Fault tolerant resource estimation of quantum random-access memories

Quantum random-access look-up of a string of classical bits is a necessary ingredient in several important quantum algorithms. In some cases, the cost of such quantum random-access memory (qRAM) is the limiting factor in the implementation of the algorithm. In this paper we study the cost of fault-tolerantly implementing a qRAM. We construct and analyze generic families of circuits that function as a qRAM, discuss opportunities for qubit-time tradeoffs, and estimate their resource costs when embedded in a surface code.