Floating Point Representations in Quantum Circuit Synthesis

We provide a non-deterministic quantum protocol that approximates Rx(a2 b2) using Rx(a) and Rx(b) 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 T-count required to use our techniques and show that, with high probability, the required T-count will be lower than lower bounds for the T-count required to do ancilla-free circuit synthesis. We also discuss the T-depth of our method and show that the vast majority of the cost of the resultant circuits can be shifted offline.

Speaker Details

Nathan Wiebe received his BSc in Mathematical Physics and his MSc in Physics from Simon Fraser University. He received his PhD from the University of Calgary where his thesis focused on quantum simulation algorithms and adiabatic quantum computation. He is currently a post-doctoral fellow at the Institute for Quantum Computing at the University of Waterloo.

Series:
Microsoft Research Talks
Date:
Speakers:
Nathan Wiebe
Affiliation:
Institute for Quantum Computing

    • Portrait of Jeff Running

      Jeff Running

    • Portrait of Nathan Wiebe

      Nathan Wiebe

      Researcher

Series: Microsoft Research Talks