Related papers: Computational leakage: Grover's algorithm with imp…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
Distributed quantum computing can give substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of Grover search. This motivates studying the quantum advantage of the distributed version of…
It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum…
Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
Grover's algorithm is usually described in terms of the iteration of a compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite straightforward to verify the algebra of the iteration, this gives little insight into why…
We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system…
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…
As various quantum computing technologies continue to compete for quantum supremacy, several parameters have emerged as benchmarks for the quality of qubits. These include fidelity, coherence times, connectivity, and a few others. In this…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target…
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…
Quantum computing (QC) emulators, which simulate quantum algorithms on classical hardware, are indispensable platforms for testing quantum algorithms before scalable quantum computers become widely available. A critical challenge in QC…
The Grover search algorithm is a pivotal advancement in quantum computing, promising a remarkable speedup over classical algorithms in searching unstructured large databases. Here, we report results for the implementation and…
Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator…