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

TL;DR

This paper introduces a Q# implementation of quantum lookup tables for fixed-point arithmetic functions, offering a potentially more efficient alternative to traditional methods when input domains are bounded and some error tolerance is acceptable.

Contribution

The paper presents a practical Q# implementation of quantum lookup tables for arithmetic functions, including error analysis and resource comparison with existing methods.

Findings

LUT-based implementations can be more resource-efficient under certain conditions.

The approach provides a clear benchmark for quantum arithmetic circuit efficiency.

Approximation errors are well-characterized and manageable.

Abstract

In this paper, we present Q# implementations for arbitrary single-variabled fixed-point arithmetic operations for a gate-based quantum computer based on lookup tables (LUTs). In general, this is an inefficent 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\# and its approximation errors. We then 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 some commonly used arithmetic functions. The implementation of the LUT is designed for use by practitioners to use when implementing end-to-end quantum algorithms. In addition, given its well-defined approximation errors, the LUT implementation makes for a clear benchmark for evaluating the efficiency of bespoke quantum arithmetic circuits .