Distributed Phase Estimation Algorithm and Distributed Shor's Algorithm

TL;DR

This paper introduces a distributed phase estimation algorithm that reduces qubit requirements and communication complexity for Shor's algorithm, making quantum factoring more feasible in the NISQ era.

Contribution

The paper proposes a novel distributed phase estimation algorithm that eliminates quantum communication and reduces qubit needs for Shor's algorithm.

Findings

Reduces qubit requirements per node by a factor depending on the number of nodes and integer size.

Eliminates the need for quantum communication in the distributed phase estimation.

Achieves a communication complexity of O(kL) for the distributed order-finding algorithm.

Abstract

Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the NISQ (Noisy Intermediate-scale Quantum) era. To reduce the resources required for Shor's algorithm, in this paper we first propose a new distributed phase estimation algorithm. Our distributed phase estimation algorithm does not require quantum communication and it reduces the number of qubits of a single node compared to the traditional phase estimation algorithm (non-iterative version). Then we apply our distributed phase estimation algorithm to form a distributed order-finding algorithm for Shor's algorithm. Compared with the traditional Shor's algorithm (non-iterative version), the maximum number of qubits required by a single node of our dristributed order-finding algorithm is reduced by $(2-\dfrac{2}{k})L-\log_2k-O(1)$ when factoring an $L$-bit integer ($k$ is the number of compute nodes). The communication complexity of our distributed order-finding algorithm is $O(kL)$.