Related papers: Obtaining the Quantum Fourier Transform from the C…

Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…

Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…

Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…

Understanding quantum speed-up over classical computing is fundamental for the development of efficient quantum algorithms. In this paper, we study such problem within the framework of the Quantum Query Model, which represents the…

The block canonical coset decomposition is developed as a universal algorithmic tool to synthesize n-qubit quantum gates out of experimentally realizable NMR elements. The two-, three-, and four-qubit quantum Fourier transformations are…

Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale…

Quantum machine learning was recently applied to various applications and leads to results that are comparable or, in certain instances, superior to classical methods, in particular when few training data is available. These results warrant…

In this paper, we propose a quantum version of the differential cryptanalysis which offers a quadratic speedup over the existing classical one and show the quantum circuit implementing it. The quantum differential cryptanalysis is based on…

As quantum computers continue to become more capable, the possibilities of their applications increase. For example, quantum techniques are being integrated with classical neural networks to perform machine learning. In order to be used in…

The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…

Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than…

We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…

The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…

Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for…

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does…

The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of…