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Present-day quantum systems face critical bottlenecks, including limited qubit counts, brief coherence intervals, and high susceptibility to errors-all of which obstruct the execution of large and complex circuits. The advancement of…
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…
Shor's algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm, showing that the coherence in each step relies on the…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…
Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…
Shor's algorithm, which given appropriate hardware can factorise an integer $N$ in a time polynomial in its binary length $L$, has arguable spurred the race to build a practical quantum computer. Several different quantum circuits…
Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the…
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…
We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…
The main objective of this paper is to develop the two different ways in which round robin architecture is modified and made suitable to be implemented in real time and embedded systems. The scheduling algorithm plays a significant role in…
To improve the utility of learning applications and render machine learning solutions feasible for complex applications, a substantial amount of heavy computations is needed. Thus, it is essential to delegate the computations among several…
The optimal design of a fault-tolerant quantum computer involves finding an appropriate balance between the burden of large-scale integration of noisy components and the load of improving the reliability of hardware technology. This balance…
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally…
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling…
In this paper, we propose Peacock, a new distributed probe-based scheduler which handles heterogeneous workloads in data analytics frameworks with low latency. Peacock mitigates the \emph{Head-of-Line blocking} problem, i.e., shorter tasks…
These are pedagogical notes on Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the…