Variational-Cartan Quantum Dynamics Simulations of Excitation Dynamics
- URL: http://arxiv.org/abs/2406.14127v2
- Date: Wed, 28 Aug 2024 13:01:38 GMT
- Title: Variational-Cartan Quantum Dynamics Simulations of Excitation Dynamics
- Authors: Linyun Wan, Jie Liu, Zhenyu Li, Jinlong Yang,
- Abstract summary: Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing.
Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent.
In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational Hamiltonian simulation.
- Score: 7.865137519552981
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics simulations become impratical on near-term quantum processors. The Hamiltonian simulation algorithm based on Cartan decomposition (CD) provides an appealing scheme for QDSs with fixed-depth circuits while limited to time-independent case. In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational Hamiltonian simulation. The time-dependent and time-independent parts of the Hamiltonian are treated with the variational approach and the CD-based Hamiltonian simulation algorithms, respectively. As such, only fixed-depth quantum circuits are required in this hybrid Hamiltonian simulation algorithm while still maintaining high accuracy. We apply this new algorithm to study the response of spin and molecular systems to $\delta$-kick electric fields and obtain accurate spectra for these excitation processes.
Related papers
- A hybrid quantum-classical algorithm for multichannel quantum scattering
of atoms and molecules [62.997667081978825]
We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions.
The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix.
We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
arXiv Detail & Related papers (2023-04-12T18:10:47Z) - Optimal/Nearly-optimal simulation of multi-periodic time-dependent
Hamiltonians [0.0]
We establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time-periodicity.
Overcoming the difficulty of time-dependency, our protocol can simulate the dynamics under multi-periodic time-dependent Hamiltonians.
arXiv Detail & Related papers (2023-01-16T01:53:09Z) - Time Dependent Hamiltonian Simulation Using Discrete Clock Constructions [42.3779227963298]
We provide a framework for encoding time dependent dynamics as time independent systems.
First, we create a time dependent simulation algorithm based on performing qubitization on the augmented clock system.
Second, we define a natural generalization of multiproduct formulas for time-ordered exponentials.
arXiv Detail & Related papers (2022-03-21T21:29:22Z) - 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) - An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian
Simulation [55.41644538483948]
Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates.
We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions.
The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
arXiv Detail & Related papers (2021-08-06T19:38:03Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - 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) - Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum
Computers [0.0]
We present a method for generating circuits that are constant in depth with increasing simulation time for a subset of one-dimensional materials Hamiltonians.
By removing the effective limit on the number of feasibly simulatable time-steps, the constant-depth circuits enable Trotter error to be made negligibly small.
This paves the way for simulations of long-time dynamics for scientifically and technologically relevant quantum materials.
arXiv Detail & Related papers (2021-03-12T17:47:02Z) - 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.