Related papers: Novel linear algebraic theory and one-hundred-mill…
Quantum mechanics predicts a number of at first sight counterintuitive phenomena. It is therefore a question whether our intuition is the best way to find new experiments. Here we report the development of the computer algorithm Melvin…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant…
We develop K$\omega$, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations $(z_k I-H)x^{(k)}=b\, (k=0,1,2,...)$ for a given matrix $H$ and a vector $b$,…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system…
Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in…
Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by…
We propose a new numerical method to solve linear ordinary differential equations of the type $\frac{\partial u}{\partial t}(t,\varepsilon) = A(\varepsilon) \, u(t,\varepsilon)$, where $A:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
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…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
We experimentally demonstrate that a hybrid quantum-classical algorithm can outperform purely classical, off-the-shelf selected configuration interaction methods. First, we construct a class of local Hamiltonian problems with sparse ground…
Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. The most widely known quantum algorithm for ground state approximation, quantum phase…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
A new dimensional scaling method for the calculation of excited states of multielectron atoms is introduced. By including the principle and orbital quantum numbers in the dimension parameter, we obtain an energy expression for excited…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…