Quantum Cicruit of Modular Exponentiation in Qiskit

We are constructing a circuit for Modular Exponentiation in Qiskit.

This is based on the paper "Quantum Networks for Elementary Arithmetic Operations" by Vlatko Vedral, Adriano Barenco and Artur Ekert in this circuit.

We assume that $gcd(a,N)=1$ which is not mentioned in the paper. However, this is infact necessary to preserve the unitarity of certain operations that we perform.

We also note that $a$ and $x$ used in the modular exponentiation are bounded by the value of $N$. Specifically. since $a\leq N$ and $x\leq N^2$ for the purpose of Shor's algorithms, $a$ is encoded in $\log(N)$ bits and $x$ is encoded in $2\log(N)$ bits.

Computing for $n=4$ and above require a large number of qubits and will have to be run on 'ibmq_qasm_simulator'

Contributers

• Writika Sarkar
• Soham Chatterjee
• Shree Ganesh SJ