Related papers: Variable time amplitude amplification and a faster…
We create a variety of new quantum algorithms that use Grover's algorithm and similar techniques to give polynomial speedups over their classical counterparts. We begin by introducing a set of tools that carefully minimize the impact of…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the…
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$,…
We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…
Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical…
We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
We introduce the Real Quantum Amplitude Estimation (RQAE) algorithm, an extension of Quantum Amplitude Estimation (QAE) which is sensitive to the sign of the amplitude. RQAE is an iterative algorithm which offers explicit control over the…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…