Related papers: Simulating Factorization with a Quantum Computer

Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…

Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the…

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq…

We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…

Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…

Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation…

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…

Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…

The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…

Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…

We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a…

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…

We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…

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…

This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the…

It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…

Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is…

Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…

A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient.…