Near Term Algorithms for Linear Systems of Equations

• URL: http://arxiv.org/abs/2108.11362v2
• Date: Thu, 26 Aug 2021 14:16:04 GMT
• Title: Near Term Algorithms for Linear Systems of Equations
• Authors: Aidan Pellow-Jarman, Ilya Sinayskiy, Anban Pillay, and Francesco Petruccione
• Abstract summary: This paper makes contributions that include: the first application of the Evolutionary Ansatz to the VQLS (EAVQLS), the first implementation of the Logical Ansatz VQLS (LAVQLS), and the first proof of principle demonstration of the CQS method on real quantum hardware.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an exponential speed-up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, which is unlikely to be available in the near term. Thus, attention has turned to the investigation of quantum algorithms for noisy intermediate-scale quantum (NISQ) devices where several near-term approaches to solving systems of linear equations have been proposed. This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods. This paper makes several contributions that include: the first application of the Evolutionary Ansatz to the VQLS (EAVQLS), the first implementation of the Logical Ansatz VQLS (LAVQLS), based on the Classical Combination of Quantum States (CQS) method, the first proof of principle demonstration of the CQS method on real quantum hardware and a method for the implementation of the Adiabatic Ansatz (AAVQLS). These approaches are implemented and contrasted.

Related papers

• Integrating Quantum Algorithms Into Classical Frameworks: A Predictor-corrector Approach Using HHL [0.562479170374811]
  We adapt a well-known algorithm for linear systems of equations, originally proposed by Harrow, Hassidim and Lloyd (HHL), by adapting it into a predictor-corrector instead of a direct solver. This strategy enables the intelligent omission of computationally costly steps commonly found in many classical algorithms, while simultaneously mitigating the notorious readout problems associated with extracting a quantum state. The versatility of the approach is illustrated through applications in various fields such as smoothed particle hydrodynamics, plasma simulations, and reactive flow configurations.
  arXiv  Detail & Related papers  (2024-06-28T15:31:10Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation [0.0]
  Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other.
  arXiv  Detail & Related papers  (2023-12-30T21:23:15Z)
• Hybrid quantum-classical and quantum-inspired classical algorithms for solving banded circulant linear systems [0.8192907805418583]
  We present an efficient algorithm based on convex optimization of combinations of quantum states to solve for banded circulant linear systems. By decomposing banded circulant matrices into cyclic permutations, our approach produces approximate solutions to such systems with a combination of quantum states linear to $K$. We validate our methods with classical simulations and actual IBM quantum computer implementation, showcasing their applicability for solving physical problems such as heat transfer.
  arXiv  Detail & Related papers  (2023-09-20T16:27:16Z)
• Variational Quantum Approximate Spectral Clustering for Binary Clustering Problems [0.7550566004119158]
  We introduce the Variational Quantum Approximate Spectral Clustering (VQASC) algorithm. VQASC requires optimization of fewer parameters than the system size, N, traditionally required in classical problems. We present numerical results from both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-09-08T17:54:42Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection [80.28858481461418]
  Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices. Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
  arXiv  Detail & Related papers  (2021-07-11T10:56:24Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)
• Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices [0.0]
  Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources. We develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics.
  arXiv  Detail & Related papers  (2020-08-12T13:49:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.