Mean-Operator Theorywith Hybrid Quantum-Classical Algorithm

Entanglement phenomena in quantum many-body systems is uncovered by recent advances in quantum science and technology, manifested in quantum advantage and observation of fractionalized particles. The traditional standard description of many-body physics, mean-field theory (MFT), fundamentally fails because entanglement of quantum many-body states cannot be captured. Here, we propose a quantum-mechanically entangled mean-operator theory (MOT) to overcome the fundamental limitation of MFT. Introducing entangled operators, it is demonstrated that MOT naturally describes highly-entangled phenomena such as topological phases and their transitions. A systematic improvement of MFT is also achieved by implanting the hybrid quantum-classical algorithm. Most notably, competition physics between spontaneously symmetry-broken and topological phases is demonstrated. A minimal set of mean-field operators is provided to prepare a non-trivial many- body state, which may be realized in near-term quantum simulations.