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][4][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][8][9][10][11][12][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.In this experiment, we scaled-up from an architecture initially implemented with two qubits and three resonators [7] to a nine-element quantum processor (QuP) capable of realizing rapid entanglement and a compiled version of Shor's algorithm. The device is composed of four phase qubits and five superconducting coplanar waveguide (CPW) resonators, where the resonators are used as qubits by accessing only the two lowest levels. Four of the five CPWs can be used as quantum memory elements as in Ref. [7] and the fifth can be used to mediate entangling operations.The QuP can create entanglement and execute quantum circuits [16,17] with high-fidelity single-qubit gates (X, Y , Z, and H), [18,19]combined with swaps and controlled-phase (C φ ) gates [7,13,20], where one qubit interacts with a resonator at a time. The QuP can also utilize "fast-entangling logic" by bringing all participating qubits on resonance with the resonator at the same time to generate simultaneous entanglement [21]. At present, this combination of entangling capabilities has not been demonstrated on a single device. Previous examples have shown: spectroscopic evidence of the increased coupling for up to three qubits coupled to a resonator [14], as well as coherent interactions between two and three qubits with a resonator [12], although these lacked tomographic evidence of entanglement.Here we show coherent interactions for up to four qubits with a resonator and verify genuine bi-and tripartite entanglement including Bell [9] and |W -states [10] with quantum state tomography (QST). This QuP has the further advantage of creating entanglement at a rate more than twice that of previous demonst...
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