Related papers: Factorization of large tetra and penta prime numbe…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the…
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
This work tests the performance of Grover's search circuits on some IBM superconducting quantum devices in case of the size of search space $N=2^4$ and $N=2^5$. Ideally, we expect to get an outcome probability distribution that is clearly…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…
In ensemble (or bulk) quantum computation, measurements of qubits in an individual computer cannot be performed. Instead, only expectation values can be measured. As a result of this limitation on the model of computation, various important…
Quantum computing is in an era of limited resources. Current hardware lacks high fidelity gates, long coherence times, and the number of computational units required to perform meaningful computation. Contemporary quantum devices typically…
We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21.…