Typical Unpreparability of Quantum States with Quantum Circuit Model

The quantum entanglement is an interesting resource in quantum information processing, especially in measurement-based quantum computing. However, most quantum states may be too entangled to be prepared efficiently in terms of quantum circuit theory, in that high values of the geometric measure of entanglement preclude states from holding a polynomial quantum preparation circuit. We prove that this phenomenon experiences occurs in a dramatic majority of all states using a novel circuit tree-state correspondence. This work highlights new aspects of the roles both entanglement and quantum circuit theory play for quantum information processing.