Improved quantum algorithms for linear and nonlinear differential equations

H Krovi - Quantum, 2023 - quantum-journal.org
We present substantially generalized and improved quantum algorithms over prior work for
inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we …

The cost of solving linear differential equations on a quantum computer: fast-forwarding to explicit resource counts

D Jennings, M Lostaglio, RB Lowrie, S Pallister… - Quantum, 2024 - quantum-journal.org
How well can quantum computers simulate classical dynamical systems? There is
increasing effort in develo** quantum algorithms to efficiently simulate dynamics beyond …

Efficient quantum amplitude encoding of polynomial functions

J Gonzalez-Conde, TW Watts, P Rodriguez-Grasa… - Quantum, 2024 - quantum-journal.org
Loading functions into quantum computers represents an essential step in several quantum
algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency …

End-to-end resource analysis for quantum interior-point methods and portfolio optimization

AM Dalzell, BD Clader, G Salton, M Berta, CYY Lin… - PRX Quantum, 2023 - APS
We study quantum interior-point methods (QIPMs) for second-order cone programming
(SOCP), guided by the example use case of portfolio optimization (PO). We provide a …

From Vlasov-Poisson to Schrödinger-Poisson: Dark matter simulation with a quantum variational time evolution algorithm

L Cappelli, F Tacchino, G Murante, S Borgani… - Physical Review …, 2024 - APS
Cosmological simulations describing the evolution of density perturbations of a self-
gravitating collisionless dark matter (DM) fluid in an expanding background provide a …

Quantum linear system solvers: A survey of algorithms and applications

MES Morales, L Pira, P Schleich, K Koor… - arxiv preprint arxiv …, 2024 - arxiv.org
Solving linear systems of equations plays a fundamental role in numerous computational
problems from different fields of science. The widespread use of numerical methods to solve …

Double-Logarithmic Depth Block-Encodings of Simple Finite Difference Method's Matrices

S Ty, R Vilmart, A Tahmasebimoradi… - arxiv preprint arxiv …, 2024 - arxiv.org
Solving differential equations is one of the most computationally expensive problems in
classical computing, occupying the vast majority of high-performance computing resources …

Tight quantum depth lower bound for solving systems of linear equations

Q Wang, Z Zhang - Physical Review A, 2024 - APS
Since Harrow et al.[AW Harrow, A. Hassidim, and S. Lloyd, Phys. Rev. Lett. 103, 150502
(2009) 0031-9007 10.1103/PhysRevLett. 103.150502] showed that a system of linear …

A near-term quantum algorithm for solving linear systems of equations based on the woodbury identity

D O'Malley, JM Henderson, E Pelofske, S Greer… - arxiv preprint arxiv …, 2022 - arxiv.org
Quantum algorithms for solving linear systems of equations have generated excitement
because of the potential speed-ups involved and the importance of solving linear equations …

Quantum sampling algorithms for quantum state preparation and matrix block-encoding

J Lemieux, M Lostaglio, S Pallister, W Pol… - arxiv preprint arxiv …, 2024 - arxiv.org
The problems of quantum state preparation and matrix block-encoding are ubiquitous in
quantum computing: they are crucial parts of various quantum algorithms for the purpose for …