Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

• URL: http://arxiv.org/abs/2301.01203v1
• Date: Tue, 3 Jan 2023 17:00:40 GMT
• Title: Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods
• Authors: Ryan Babbush, William J. Huggins, Dominic W. Berry, Shu Fay Ung, Andrew Zhao, David R. Reichman, Hartmut Neven, Andrew D. Baczewski and Joonho Lee
• Abstract summary: Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory. We show that certain first quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and fewer functional operations in basis set size.
• Score: 0.4215938932388722
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the $k$-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

Related papers

• An Efficient Classical Algorithm for Simulating Short Time 2D Quantum Dynamics [2.891413712995642]
  We introduce an efficient classical algorithm for simulating short-time dynamics in 2D quantum systems. Our results reveal the inherent simplicity in the complexity of short-time 2D quantum dynamics. This work advances our understanding of the boundary between classical and quantum computation.
  arXiv  Detail & Related papers  (2024-09-06T09:59:12Z)
• 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 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)
• Polynomial-time classical sampling of high-temperature quantum Gibbs states [0.22843885788439797]
  computational complexity of simulating quantum many-body systems scales exponentially with the number of particles. We present a classical algorithm that discovering samples from a high-temperature quantum Gibbs state in a computational (product) basis. Our result implies that measurement-based quantum computation on a Gibbs state can provide exponential speed up only at sufficiently low temperature.
  arXiv  Detail & Related papers  (2023-05-29T18:00:00Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• 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)
• Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding [0.5872014229110214]
  ab initio simulation of solid-state materials on quantum computers is still in its early stage. We introduce an orbital-based multi-fragment approach on top of the periodic density matrix embedding theory. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials.
  arXiv  Detail & Related papers  (2022-09-07T15:02:01Z)
• Recompilation-enhanced simulation of electron-phonon dynamics on IBM Quantum computers [62.997667081978825]
  We consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems. We perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation.
  arXiv  Detail & Related papers  (2022-02-16T19:00:00Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Quantum simulations of molecular systems with intrinsic atomic orbitals [0.0]
  We explore the use of intrinsic atomic orbitals (IAOs) in quantum simulations of molecules. We investigate ground-state energies and one- and two-body density operators in the framework of the variational quantum eigensolver. We also demonstrate the use of this approach in the calculation of ground- and excited-states energies of small molecules.
  arXiv  Detail & Related papers  (2020-11-16T18:01:44Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)

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.