1. A method of operating a classical computer to calculate a total SEO (Sequence of Elementary Operations) represented by a quantum circuit, wherein an elementary operation acts on one, two, or three qubits at a time, wherein said total SEO depends on a positive real number Δt, a unitary operator V, a Hermitian operator A, and a function ƒ( ) wherein said total SEO acts on N Bj atom qubits, N B probe qubits, and one ancilla qubit, wherein said total SEO is calculated for applying said total SEO to a quantum computer to induce said quantum computer to yield readings that facilitate the calculation of an estimate of the quantity μ(x 0 ) equal to x 0 |V † ƒ(A)V|x 0 for a predetermined point x 0 in {0, 1} N B , said method comprising the steps of: storing in said classical computer: a V-SEO that approximates the unitary operator V, a pth-SEO that approximates exp(i2 p AΔt) for each pε{0, 1,. .. , N Bj −1}, calculating using said classical computer, a phase-estimation-SEO that encodes information about the eigenvalues of A into the state of said probe qubits, said phase-estimation-SEO comprising: for each probe qubit β, said pth-SEO for some pε{0, 1,. .. , N Bj −1}, wherein said pth-SEO acts on the atom qubits and is applied depending on the state of said probe qubit β; a SEO approximating the quantum Fourier operator or the Hermitian conjugate thereof acting on the probe qubits; calculating using said classical computer, a multiplexor-SEO, wherein said multiplexor-SEO is a SEO which approximately equals a quantum multiplexor operator whose controls are said probe qubits and whose target is said ancilla qubit, wherein the parameters of said quantum multiplexor operator depend on said function ƒ( ), said multiplexor-SEO comprising: a 2-dimensional rotation R j = [ c j - s j s j c j ] , c j = Yf ⁡ ( 2 ⁢ π ⁢ ⁢ j Δ ⁢ ⁢ tN S j _ ) , s j = 1 - c j 2 , where γ is a positive real value and N Sj =2 N Bj ; outputting said total SEO; wherein said total SEO contains said V-SEO, said phase-estimation-SEO, and said multiplexor-SEO.