Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications

Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply stabilizer states to tackle quantum many-body ground state problems and introduce the concept of stabilizer ground states. We establish an equivalence formalism for identifying stabilizer ground states of general Pauli Hamiltonians. Moreover, we develop an exact and linear-scaled algorithm to obtain stabilizer ground states of 1D local Hamiltonians and thus free from discrete optimization. This proposed equivalence formalism and linear-scaled algorithm are not only applicable to finite-size systems, but also adaptable to infinite periodic systems. The scalability and efficiency of the algorithms are numerically benchmarked on different Hamiltonians. Finally, we demonstrate that stabilizer ground states are promising tools for not only qualitative understanding of quantum systems, but also cornerstones of more advanced classical or quantum algorithms.