Oversimplifying quantum factoring

@article{Smolin2013OversimplifyingQF,
  title={Oversimplifying quantum factoring},
  author={John A. Smolin and Graeme Smith and Alexander Vargo},
  journal={Nature},
  year={2013},
  volume={499},
  pages={163-165},
  url={https://api.semanticscholar.org/CorpusID:4422110}
}
All composite numbers admit simplification of the quantum factoring algorithm to a circuit equivalent to flipping coins, and the difficulty of a particular experiment depends on the level of simplification chosen, not the size of the number factored.
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98 Citations
Highly Influential Citations
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Background Citations
25
Methods Citations
13

98 Citations

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Using Shor’s algorithm on near term Quantum computers: a reduced version

A reduced version of Shor’s algorithm is introduced that proposes a step forward in increasing the range of numbers that can be factorized on noisy Quantum devices by reducing the number of gates in the modular arithmetic and the Quantum Fourier Transform.

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Large-Scale Simulation of Shor’s Quantum Factoring Algorithm

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21 References

Factoring 51 and 85 with 8 qubits

We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257 and 65537. Such composites, including the previously…

Shor’s Quantum Factoring Algorithm on a Photonic Chip

The demonstration of a compiled version of Shor’s quantum factoring algorithm on an integrated waveguide silica-on-silicon chip that guides four single-photon qubits through the computation to factor 15 is reported.

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For the first time, the core processes, coherent control, and resultant entangled states required in a full-scale implementation of Shor's powerful quantum algorithm for factoring are demonstrated in a photonic system.

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

A simple, parameter-free but predictive model of decoherence effects in the authors' system is presented, which is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work.

Shor's algorithm with fewer (pure) qubits

This note gives a circuit for which none of the about 2n qubits need to be initialised, and shows how the modular additions in the algorithm can be carried out with a superposition of an arithmetic sequence, which makes parallelisation of Shor's algorithm easier.

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It is shown that the Fourier transform preceding the final measurement in Shor's algorithm for factorization on a quantum computer can be carried out in a semiclassical way by using the ``classical''…

Computing prime factors with a Josephson phase qubit quantum processor

A nine-quantum-element solid-state quantum processor is demonstrated and three experiments are shown to highlight its capabilities: a three-qubit compiled version of Shor’s algorithm to factor the number 15, and successfully find the prime factors 48% of the time.

Accuracy threshold for postselected quantum computation

This proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected.