Related papers: A quantum Fourier transform (QFT) based note detec…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of…
A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a…
We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21.…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…
We study quantum period finding algorithms such as Simon and Shor (and its variants Eker{\aa}-H{\aa}stad and Mosca-Ekert). For a periodic function $f$ these algorithms produce -- via some quantum embedding of $f$ -- a quantum superposition…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis and compression in diagnostics, astronomy, chemistry and broadcasting…
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…
Analysis and verification of quantum circuits are highly challenging, given the exponential dependence of the number of states on the number of qubits. For analytical derivation, we propose a new quantum polynomial representation (QPR) to…
Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…
Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum…