Related papers: Quantum factoring, discrete logarithms and the hid…
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…
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…
The hidden subgroup problem (HSP) plays an important role in quantum computation, because many quantum algorithms that are exponentially faster than classical algorithms can be casted in the HSP structure. In this paper, we present a new…
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…
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 conjecture that one of the main obstacles to creating new non-abelian quantum hidden subgroup algorithms is the correct choice of a transversal.
In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally solved by Simon in a landmark work. The second is the Fully…
This is continuation of the approach to performing quantum algorithms using geometric structures which was presented by Aerts and Czachor. We solve the Simon's problem which, next to the Shor's alghorithm, is a representative of a quantum…
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 approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the…
Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how…
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…
Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of…
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a…
An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to…
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to \emph{nonabelian} groups…
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…
Nowadays, predominant asymmetric cryptographic schemes are considered to be secure because discrete logarithms are believed to be hard to be computed. The algorithm of Shor can effectively compute discrete logarithms, i.e. it can brake such…