Related papers: Effects of Imperfect Gate Operations in Shor's Pri…
It is shown that a simplified version of the error correction code recently suggested by Shor exhibits manifestation of the quantum Zeno effect. Thus, under certain conditions, protection of an unknown quantum state is achieved. Error…
When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam.…
Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the…
We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum…
An important step in developing multi-qubit gates is to construct efficient benchmarking protocols for them. In our previous paper (arXiv: 2210.04330), we developed metrological protocols to measure the reduced Choi matrix i.e., the…
Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the…
Algorithmic predictions are inherently uncertain: even models with similar aggregate accuracy can produce different predictions for the same individual, raising concerns that high-stakes decisions may become sensitive to arbitrary modeling…
In this note we consider optimised circuits for implementing Shor's quantum factoring algorithm. First I give a circuit for which none of the about 2n qubits need to be initialised (though we still have to make the usual 2n measurements…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
Qubit loss and gate failure are significant obstacles for the implementation of scalable quantum computation. Recently there have been several proposals for overcoming these problems, including schemes based on parity and cluster states.…
We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more…
The efficiency of sorting techniques has a significant impact on the overall efficiency of a program. The efficiency of Shell, Heap and Treap sorting techniques in terms of both running time and memory usage was studied, experiments…
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…
As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
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…
I give a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits, and I review work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system…
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His…
We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \log^{2 +…
Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set…