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Computing prime factors with a Josephson phase qubit quantum processor
Erik Lucero, Rami Barends, Yu Chen, Julian Kelly, Matteo Mariantoni, Anthony Megrant, Peter O'Malley, Daniel Sank, Amit Vainsencher, James Wenner, Ted White, Yi Yin, Andrew N. Cleland, John M. Martinis
TL;DR
The paper addresses the lack of a solid-state demonstration of compiled Shor factoring. It builds a nine-element superconducting quantum processor, verifies scalable entanglement, and factors 15 with the prime factors found 48% of the time.
Problem
Compiled Shor's algorithm had not yet been demonstrated using solid-state qubits, motivating a superconducting implementation.
Method
The authors construct a nine-element processor, characterize coherent resonator-mediated interactions and entanglement using QST, then run a calibrated three-qubit compiled Shor circuit for N = 15.
Results
48% of runs successfully find the prime factors 3 and 5 of 15; the processor also verifies Bell and three-qubit entangled states and observes N-dependent coupling.
Takeaways & Limitations
The demonstrations establish a superconducting-qubit platform capable of coherent multi-qubit entanglement and a compiled factoring computation.
Abstract
from arXiv · showhide
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.