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

@article{Vandersypen2001ExperimentalRO,
  title={Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance},
  author={Lieven M. K. Vandersypen and Matthias Steffen and Gregory Breyta and Costantino S. Yannoni and Mark H. Sherwood and Isaac L. Chuang},
  journal={Nature},
  year={2001},
  volume={414},
  pages={883-887},
  url={https://api.semanticscholar.org/CorpusID:4400832}
}
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.

Factoring integers with sublinear resources on a superconducting quantum processor

A universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA), making it the most qubit-saving factorization algorithm to date.

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

A scalable version of Shor's algorithm is demonstrated in which the n-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.

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.

Factoring larger integers with fewer qubits via quantum annealing with optimized parameters

This study optimize the problem Hamiltonian to reduce the number of qubits involved in the final Hamiltonian while maintaining the QUBO coefficients in a reasonable range, enabling the improved algorithm to factorize larger integers with fewer qubits.

Exact search algorithm to factorize large biprimes and a triprime on IBM quantum computer

It has been concluded that the solution to this problem depends on the level of simplification chosen, not the size of the number factored, and in principle, the results can be extended to factorize any multi-prime integer with minimum quantum resources.

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%.

Shor’s factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers

This paper endeavors to explain, in a fashion comprehensible to the nonexpert, the RSA encryption protocol; the various quantum computer manipulations constituting the Shor algorithm; how theShor algorithm performs the factoring; and the precise sense in which a quantum computer employing Shor’s algorithm can be said to accomplish the factored of very large numbers with less computational effort than a classical computer.

Quantum Fourier Transform and Its Application in Shor’s Algorithm

The effect of quantum entanglement might be crucial to the speed boost of factoring large integers in Shor’s algorithm, which was proposed by Peter Shor to factor large integers on quantum computers.

Quantum Factoring Algorithm: Resource Estimation and Survey of Experiments

    N. Kunihiro
    Computer Science, Physics
  • 2020
This study investigates the details of quantum circuits used in several factoring experiments and indicates that some of the circuits have been constructed under the condition that the order of an element modulo a target composite is known in advance.

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.
...

Quantum Computers, Factoring, and Decoherence

Here it is shown how the decoherence process degrades the interference pattern that emerges from the quantum factoring algorithm, a problem of practical significance for cryptographic applications.

Quantum Computation and Shor's Factoring Algorithm

The authors give an exposition of Shor's algorithm together with an introduction to quantum computation and complexity theory, and discuss experiments that may contribute to its practical implementation.

Algorithms for quantum computation: discrete logarithms and factoring

    P. Shor
    Computer Science, Physics
  • 1994
Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.

An algorithmic benchmark for quantum information processing

An experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits is reported, which can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Efficient randomized algorithms are given for factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems.

Experimental realization of an order-finding algorithm with an NMR quantum computer.

A nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations is realization, demonstrating a quantum algorithm for order finding which has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially.

Implementation of a three-quantum-bit search algorithm

The experimental implementation of Grover’s quantum search algorithm on a quantum computer with three quantum bits is reported, made possible by the introduction of two techniques which significantly reduce the complexity of the experiment and by the surprising degree of cancellation of systematic errors.

Ensemble quantum computing by NMR spectroscopy

A new computational model is presented, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof, which can solve nondeterministic polynomial-time complete problems inPolynomial time.

Molecular scale heat engines and scalable quantum computation

N procedure that extracts the asymptotically optimal fraction of purified bits is given, and a quasi-linear time implementation of the procedure is given in a model motivated by NMR quantum computing.

A silicon-based nuclear spin quantum computer

A scheme for implementing a quantum-mechanical computer where information is encoded onto the nuclear spins of donor atoms in doped silicon electronic devices.