A Proposed Quantum Hamiltonian Encoding Framework for Time Evolution Operator Design of Potential Energy Function

• URL: http://arxiv.org/abs/2308.06491v2
• Date: Tue, 3 Oct 2023 10:46:14 GMT
• Title: A Proposed Quantum Hamiltonian Encoding Framework for Time Evolution Operator Design of Potential Energy Function
• Authors: Mostafizur Rahaman Laskar, Kalyan Dasgupta, Atanu Bhattacharya
• Abstract summary: This research delves into time evolution operation due to potential energy functions for applications spanning quantum chemistry and condensed matter physics. The algorithms were implemented in simulators and IBM quantum hardware to prove their efficacy.
• Score: 1.2277343096128712
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The exploration of potential energy operators in quantum systems holds paramount significance, offering profound insights into atomic behaviour, defining interactions, and enabling precise prediction of molecular dynamics. By embracing the Born-Oppenheimer picture, we delve into the intricate quantum evolution due to potential energy, facilitating accurate modelling and simulation of atomic phenomena with improved quantum fidelity. This research delves into time evolution operation due to potential energy functions for applications spanning quantum chemistry and condensed matter physics. Challenges in practical implementation, encompassing the formidable curse of dimensionality and intricate entangled interactions, are thoughtfully examined. Drawing upon seminal works, we lay a robust foundation for comprehensive investigations into potential energy landscapes with two proposed algorithms. In one methodology, we have shown a systematic decomposition of the potential energy function into Hadamard bases with composite construction of Pauli-Z, identity and RZ gates which can construct the unitary time evolution operator corresponding to the potential energy with a very high fidelity. The other method is a trade-off between complexity and fidelity, where we propose a novel quantum framework that can reduce the gate complexity from {\Theta}(2n) to {\Theta}(nCr ) (for some r < n). The proposed quantum algorithms are capable of efficiently simulating potential energy operators. The algorithms were implemented in simulators and IBM quantum hardware to prove their efficacy

Related papers

• 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)
• Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic Energy Operator [2.184775414778289]
  The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers. We have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator.
  arXiv  Detail & Related papers  (2023-10-05T05:25:38Z)
• 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)
• On-the-fly Tailoring towards a Rational Ansatz Design for Digital Quantum Simulations [0.0]
  It is imperative to develop low depth quantum circuits that are physically realizable in quantum devices. We develop a disentangled ansatz construction protocol that can dynamically tailor an optimal ansatz. The construction of the ansatz may potentially be performed in parallel quantum architecture through energy sorting and operator commutativity prescreening.
  arXiv  Detail & Related papers  (2023-02-07T11:22:01Z)
• A Probabilistic Imaginary Time Evolution Algorithm Based on Non-unitary Quantum Circuit [13.1638355883302]
  We propose a probabilistic algorithm for implementing imaginary time evolution based on non-unitary quantum circuit. We demonstrate the feasibility of this method by solving the ground state energy of several quantum many-body systems.
  arXiv  Detail & Related papers  (2022-10-11T09:43:30Z)
• Recent Advances for Quantum Neural Networks in Generative Learning [98.88205308106778]
  Quantum generative learning models (QGLMs) may surpass their classical counterparts. We review the current progress of QGLMs from the perspective of machine learning. We discuss the potential applications of QGLMs in both conventional machine learning tasks and quantum physics.
  arXiv  Detail & Related papers  (2022-06-07T07:32:57Z)
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface [68.8204255655161]
  Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. From the perspective of three domain science theorists, this article compiles thoughts about the interface on entanglement, complexity, and quantum simulation.
  arXiv  Detail & Related papers  (2021-07-10T06:12:06Z)
• 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)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum Algorithms for Open Lattice Field Theory [0.0]
  We develop non-Hermitian quantum circuits and explore their promise on a benchmark, the quantum one-dimensional Ising model with complex longitudinal magnetic field. The development of attractors past critical points in the space of complex couplings indicates a potential for study on near-term noisy hardware.
  arXiv  Detail & Related papers  (2020-12-09T19:00:18Z)
• Entanglement generation via power-of-SWAP operations between dynamic electron-spin qubits [62.997667081978825]
  Surface acoustic waves (SAWs) can create moving quantum dots in piezoelectric materials. We show how electron-spin qubits located on dynamic quantum dots can be entangled.
  arXiv  Detail & Related papers  (2020-01-15T19:00:01Z)

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.