Related papers: Realization of Shor's Algorithm at Room Temperatur…
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…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the…
Continuous improvements in quantum computing hardware are exposing the need for simultaneous advances in software. Large-scale implementation of quantum algorithms requires rapid and automated compilation routines such as circuit synthesis…
Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms…
We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The…
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…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
Classical simulation of quantum computation has often been viewed as the method to determine where the horizon of quantum supremacy is located---that is, where quantum computation can no longer be simulated by classical methods. As of now,…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
We study a hybrid computational model for integer factorization in which the only non-classical resource is access to an \emph{iterated diffusion process} on a finite graph. Concretely, a \emph{diffusion step} is defined to be one…
Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm…
We show that under the matrix product state formalism the states produced in Shor's algorithm can be represented using O(max($4lr^2$, $2^{2l}$)) space, where l is the number of bits in the number to factorise, and r is the order and the…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength…
The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…