Patent ID: 8543627

Claim:
A method of operating a classical computer to calculate a total SEO, with the purpose of using said total SEO to operate a quantum computer, and to induce said quantum computer to approximately sample a probability distribution π(x) defined for all x∈{0,1} N B , said method comprising the steps of: storing in said classical computer a data trove comprising a positive number ε, a point x 0 ∈{0,1} N B such that π(x 0 ) is nonzero, and a data-set that specifies said probability distribution π(x), calculating using said classical computer and using said data trove, a sequence of unitary operators U 0 , U 1 , U 2 , . . . , U M , wherein M depends on ε, wherein there are unit vectors |Φ 1 and |Φ 2 (x) such that if ERR=∥v 1 −| 2 | 2 where |v 1 =U M . . . U 1 U 0 |x 0 |Φ 1 and |v 2 =Σ x √{square root over (π(x))}|x |Φ 2 (x) , then ERR≦ε, calculating using said classical computer for each j=0,1,2, . . . M, a SEO Σ j corresponding to U j , wherein said total SEO equals the product Σ M . . . Σ 1 Σ 0 .