One of the most important applications of quantum computing is to crack classical cryptosystem. Previous studies showed that the number of qubits required to crack the widely used 2048-bit RSA cipher is about 20 million, which is far beyond the current technology for quantum computing. Recently, É. Gouzien and N. Sangouard of the French Alternative Energies and Atomic Energy Commission proposed a quantum computing architecture based on a two-dimensional grid of superconducting qubits and a three-dimensional multimode quantum memory. They showed that only 13k qubits are required to crack a 2048-bit RSA integer with the help of a long-lived quantum memory with 28 million spatial modes and 45 temporal modes. Their results clearly demonstrate the values of quantum memories in quantum computing and provide an alternative approach for building practically useful quantum computers. Quantum computers require quantum memories to work at microwave band, which remains an outstanding challenge. Based on a detailed analysis of atomic radiations during the quantum storage process, we recently proposed a noiseless-photon-echo protocol which can successfully eliminate the spontaneous emission noise in photon echoes. This protocol is expected to further enable microwave quantum storage and the construction of “quantum memory” quantum computers.