Related papers: On Arbitrary Phases in Quantum Amplitude Amplifica…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
We discuss the implementation of an iterative quantum phase estimation algorithm, with a single ancillary qubit. We suggest using this algorithm as a benchmark for multi-qubit implementations. Furthermore we describe in detail the smallest…
Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional…
Quantum amplitude amplification and quantum phase estimation are two fundamental quantum algorithms. All known quantum algorithms are derived from these two algorithms. Even the adiabatic quantum algorithms can also be efficiently simulated…
Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies…
We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…
Quantum amplitude amplification algorithm is an important and basic technique in quantum computing. In this paper, our goal is to study distributed quantum amplitude amplification algorithms, and the main contributions are: (1) A…
We propose a scheme to realize the phase-preserving amplification without the restriction of resolved sideband condition. As a result, our gain-bandwidth product is about one magnitude larger than the existing proposals. In our model, an…
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
The quantum simulation of classical fluids often involves the use of probabilistic algorithms that encode the result of the dynamics in the form of the amplitude of the selected quantum state. In most cases, however, the amplitude…
Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…
A misunderstanding that an arbitrary phase rotation of the marked state together with the inversion about average operation in Grover's search algorithm can be used to construct a (less efficient) quantum search algorithm is cleared. The…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
In this paper we derived the precise formula in a sine function form of the norm of the amplitude in the desired state, and by means of he precise formula we presented the necessary and sufficient phase condition for any quantum algorithm…
Building quantum devices using fixed operators is a must to simplify the hardware construction. Quantum search engine is not an exception. In this paper, a fixed phase quantum search algorithm that searches for M matches in an unstructured…
We investigate the response to noise, in the form of glassy disorder present in circuit elements, in the success probability of the quantum phase estimation algorithm, a subroutine used to determine the eigenvalue - a phase - corresponding…
Most of the schemes for "noiseless" amplification of coherent states, which have recently been attracting theoretical and experimental interest, share a common trait: the amplification is not truly noiseless, or perfect, for non-zero…
In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…