Floating point representation error propagation analysis in quantum computing from a fixed point example

Abstract

This study is motivated by the search for a minimum precision benchmark required of a binary computer to simulate a quantum computing algorithm. In using the floating point system, there is an inherent representation error due to limited memory of the computer to express numbers that cannot be perfectly represented in binary. The case of a test function iterated about a fixed point was used to demonstrate a procedure for the accounting for error propagation, where the argument is misrepresented to some other value 1/n + δ. For i iterations, the error, δ was found to grow by (n+1)ⁱ and decrease at a rate 2^-f to mantissa precision. This procedure was applied in the case of quantum computing, to account for the error propagation of a misrepresented qubit and gate  ρ =  ρ + Δ _ρ and G' = G + Δ_G, which was shown for 1 operation.