Pureum Noh

We provide a guiding principle to generate entanglement of quantum many-body states by applying key ideas of the Higgs mechanism to systems without gauge structures. Unitary operators associated with the Higgs mechanism are constructed, named as mean-operators, and employed to prepare entangled many-body states out of a trivial state. We uncover a symmetry-protectedtopological state with two Ising symmetries on a square lattice and find entangled states with different symmetries and lattices. Plausible applications to quantum simulators such as Rydberg atoms and trapped ions, are also discussed, interpreting the mean-operators as the Ising coupling gates.

Entanglement in quantum many-body systems is the key concept for future technology and science, opening up a possibility to explore uncharted realms in an enormously large Hilbert space. The hybrid quantum-classical algorithms have been suggested to control quantum entanglement of many-body systems, and yet their applicability is intrinsically limited by the numbers of qubits and quantum operations. Here we propose a theory which overcomes the limitations by combining advantages of the hybrid algorithms and the standard mean-field-theory in condensed matter physics, named as mean-operator-theory. We demonstrate that the number of quantum operations to prepare an entangled target many-body state such as symmetry-protected-topological states is significantly reduced by introducing a mean-operator. We also show that a class of mean-operators is expressed as time-evolution operators and our theory is directly applicable to quantum simulations with $^{87}$Rb neutral atoms or trapped $^{40}$Ca$^+$ ions.