Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow

• URL: http://arxiv.org/abs/2402.08617v3
• Date: Fri, 19 Sep 2025 15:49:39 GMT
• Title: Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow
• Authors: Parikshit Pareek, Abhijith Jayakumar, Carleton Coffrin, Sidhant Misra,
• Abstract summary: Quantum computers hold promise for solving problems intractable for classical computers.<n>Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem exceeds that required by a quantum algorithm.<n>Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms.
• Score: 1.0032961794537367
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. We investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.

Related papers

• RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations [44.13836547616739]
  Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers.<n> choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.<n>Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem.
  arXiv  Detail & Related papers  (2025-06-04T08:30:35Z)
• Quantum Computing for Optimizing Aircraft Loading [1.055551340663609]
  The aircraft loading optimization problem is a computationally hard problem with the best known classical algorithm scaling exponentially with the number of objects. We propose a quantum approach based on a multi-angle variant of the QAOA algorithm (MAL-VQA) designed to utilize a smaller number of two qubit gates in the quantum circuit. We demonstrate the performance of the algorithm on different instances of the aircraft loading problem by execution on IonQ QPUs Aria and Forte.
  arXiv  Detail & Related papers  (2025-04-02T10:10:11Z)
• Variational Quantum Algorithms for Combinatorial Optimization [0.571097144710995]
  Variational Algorithms (VQA) have emerged as one of the strongest candidates towards reaching practical applicability of NISQ systems. This paper explores the current state and recent developments of VQAs, emphasizing their applicability to Approximate optimization. We implement QAOA circuits with varying depths to solve the MaxCut problem on graphs with 10 and 20 nodes.
  arXiv  Detail & Related papers  (2024-07-08T22:02:39Z)
• 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)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Polynomial-Time Classical Simulation of Noisy IQP Circuits with Constant Depth [0.5188841610098435]
  We show that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, the output distribution can be efficiently sampled by a classical computer. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit.
  arXiv  Detail & Related papers  (2024-03-21T17:55:26Z)
• 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)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Noise-Resilient Quantum Power Flow [11.828274912580074]
  This paper devises a NISQ-QPF algorithm, which enables power flow calculation on noisy quantum computers. Case studies validate the effectiveness and accuracy of NISQ-QPF on IBM's real, noisy quantum devices.
  arXiv  Detail & Related papers  (2022-11-19T01:19:56Z)
• 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)
• Towards Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry [12.724648200604134]
  We introduce a framework of equi convolutional quantum algorithms which is tailored for a number of machine-learning tasks. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+.
  arXiv  Detail & Related papers  (2022-07-15T01:41:53Z)
• Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization [44.96576908957141]
  We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linear iterations problems on quantum computers.
  arXiv  Detail & Related papers  (2022-03-23T18:00:03Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• Quantum Power Flow [11.828274912580074]
  This letter is a proof of concept for quantum power flow (QPF) algorithms. It underpins various unprecedentedly efficient power system analytics exploiting quantum computing.
  arXiv  Detail & Related papers  (2021-04-11T01:03:18Z)
• Fast-Forwarding with NISQ Processors without Feedback Loop [0.0]
  We present the Classical Quantum Fast Forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. Our work provides a $104$ improvement over the previous record.
  arXiv  Detail & Related papers  (2021-04-05T14:29:33Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Towards quantum advantage via topological data analysis [0.0]
  We study the quantum-algorithmic methods behind the algorithm for topological data analysis of Lloyd, Garnerone and Zanardi. We provide a number of new quantum algorithms for problems such as rank estimation and complex network analysis.
  arXiv  Detail & Related papers  (2020-05-06T06:31:24Z)

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.