Recent advances in logic schemes and fabrication processes have renewed interest in using superconductor electronics for energy-efficient computing and quantum control processors. However, scalable superconducting memory still poses a challenge. To address this issue, we present an alternative to approaches that solely emphasize storage cell miniaturization by exploiting the minimal attenuation and dispersion properties of superconducting passive transmission lines to develop a delay-line memory system. This fully superconducting design operates at speeds between 20 GHz and 100 GHz, with $\pm$24\% and $\pm$13\% bias margins, respectively, and demonstrates data densities in the 10s of Mbit/cm$^2$ with the MIT Lincoln Laboratory SC2 fabrication process. Additionally, the circulating nature of this design allows for minimal control circuitry, eliminates the need for data splitting and merging, and enables inexpensive implementations of sequential access and content-addressable memories. Further advances in fabrication processes suggest data densities of 100s of Mbit/cm$^2$ and beyond

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