Floating Point Representations in Quantum Circuit Synthesis

Understand

We provide a non-deterministic quantum protocol that approximates the single qubit rotations R_x(2a^2 b^2)$ using R_x(2a) and R_x(2b) and a constant number of Clifford and T operations.

• We then use this method to construct a "floating point" implementation of a small rotation wherein we use the aforementioned method to construct the exponent part of the rotation and also to combine it with a mantissa.
• This causes the cost of the synthesis to depend more strongly on the relative (rather than absolute) precision required.
• We analyze the mean and variance of the \Tcount required to use our techniques and provide new lower bounds for the T-count for ancilla free synthesis of small single-qubit axial rotations.