Asymptotically faster quantum algorithms to solve multivariate quadratic equations.

This paper designs and analyzes a quantum algorithm to solve a system of m quadratic equations in n variables over a finite field ({mathbf {F}}_q). In the case (m=n) and (q=2), under standard assumptions, the algorithm takes time (2^{(t+o(1))n}) on a mesh-connected computer of area (2^{(a+o(1))n}), where (tapprox 0.45743) and (aapprox 0.01467). The area-time product has asymptotic exponent (t+aapprox 0.47210).