Computing prime factors with a Josephson phase qubit quantum processor

A quantum processor can be used to exploit quantum mechanics to find the prime factors of composite numbers(1). Compiled versions of Shor's algorithm and Gauss sum factorizations have been demonstrated on ensemble quantum systems(2), photonic systems(3-6) and trapped ions(7). Although proposed(8), these algorithms have yet to be shown using solid-state quantum bits. Using a number of recent qubit control and hardware advances(9-16), here we demonstrate a nine-quantum-element solid-state quantum processor and show three experiments to highlight its capabilities. We begin by characterizing the device with spectroscopy. Next, we produce coherent interactions between five qubits and verify bi- and tripartite entanglement through quantum state tomography(10,14,17,18). 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.