Related papers: Simulating Factorization with a Quantum Computer
Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. P\'olya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian…
The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports P\'olya's and Hilbert's conjecture to prove Riemann's hypothesis. The energies of this system, being…
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…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
The natural Hilbert Space of quantum particles can implement maximum-likelihood (ML) decoding of classical information. The 'Quantum Product Algorithm' (QPA) is computed on a Factor Graph, where function nodes are unitary matrix operations…
The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process. There are many algorithms has been implemented in the…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…