Related papers: Quantum simulation of the integer factorization pr…
Factoring integers is considered as a computationally-hard problem for classical methods, whereas there exists polynomial-time Shor's quantum algorithm for solving this task. However, requirements for running the Shor's algorithm for…
For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
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…
We report the first experimental realization of the prime number quantum potential $V_N(x)$, defined as the potential entering the single-particle Schr\"{o}dinger Hamiltonian with eigenvalues given by the first $N$ prime numbers. We use…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…
Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that…
We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a…
We propose a quantum circuit that creates a pure state corresponding to the quantum superposition of all prime numbers less than 2^n, where n is the number of qubits of the register. This Prime state can be built using Grover's algorithm,…
Photons are natural carriers of quantum information due to their ease of distribution and long lifetime. This thesis concerns various related aspects of quantum information processing with single photons. Firstly, we demonstrate N-photon…
We investigate the feasibility of using electrons in a linear Paul trap as qubits in a future quantum computer. We discuss the necessary experimental steps to realize such a device through a concrete design proposal, including trapping,…
We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
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…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
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…
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…
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…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…