Implementing Quantum Gates Using Length-3 Dynamic Quantum Walks

TL;DR

This paper introduces a method to implement any single-qubit quantum gate, including controlled gates, using concise length-3 dynamic quantum walks, simplifying quantum gate construction.

Contribution

It presents a novel length-3 dynamic quantum walk approach for implementing universal single-qubit and controlled gates efficiently.

Findings

Implemented Draper's quantum addition circuit with dynamic quantum walks.

Achieved shorter sequences for quantum gate implementation.

Demonstrated universal gate implementation with minimal graph sequences.

Abstract

It is well-known that any quantum gate can be decomposed into the universal gate set {T, H, CNOT}, and recent results have shown that each of these gates can be implemented using a dynamic quantum walk, which is a continuous-time quantum walk on a sequence of graphs. This procedure for converting a quantum gate into a dynamic quantum walk, however, can result in long sequences of graphs. To alleviate this, in this paper, we develop a length-3 dynamic quantum walk that implements any single-qubit gate. Furthermore, we extend this result to give length-3 dynamic quantum walks that implement any single-qubit gate controlled by any number of qubits. Using these, we implement Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a dynamic quantum walk.