相关论文: Entanglement and its Role in Shor's Algorithm

We argue that entanglement is the essential non-classical ingredient which provides the computational speed-up in quantum algorithms as compared to algorithms based on the processes of classical physics.

Entanglement plays a crucial role in quantum processes particularly those pertaining to quantum information and computation. An analytical expression for entanglement measure defined in terms of success rate of Grover's search algorithm has…

Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels…

We consider quantum computing with pseudo-pure states. This framework arises in certain implementations of quantum computing using NMR. We analyze quantum computational protocols which aim to solve exponential classical problems with…

Entanglement plays a crucial role in quantum processes particularly those pertaining to quantum information and computation. An analytical expression for an entanglement measure defined in terms of success rate of Grover's search algorithm…

We investigate how to attack Shor's quantum algorithm for factorization with an entangling probe. We show that an attacker can steal an exact solution of Shor's algorithm outside an institute where the quantum computer is installed if he…

Entanglement is a key resource of quantum science for tasks that require it to be shared among participants. Within atomic, condensed matter and photonic many-body systems the distribution and sharing of entanglement is of particular…

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…

Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or…

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure…

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…

Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in…

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…

Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…

Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…

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…

Entanglement is an essential resource in current experimental implementations for quantum information processing. We review a class of experiments exploiting photonic entanglement, ranging from one-way quantum computing over quantum…

We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The…

Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…

Entanglement is widely considered the cornerstone of quantum information and an essential resource for relevant quantum effects, such as quantum teleportation, quantum cryptography, or the speed-up of quantum computing, as in Shor's…