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Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
Quantum hardware continues to advance, yet finding new quantum algorithms - quantum software - remains a challenge, with classically trained computer programmers having little intuition of how computational tasks may be performed in the…
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more…
Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper aims to generalize these algorithms to the problem of calculating an…
Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state…
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…
We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…
This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
We present "Diagrams of States", a way to graphically represent and analyze how quantum information is elaborated during the execution of quantum circuits. This introductory tutorial illustrates the basics, providing useful examples of…
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…
Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…