  Integer factorization has been one of the cornerstone applications of the
field of quantum computing since the discovery of an efficient algorithm for
factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well
beyond the capabilities of today's noisy intermediate-scale quantum (NISQ)
devices. In this work, we revisit the problem of factoring, developing an
alternative to Shor's algorithm, which employs established techniques to map
the factoring problem to the ground state of an Ising Hamiltonian. The proposed
variational quantum factoring (VQF) algorithm starts by simplifying equations
over Boolean variables in a preprocessing step to reduce the number of qubits
needed for the Hamiltonian. Then, it seeks an approximate ground state of the
resulting Ising Hamiltonian by training variational circuits using the quantum
approximate optimization algorithm (QAOA). We benchmark the VQF algorithm on
various instances of factoring and present numerical results on its
performance.
