Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance

By Lieven M. K. Vandersypen, Matthias Steffen, Gregory Breyta, C. S. Yannoni, M. Sherwood, Isaac L. Chuang. Nature, 2001

1,634 citations recorded by the source corpus.

The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/eec83aa6e6746cab27ca7b5dd7e9535646ee65a2

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Citations in the corpus

Demonstration of an all-optical quantum controlled-NOT gate (2003, methodology): “Nuclear magnetic resonance techniques have been used to implement the most advanced quantum algorithms to dat”
Quantum computing with trapped ions (2008, methodology): “In particular, liquid-state nuclear magnetic resonance was used to demonstrate a quantum algorithm (Gershenfeld and Chuang, 1997; Chuang et al., 1998b; Jones and Mosca, 1998) and later even Shor’s algorithm was implemented on a seven qubit register (Vandersypen et al., 2001).”
Circuit for Shor's algorithm using 2n+3 qubits (2002, methodology): “The number 15 was factored using NMR with seven qubits in an impressive display of quantum control by Vandersypen, Steffen, Breyta, Yannoni, Sherwood and Chuang [ 14 ].”
Bang–bang control of fullerene qubits using ultrafast phase gates (2006, background): “Here we demonstrate a phase gate of unprecedented speed [4, 5] on a nuclear spin qubit in a fullerene molecule, and use it to bang-bang decouple the qubit from a strong environmental interaction.”
A Survey on Quantum Channel Capacities (2018, background): “By contrast, the materials considered at the time of writing for building quantum devices, including trapped ions [460] and solid state Nuclear Magnetic Resonance [519], exhibit asymmetric depolarization property defined as the ratio of the phase flip probability over the bit flip probability, where”
Qudits and High-Dimensional Quantum Computing (2020, methodology): “For many of the physical systems such as photons [113, 132]; super conducting systems [29, 31]; trapped ions [14, 15]; magnetic [7, 18, 32, 148] and non-magnetic molecules [30, 152] there are usually more than two available physical states available for the applications.”
Experimental realization of Shor's quantum factoring algorithm using qubit recycling (2011, background): “There are several steps to compilations, common to previous demonstrations 6–9 ,21 .”
High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges (2019, background): “in quantum computing [1–5], communication [6–9] and simulation [10–14].”