QRAM

Introduction

Theory

The address and output registers of QRAM are composed of qubits instead of bits, though the memory array can be either quantum or classical.

Address register $a$ : superposition $\sum _{i}\alpha _{i}|i\rangle _{a}$ .

Data register $d$ with $D_{i}$ being the content of $i$ th memory cell. QRAM is the operation $\sum _{i}\alpha _{i}|i\rangle _{a}\to \sum _{i}\alpha _{i}|i\rangle _{a}|D_{i}\rangle _{d}$ .

Example

Store the data array $[1,2,5,7]=[1,10,101,111]_{2}$ into a Qram addresses $[0,1]$ . Address register is $\sum _{i=0}^{1}\alpha _{i}|i\rangle _{a}=\alpha _{0}|0\rangle _{a}+\alpha _{1}|1\rangle _{a}$ .