In quantum field theory, quantum fields are fundamental entities that exist throughout spacetime. These fields are associated with elementary particles and their interactions. While it is true that quantum fields can carry energy, it would be more accurate to say that energy is a property of quantum fields rather than something from which they originate.
According to quantum field theory, particles are described as excitations or disturbances in their respective quantum fields. For example, the electromagnetic field is associated with photons, and the electron field is associated with electrons. These fields pervade all of spacetime and are in a state of constant fluctuation.
Quantum fields can have different energy states, and the excitations or particles associated with those fields can have varying amounts of energy. In quantum field theory, the energy of a field is often quantized, meaning it can only take on certain discrete values. The particles that arise from these fields can have different energy levels corresponding to different excitation states.
So, while quantum fields can carry energy and the energy of particles arises from the fields, it is more accurate to say that quantum fields and energy are intertwined rather than one arising directly from the other. Quantum fields provide a framework for describing the behavior of elementary particles and their interactions, including their energy properties.