Computing prime factors with a Josephson phase qubit quantum processor

TL;DR

This paper demonstrates the use of a superconducting Josephson phase qubit quantum processor to perform prime factorization of 15 using a compiled version of Shor's algorithm, marking progress in solid-state quantum computing.

Contribution

The authors implement and test a nine-qubit superconducting quantum processor capable of executing a three-qubit version of Shor's algorithm for the first time.

Findings

Successfully factored 15 with 48% probability

Demonstrated coherent interactions and entanglement among five qubits

Characterized device with spectroscopy and quantum state tomography

Abstract

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5], however this has yet to be shown using solid state quantum bits (qubits). Two advantages of superconducting qubit architectures are the use of conventional microfabrication techniques, which allow straightforward scaling to large numbers of qubits, and a toolkit of circuit elements that can be used to engineer a variety of qubit types and interactions[6, 7]. Using a number of recent qubit control and hardware advances [7-13], here we demonstrate a nine-quantum-element solid-state QuP and show three experiments to highlight its capabilities. We begin by characterizing the device with spectroscopy. Next, we produces coherent interactions between five qubits and verify bi- and tripartite entanglement via quantum state tomography (QST) [8, 12, 14, 15]. In the final experiment, we run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48% of the time. Improvements in the superconducting qubit coherence times and more complex circuits should provide the resources necessary to factor larger composite numbers and run more intricate quantum algorithms.