Quantum algorithms for grid-based variational time evolution

• URL: http://arxiv.org/abs/2203.02521v3
• Date: Tue, 26 Sep 2023 14:56:51 GMT
• Title: Quantum algorithms for grid-based variational time evolution
• Authors: Pauline J Ollitrault, Sven Jandura, Alexander Miessen, Irene Burghardt, Rocco Martinazzo, Francesco Tacchino, Ivano Tavernelli
• Abstract summary: We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
• Score: 36.136619420474766
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual reduction in circuit depth conferred by variational approaches, this algorithm also enjoys several advantages compared to previously proposed ones. For instance, variational approaches suffer from the need for a large number of measurements. However, the grid encoding of first quantized Hamiltonians only requires measuring in position and momentum bases, irrespective of the system size. Their combination with variational approaches is therefore particularly attractive. Moreover, heuristic variational forms can be employed to overcome the limitation of the hard decomposition of Trotterized first quantized Hamiltonians into quantum gates. We apply this quantum algorithm to the dynamics of several systems in one and two dimensions. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches. We show how they can be significantly attenuated through subspace diagonalization at a cost of an additional $\mathcal{O}(MN^2)$ 2-qubit gates where $M$ is the number of dimensions and $N^M$ is the total number of grid points.

Related papers

• Estimating quantum amplitudes can be exponentially improved [11.282486674587236]
  Estimating quantum amplitudes is a fundamental task in quantum computing. We present a novel framework for estimating quantum amplitudes by transforming pure states into their matrix forms. Our framework achieves the standard quantum limit $epsilon-2$ and the Heisenberg limit $epsilon-1$, respectively.
  arXiv  Detail & Related papers  (2024-08-25T04:35:53Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• The Algorithm for Solving Quantum Linear Systems of Equations With Coherent Superposition and Its Extended Applications [8.8400072344375]
  We propose two quantum algorithms for solving quantum linear systems of equations with coherent superposition. The two quantum algorithms can both compute the rank and general solution by one measurement. Our analysis indicates that the proposed algorithms are mainly suitable for conducting attacks against lightweight symmetric ciphers.
  arXiv  Detail & Related papers  (2024-05-11T03:03:14Z)
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval [1.6421520075844793]
  A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable problem. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems.
  arXiv  Detail & Related papers  (2024-02-09T15:01:56Z)
• Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms [0.0]
  We show how many techniques from randomized linear algebra can be adapted to work under this weaker assumption. We also apply these results to obtain a robust dequantization of many quantum machine learning algorithms.
  arXiv  Detail & Related papers  (2023-04-11T02:09:13Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• 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)
• 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)
• A Grand Unification of Quantum Algorithms [0.0]
  A number of quantum algorithms were recently tied together by a technique known as the quantum singular value transformation. This paper provides a tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform. We then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation.
  arXiv  Detail & Related papers  (2021-05-06T17:46:33Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)

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.