Hybrid quantum-classical algorithms have been suggested to control the quantum entanglement of many-body systems in noisy intermediate-scale quantum technology, and yet their applicability is limited by the numbers of qubits and quantum operations. Here, we propose a mean-operator theory which overcomes limitations by combining the advantages of hybrid algorithms and standard mean-field theory. We demonstrate that an introduction of a mean operator prepares an entangled target many-body state with a significantly reduced number of quantum operations. We also show that a class of mean operators is expressed as time-evolution operators, which indicates that our theory is directly applicable to quantum simulations with Rydberg atoms and trapped ions.

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• Atom & ion trapping & guiding
• Quantum algorithms
• Quantum phase transitions
• Quantum simulation
• Strongly correlated systems
• Ultracold gases
• Symmetries in condensed matter
• Tensor network methods
• Variational wave functional methods