Experimental study of Shor's factoring algorithm using the IBM Q Experience

@article{Amico2019ExperimentalSO,
  title={Experimental study of Shor's factoring algorithm using the IBM Q Experience},
  author={Mirko Amico and Zain Saleem and M. Kumph},
  journal={Physical Review A},
  year={2019}
}
We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and $35$. The semi-classical quantum Fourier transform is used to implement the algorithm with only a small number of physical qubits and the circuits are designed to reduce the number of gates to the minimum. We use the square of the statistical overlap to give a quantitative measure of the similarity between the experimentally obtained… 

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References

SHOWING 1-10 OF 20 REFERENCES

Experimental realisation of Shor's quantum factoring algorithm using qubit recycling

This work demonstrates a scalable version of Shor's quantum factoring algorithm in which then qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol.

Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits.

An experimental demonstration of a complied version of Shor's algorithm using four photonic qubits using a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semiclassical quantum Fourier transformation.

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 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.

Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement.

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.

Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System

The implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits confined in a segmented multizone trap incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fouriers transform to a large number of qubits as required for a useful quantum factoring algorithm.

Semiclassical Fourier transform for quantum computation.

  • GriffithsNiu
  • Physics, Computer Science
    Physical review letters
  • 1996
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''

Oversimplifying quantum factoring

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.

Realization of a scalable Shor algorithm

The realization of a scalable Shor algorithm, as proposed by Kitaev, is presented, which has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

Computing prime factors with a Josephson phase qubit quantum processor

Shor’s quantum algorithm factorizes integers, and implementing this is a benchmark test in the early development of quantum processors. Researchers now demonstrate this important test in a