Computational Library Using P-adic Arithmetic for Exact Computation With Rational Numbers in Quantum Computing

摘要

Many classes of physical problems can be modeled through the use of sets of linear equations. The solution of the sets of equations is equivalent to calculation of a matrix inverse or generalized inverse, or to the reduction of the matrix to some type of canonical form, including determination of characteristic equation. Conventional machine computation relies on p-ary (for a radix number p such as 2 or 10), or floating-point computation, poor conditioning in connection with round-off error can result in unreliable answers. For scientific computations related to quantum physics, a possible approach is to use techniques of exact linear computation.