相关论文: The modular multiplication operator and the quanti…

We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a "global Hadamard operation", i.e. apply a Hadamard operation to every qubit…

Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…

We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…

The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…

The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently a quantum approximate Bayesian optimization algorithm (QABOA) that includes two…

Shor's factoring algorithm guarantees a success probability of at least one half for any fixed modulus N = pq with distinct primes p and q. We show that this guarantee does not extend to the asymptotic regime. As N -> infinity, the…

Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…

Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the…

In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are…

We show how the execution time of algorithms on quantum computers depends on the architecture of the quantum computer, the choice of algorithms (including subroutines such as arithmetic), and the ``clock speed'' of the quantum computer. The…

In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…

Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…

Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…

We introduce a family of area preserving generalized baker's transformations acting on the unit square and having sharp polynomial rates of mixing for Holder data. The construction is geometric, relying on the graph of a single variable…

Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and…

Operator spreading under unitary time evolution has attracted a lot of attention recently, as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOC) do distinguish interacting from…

Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…

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…

We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos…

Very recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. In this note, we remark that the report is somewhat misleading because there…