Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr\"odinger Equation

• URL: http://arxiv.org/abs/2111.03103v2
• Date: Mon, 11 Apr 2022 19:18:45 GMT
• Title: Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr\"odinger Equation
• Authors: Dong An, Di Fang, Lin Lin
• Abstract summary: We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. For the simulation of the Schr"odinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate.
• Score: 2.973326951020451
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schr\"odinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

Related papers

• Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits [1.6268784011387605]
  This paper presents a method that enables us to explicitly implement the quantum circuit for Hamiltonian simulation. We show that the space and time complexities of the constructed circuit are exponentially smaller than those of conventional classical algorithms.
  arXiv  Detail & Related papers  (2024-02-28T15:17:41Z)
• Quantum computing of reacting flows via Hamiltonian simulation [13.377719901871027]
  We develop the quantum spectral and finite difference methods for simulating reacting flows in periodic and general conditions. The present quantum computing algorithms offer a one-shot'' solution for a given time without temporal discretization.
  arXiv  Detail & Related papers  (2023-12-13T04:31:49Z)
• Digital quantum simulator for the time-dependent Dirac equation using discrete-time quantum walks [0.7036032466145112]
  We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Our findings indicate that relativistic dynamics is achievable with quantum computers.
  arXiv  Detail & Related papers  (2023-05-31T05:36:57Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation [3.3917542048743865]
  We develop fully-coherent simulation algorithms based on quantum signal processing (QSP) We numerically analyze these algorithms by applying them to the simulation of spin dynamics of the Heisenberg model.
  arXiv  Detail & Related papers  (2021-10-21T17:56:33Z)
• 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)
• 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)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• 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)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)

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.