# Are there any other published quantum factoring algorithms that are simpler or more efficient than Shor’s?

How many qubits and what is the minimum number of gate operations needed to factor an n-bit integer? Are there any other published algorithms that are simpler or more efficient?

The adiabatic factoring algorithm paper notes that factoring can be recast as an optimization problem. More specifically, the adiabatic algorithm notes that in order to factor a number $$N=p\times q$$, it suffices to find an $$(x,y)\in\mathbb{N}^2$$ such that $$f(x,y)=(N-xy)^2$$ obtains a minimum.
Thus, to answer the questions, there are other quantum factoring algorithms that don't require the same repeated squaring/QFT/classical post-processing of Shor's algorithm, and that uses fewer qubits. The runtime may also grow polynomially as in s algorithm, but proving that the runtime is quadratic or even polynomial in the number of qubits (bits of $$N$$) is difficult.