Related papers: A mixed-precision quantum-classical algorithm for …
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.…
We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Quantum machine learning is at the crossroads of two of the most exciting current areas of research; quantum computing and classical machine learning. It explores the interaction between quantum computing and machine learning, investigating…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically,…
Quantum computation consists of a quantum state corresponding to a solution, and measurements with some observables. To obtain a solution with an accuracy $\epsilon$, measurements $O(n/\epsilon^2)$ are required, where $n$ is the size of a…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The VQE algorithm has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, we introduce Quantum Sampling Regression (QSR), an alternative…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…