# Variational Quantum Factoring

Improve the computational resiliency of Variational Quantum Factoring on noisy quantum computers.

Quantum computing is prophesized to solve integer factorization which is the basis of the RSA based cryptosystem. Quantum factoring using Shorâ€™s algorithm has demonstrated the potential to factor large integers in polynomial time compared to classical computers which take exponential time. However, it requires an excessive number of qubits to factor even trivial numbers e.g. 21 precluding its application in todayâ€™s Noisy-Intermediate-Scale-Quantum (NISQ) computers that possess a limited number of qubits. To make the best use of the limited quantum resources, an alternative approach is to transform the factoring problem into a combinatorial optimization problem which is then solved using a hybrid quantum-classical solver known as Variational Quantum Factoring (VQF).

In the NISQ era quantum computers, the performance of VQF can be affected by the quantum noises e.g., gate error and decoherence. Gate error is the imprecision of applying a quantum gate whereas decoherence noise is roote in the qubitsâ€™ loss of information due to the interaction with the environment. Quantum noises can deviate the modulation of a quantum state from its original planned path thus affecting the performance VQF.In this study, we quantified the impact of noise on VQF and improve its performance using various mathematical transformations.

**Technical Overview**: The simulation of quantum circuits are conducted using Qiskit, a quantum computing simulation package in Python developed by IBM. In addition, to improve the time efficiency of experiment, I developed a Python based framework to automatically map a factoring problem into a parametric quantum circuit.

## Paper

Resiliency Analysis and Improvement of Variational Quantum Factoring in Superconducting Qubit

**Ling Qiu**, Mahabubul Alam, Abdullah Ash-Saki, Swaroop Ghosh.

Proceedings of ACM/IEEE International Symposium on Low Power Electronics and Design **(ISLPED 2020)** (Acceptance rate: ~25%)