Related papers: Distributed Quantum Amplitude Amplification
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle $U_\varphi$ on an eigenstate $|x\rangle$ is to apply a state-dependent…
We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…
We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the…
A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and…
Amplitude amplification provides a quadratic speed-up for an array of quantum algorithms when run on a quantum machine perfectly isolated from its environment. However, the advantage is substantially diminished as the NISQ-era quantum…
We first show that the standard deviation error of quantum amplitude estimation is asymptotically lower bounded by approximately $1.28 L^{-1}$, where $L$ is the number of queries. Then we propose a generalized qubitization that can…
For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
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…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of…
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…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Privacy amplification is an indispensable step in the post-processing of quantum key distribution, which can be used to compress the redundancy of shared key and improve the security level of the key. The commonly used privacy amplification…
The evolution of quantum computing technologies has been advancing at a steady pace in the recent years, and the current trend suggests that it will become available at scale for commercial purposes in the near future. The acceleration can…
Simon's problem is one of the most important problems demonstrating the power of quantum computing. Recently, an interesting distributed quantum algorithm for Simon's problem was proposed, where a key sorting operator requiring a large…
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…