A variational quantum algorithm for tackling multi-dimensional Poisson equations with inhomogeneous boundary conditions
arXiv:2411.03009 · doi:10.1088/1367-2630/add8b4
Abstract
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated with the concept of the minimal potential energy, we not only present in-depth discussion on the cost-efficient & noise-robust design of quantum circuits that are essential for evaluation of the objective function, but, more remarkably, employ the proposed algorithm to calculate bias-dependent spatial distributions of electric fields in semiconductor systems that are described with a two-dimensional domain and up to 10-qubit circuits. Extending the application scope to multi-dimensional problems with mixed boundary conditions for the first time, fairly solid computational results of this work clearly demonstrate the potential of variational quantum algorithms to tackle Poisson equations derived from physically meaningful problems.
10 pages, 7 figures
References in corpus (17)
- Quantum Computing in the NISQ era and beyond
- A variational eigenvalue solver on a quantum processor
- Quantum algorithm for solving linear systems of equations
- Variational Quantum Algorithms
- Quantum Computational Supremacy
- From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
- Towards Practical Quantum Variational Algorithms
- Variational Quantum Linear Solver
- Quantum algorithm and circuit design solving the Poisson equation
- Atomistic simulations of low-field mobility in Si nanowires: Influence of confinement and orientation
- Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
- On the Universality of the Quantum Approximate Optimization Algorithm
- Quantitative Excited State Spectroscopy of a Single InGaAs Quantum Dot Molecule through Multi-million Atom Electronic Structure Calculations
- A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer
- Efficient computation of permanents, with applications to boson sampling and random matrices
- Variational quantum algorithms for Poisson equations based on the decomposition of sparse Hamiltonians
- Devitalizing noise-driven instability of entangling logic in silicon devices with bias controls