Generating Approximate Ground States of Molecules Using Quantum Machine Learning

• URL: http://arxiv.org/abs/2210.05489v3
• Date: Mon, 2 Jan 2023 05:37:45 GMT
• Title: Generating Approximate Ground States of Molecules Using Quantum Machine Learning
• Authors: Jack Ceroni, Torin F. Stetina, Maria Kieferova, Carlos Ortiz Marrero, Juan Miguel Arrazola, Nathan Wiebe
• Abstract summary: We propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the potential energy surface. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. We show that gradient evaluation is efficient and numerically demonstrate our method's ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride.
• Score: 2.1286051580524523
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. However, obtaining this information is complicated by the fact that sampling a large number of ground states over a high-dimensional PES can require a vast number of state preparations. In this work, we propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the PES. The model is trained using quantum data consisting of ground-state wavefunctions associated with different classical nuclear coordinates. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. The model is trained using a fidelity loss function to optimize the neural network parameters. We show that gradient evaluation is efficient and numerically demonstrate our method's ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride. In all cases, we find that a small number of training points are needed to achieve very high overlap with the groundstates in practice. From a theoretical perspective, we further prove limitations on these protocols by showing that if we were able to learn across an avoided crossing using a small number of samples, then we would be able to violate Grover's lower bound. Additionally, we prove lower bounds on the amount of quantum data needed to learn a locally optimal neural network function using arguments from quantum Fisher information. This work further identifies that quantum chemistry can be an important use case for quantum machine learning.

Related papers

• 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)
• Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity [0.0]
  Equilibrium propagation (EP) is a procedure that has been introduced and applied to classical energy-based models which relax to an equilibrium. Here, we show a direct connection between EP and Onsager reciprocity and exploit this to derive a quantum version of EP. This can be used to optimize loss functions that depend on the expectation values of observables of an arbitrary quantum system.
  arXiv  Detail & Related papers  (2024-06-10T17:22:09Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer [0.0]
  We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver. We encode both electronic states and candidate molecular geometries as a superposition of many-qubit states. We show that the circuit depth scales as O (n_e2 poly(log n_e)) for the electron number n_e, which can be reduced to O (n_e poly(log n_e)) if extra O (n_e log n_e) qubits are available.
  arXiv  Detail & Related papers  (2022-10-18T14:18:20Z)
• Measuring Quantum Entanglement from Local Information by Machine Learning [10.161394383081145]
  Entanglement is a key property in the development of quantum technologies. We present a neural network-assisted protocol for measuring entanglement in equilibrium and non-equilibrium states of local Hamiltonians.
  arXiv  Detail & Related papers  (2022-09-18T08:15:49Z)
• Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data [5.086494083782608]
  We show that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian. Our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient QCs of molecular systems.
  arXiv  Detail & Related papers  (2022-05-28T16:22:18Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Quantum Federated Learning with Quantum Data [87.49715898878858]
  Quantum machine learning (QML) has emerged as a promising field that leans on the developments in quantum computing to explore large complex machine learning problems. This paper proposes the first fully quantum federated learning framework that can operate over quantum data and, thus, share the learning of quantum circuit parameters in a decentralized manner.
  arXiv  Detail & Related papers  (2021-05-30T12:19:27Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Variational quantum Gibbs state preparation with a truncated Taylor series [8.467503414303637]
  We propose variational hybrid quantum-classical algorithms for quantum Gibbs state preparation. Notably, this algorithm can be implemented on near-term quantum computers equipped with parameterized quantum circuits.
  arXiv  Detail & Related papers  (2020-05-18T15:17:09Z)
• Machine learning transfer efficiencies for noisy quantum walks [62.997667081978825]
  We show that the process of finding requirements on both a graph type and a quantum system coherence can be automated. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. Our results are of importance for demonstration of advantage in quantum experiments and pave the way towards automating scientific research and discoveries.
  arXiv  Detail & Related papers  (2020-01-15T18:36:53Z)

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.