Solving eigenvalue problems obtained by the finite element method on a quantum annealer using only a few qubits

• URL: http://arxiv.org/abs/2410.13740v1
• Date: Thu, 17 Oct 2024 16:39:03 GMT
• Title: Solving eigenvalue problems obtained by the finite element method on a quantum annealer using only a few qubits
• Authors: Arnaud Rémi, François Damanet, Christophe Geuzaine,
• Abstract summary: One of the main obstacles for achieving a practical quantum advantage in quantum computing lies in the relatively small number of qubits currently available in quantum hardware. We show how to circumvent this problem in the context of eigenvalue problems obtained by the finite element method. As an example, we apply AQAE to eigenvalue problems that are relevant in a wide range of contexts, such as electromagnetism, acoustics and seismology.
• Score: 0.0
• License:
• Abstract: One of the main obstacles for achieving a practical quantum advantage in quantum computing lies in the relatively small number of qubits currently available in quantum hardware. Here, we show how to circumvent this problem in the context of eigenvalue problems obtained by the finite element method, via the use of an adaptive algorithm for quantum annealers -- the Adaptive Quantum Annealer Eigensolver (AQAE) -- in a way that only a few qubits are required to achieve a high precision. As an example, we apply AQAE to eigenvalue problems that are relevant in a wide range of contexts, such as electromagnetism, acoustics and seismology, and quantify its robustness against different types of experimental errors. Our approach could be applied to other algorithms, and makes it possible to take the most of current Noisy-Intermediate-Scale Quantum devices.

Related papers

• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• 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)
• FEqa: Finite Element Computations on Quantum Annealers [0.0]
  We present a unified formulation (FEqa) to solve physical problems using quantum annealers. FEqa is a hybrid technique in which the finite element problem is formulated on a classical computer. FEqa is scalable on the classical portion of the algorithm due to its Single Program Multiple Data nature.
  arXiv  Detail & Related papers  (2022-01-19T21:58:23Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Model-Independent Error Mitigation in Parametric Quantum Circuits and Depolarizing Projection of Quantum Noise [1.5162649964542718]
  Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations. Current quantum devices still suffer from inherent quantum noise.
  arXiv  Detail & Related papers  (2021-11-30T16:08:01Z)
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm [0.0]
  This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs. We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric.
  arXiv  Detail & Related papers  (2021-11-10T11:25:32Z)
• 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)
• Quantum Approximate Optimization for Hard Problems in Linear Algebra [0.0]
  We explore using QAOA for Binary Linear Least Squares (BLLS) as a building block of several other hard problems in linear algebra. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. Our numerics show that Simulated Annealing can outperform QAOA for BLLS at a QAOA depth of $pleq3$ for the probability of sampling the ground state.
  arXiv  Detail & Related papers  (2020-06-27T20:13:24Z)
• Minimizing estimation runtime on noisy quantum computers [0.0]
  "engineered likelihood function" (ELF) is used for carrying out Bayesian inference. We show how the ELF formalism enhances the rate of information gain in sampling as the physical hardware transitions from the regime of noisy quantum computers. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond.
  arXiv  Detail & Related papers  (2020-06-16T17:46:18Z)

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.