QRAM

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 $\sum _{i=0}^{1}\alpha _{i}|i\rangle _{a}=\alpha _{0}|0\rangle _{a}+\alpha _{1}|1\rangle _{a}$.

References

https://arxiv.org/pdf/0708.1879.pdf

https://arxiv.org/pdf/2006.11761.pdf

https://github.com/qsharp-community/qram Nice animation.