Related papers: Improved Quantum Query Complexity on Easier Inputs

Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…

Quantum Machine Learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources…

The current era of quantum computing has yielded several algorithms that promise high computational efficiency. While the algorithms are sound in theory and can provide potentially exponential speedup, there is little guidance on how to…

Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…

The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…

Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…

The widespread use of machine learning has raised the question of quantum supremacy for supervised learning as compared to quantum computational advantage. In fact, a recent work shows that computational and learning advantage are, in…

In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum Advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) multivariate quadratic…

We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…

Numerically solving partial differential equations is a ubiquitous computational task with broad applications in many fields of science. Quantum computers can potentially provide high-degree polynomial speed-ups for solving PDEs, however…

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…

In the past decade, the field of quantum machine learning has drawn significant attention due to the prospect of bringing genuine computational advantages to now widespread algorithmic methods. However, not all domains of machine learning…

Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…

Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…

Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…

Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…

Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…

Quantum computing faces a key challenge: balancing the need for low circuit depth (crucial for fault tolerance) with the high accuracy required for complex computations like quantum chemistry and error correction, which typically require…

We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…