Theoretical physics, functional analysis, and algorithmic computer science are all bridge fields in quantum computation. So far, the primary goal of quantum computation research has been to demonstrate that the time required to solve particular tasks is less for a quantum computer than for a conventional computer. Quantum memory is required for the formation of a synchronization tool that can match the multiple procedures in a quantum computer, a quantum gate that retains the identity of any state, and a method for turning preset photons into on-demand photons, among other quantum information processing devices. Quantum memory may be utilized in a variety of applications, including quantum computing and quantum communication. Continuous research and experimentation have enabled the storing of qubits in quantum memory. Quantum memory is the quantum-mechanical equivalent of conventional computer memory in quantum computing. Unlike conventional memory, which stores information as binary states (represented by “1’s” and “0’s”), quantum memory saves a quantum state for subsequent retrieval. Qubits (represented by “ \(|{1}>\) ” and “ \(|{0}>\) ”), which provide important computing information, are stored in these states. Unlike traditional computer memory, the states saved in quantum memory can be in a quantum superposition, providing far more practical flexibility in quantum algorithms than traditional information storage. This chapter will present four common memory devices in quantum computing, those are Quantum Random-Access Memory (QRAM), Quantum Read-Only Memory (QROM), Quantum Programmable Read-Only Memory (QPROM), and Quantum Cache Memory. Quantum memory devices are a mandatory part of quantum computation. So the details of those four memory devices will be shown in this chapter.