Integrating Quantum Algorithms Into Classical Frameworks: A Predictor-corrector Approach Using HHL
- URL: http://arxiv.org/abs/2406.19996v1
- Date: Fri, 28 Jun 2024 15:31:10 GMT
- Title: Integrating Quantum Algorithms Into Classical Frameworks: A Predictor-corrector Approach Using HHL
- Authors: Omer Rathore, Alastair Basden, Nicholas Chancellor, Halim Kusumaatmaja,
- Abstract summary: 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.
- Score: 0.562479170374811
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address this challenge for 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. Rather than seeking the solution at the next time step, the goal now becomes determining the change between time steps. 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 solutions from a quantum state. Random or regularly performed skips instead lead to simulation failure. We demonstrate that our methodology secures a useful polynomial advantage over a conventional application of the HHL algorithm. The practicality and versatility of the approach are illustrated through applications in various fields such as smoothed particle hydrodynamics, plasma simulations, and reactive flow configurations. Moreover, the proposed algorithm is well suited to run asynchronously on future heterogeneous hardware infrastructures and can effectively leverage the synergistic strengths of classical as well as quantum compute resources.
Related papers
- Iterative Quantum Algorithms for Maximum Independent Set: A Tale of
Low-Depth Quantum Algorithms [0.0]
We study a new class of hybrid approaches to quantum optimization, termed Iterative Maximum Quantum Algorithms.
We show that for QAOA with depth $p=1$, this algorithm performs exactly the same operations and selections as the classical greedy algorithm for MIS.
arXiv Detail & Related papers (2023-09-22T18:00:03Z) - 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) - 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) - A quantum advantage over classical for local max cut [48.02822142773719]
Quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs.
Results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical.
arXiv Detail & Related papers (2023-04-17T16:42:05Z) - A Hybrid Quantum-Classical Algorithm for Robust Fitting [47.42391857319388]
We propose a hybrid quantum-classical algorithm for robust fitting.
Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs.
We present results obtained using an actual quantum computer.
arXiv Detail & Related papers (2022-01-25T05:59:24Z) - Adapting Quantum Approximation Optimization Algorithm (QAOA) for Unit
Commitment [2.8060379263058794]
We formulate and apply a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment.
Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization.
Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units.
arXiv Detail & Related papers (2021-10-25T03:37:34Z) - Near Term Algorithms for Linear Systems of Equations [0.0]
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.
arXiv Detail & Related papers (2021-08-25T17:35:52Z) - 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) - Error mitigation and quantum-assisted simulation in the error corrected
regime [77.34726150561087]
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations.
We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
arXiv Detail & Related papers (2021-03-12T20:58:41Z) - 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.