Overview of Computational Methods of Quantum Inner Product and Its Modulus

Quantum computer is one of the future development directions of computer science. It is a kind of physical device that follows the laws of quantum mechanics and can efficiently store and process quantum information. The quantum mechanical system is described by Dirac and von Neumann by using Hilbert space theory, which is a vector space given by the inner product. With the rapid development of quantum computing, the inner product of quantum states and its modulus have received extensive attention in various fields such as quantum machine learning, quantum cryptography, and quantum signal processing. Therefore, quantum inner product and its modulus were reviewed. Unlike the method of the classical algorithm, the unitary operator must be used to operate the quantum state and measurement to obtain the quantum inner product. The quantum inner product is a complex number, and both the complex number and its modulus play a critical role in quantum computing. The main content of this paper was divided into two parts: the quantum inner product modulus and the quantum inner product. The quantum state |0〉^⊗n is generally evolved from the initial state by the unitary operator. Therefore, the calculation methods of the inner product modulus and inner product of the quantum state are divided into direct methods and indirect methods according to whether the unitary operator is used in the calculation process. Then, the applications of the quantum inner product and its modulus were summarized. Finally, the shortcomings of the current research and the future research directions were put forward.