQE algorithm. Furthermore, we realize these optimized circuits on real quantum computers provided by IBM Quantum and observe the main characterizations of the SPT Haldane phase.