## Workshops Archive

### A Q# Implementation of a Quantum Lookup Table for Quantum Arithmetic Functions

**Workshop:** Third International Workshop on Quantum Computing Software

**Authors:** Rajiv Krishnakumar (Goldman Sachs Inc), Mathias Soeken and Martin Roetteler (Microsoft Corporation), and William Zeng (Goldman Sachs Inc)

**Abstract:** We present Q# implementations for arbitrary fixed-point arithmetic operations for a gate-based quantum computer based on lookup tables (LUT). In general, this is an inefficient way of implementing a function since the number of inputs can be large or even infinite. However, if the input domain can be bounded and there can be some error tolerance in the output (both of which are often the case in practical use-cases), the quantum LUT implementation of certain quantum arithmetic functions can be more efficient than their corresponding reversible arithmetic implementations. We discuss the implementation of the LUT using Q#, show examples of how to use the LUT to implement quantum arithmetic functions, and compare the resources required for the implementation with the current state-of-the-art bespoke implementations of exponential and Gaussian functions.

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