Implementation of a quantum division circuit on noisy intermediate-scale quantum devices using dynamic circuits and approximate computing

Contemporary quantum computers with tens to hundreds of physical quantum bits (qubits) are susceptible to quantum noise. As a result, running quantum circuits on these computers is error prone. In particular, deep quantum circuits with a large number of quantum gates and qubits are more likely to fail on quantum computers. In this work, we propose a design for the quantum arithmetic division operation which runs successfully on contemporary quantum computers. A quantum division circuit is needed for realization of quantum algorithms in scientific and image processing applications. While there have been a limited number of prior works on quantum division, none of them can be implemented on quantum computers due to excessive circuit complexity. We propose a different design that exploits dynamic circuits and approximate computing to deploy a quantum division circuit in quantum computers. The dynamic circuit is a new feature in recent quantum computers for midcircuit measurement in hardware. We exploit this feature to reduce the number of qubits and increase the fidelity of quantum division. We also exploit approximate computing to overcome noise in quantum hardware. We carefully tune the scope of approximation in our circuits to offer an acceptable level of accuracy. We run our division circuit on an IBM quantum computer and show that our circuit overcomes quantum noise and generates meaningful results.