New Circuit for Quantum Adder by Constant

TL;DR

This paper introduces a novel quantum circuit for in-place addition of a classical constant to a quantum integer modulo 2^n, optimizing ancilla qubits and T-count, with implementation in Q#.

Contribution

It presents a new, efficient quantum circuit for constant addition with reduced ancilla and T-count, including controlled variants and practical implementation.

Findings

Uses n-3 ancillas with T-count 4n-5 for addition

Controlled version uses n-2 ancillas with T-count 11n-15

Implemented in Q# for practical use

Abstract

We propose a new circuit for in-place addition of a classical $n$-bit constant to a quantum $n$-qubit integer modulo $2^n$. Our circuit uses $n-3$ ancilla qubits and has a T-count of $4n-5$. We also propose controlled version of this circuit that uses $n-2$ ancillas and has a T-count of $11n-15$. We implement these circuits in Q#.