Related papers: Integrated Analysis of Performance and Resource of…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
The quantum multicomputer consists of a large number of small nodes and a qubus interconnect for creating entangled state between the nodes. The primary metric chosen is the performance of such a system on Shor's algorithm for factoring…
In this paper, we briefly discuss the methodology for simulating a quantum computer which performs Shor's algorithm on a 7-qubit system to factorise 15. Using this simulation and the overlooked quantum brachistochrone method, we devised a…
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…
Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and…
This thesis deals with the problematics of the scalability of fault-tolerant quantum computing. This question is studied under the angle of estimating the resources needed to set up such computers. What we call a resource is, in principle,…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For…
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…
Post Quantum and Quantum Cryptography schemes are feasible quantum computer applications for 7G networks. These schemes could possibly replace existing schemes. These algorithms have been compromised by advances in quantum search algorithms…
The execution cost of quantum algorithms is typically quantified through asymptotic gate counts and qubit register sizes, yet these metrics do not directly capture which genuinely quantum resources, and in what amount, must be created and…
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,…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities.…
This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…
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…
Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…
Quantum computers face challenges due to hardware constraints, noise errors, and heterogeneity, and face fundamental design tradeoffs between key performance metrics such as \textit{quantum fidelity} and system utilization. This…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…