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These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
The decoherence phenomenon inevitably exists in quantum computing processes. Consequently, dynamic suppression of decoherence for instance via dynamical decoupling, quantum error correction codes (QECC) etc. is crucial in accurately…
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
The quantum information science community has seen a surge in new algorithmic developments across scientific domains. These developments have demonstrated polynomial or better improvements in computational and space complexity,…
Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
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…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…