Quantum circuit model for Hamiltonian simulation via Trotter decomposition
- URL: http://arxiv.org/abs/2405.13605v1
- Date: Wed, 22 May 2024 12:57:09 GMT
- Title: Quantum circuit model for Hamiltonian simulation via Trotter decomposition
- Authors: Rohit Sarma Sarkar, Sabyasachi Chakraborty, Bibhas Adhikari,
- Abstract summary: We devise quantum circuit implementation of exponential of scaled $n$-qubit Pauli-strings using one-qubit rotation gates and CNOT gates.
These circuits can be implemented in low-connected quantum hardware, in particular, star graph architecture for digital quantum computation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: We devise quantum circuit implementation of exponential of scaled $n$-qubit Pauli-strings using one-qubit rotation gates and CNOT gates. These circuits can be implemented in low-connected quantum hardware, in particular, star graph architecture for digital quantum computation. Then these circuits are employed to simulate classes of 1D Hamiltonian operators that include $2$-sparse Hamiltonian, Ising Hamiltonian, and both time-independent and time-dependent Random Field Heisenberg Hamiltonian and Transverse Magnetic Random Quantum Ising Hamiltonian by approximating its unitary evolution with first-order Suzuki-Trotter expansion. Finally, we perform noisy Hamiltonian simulation of these circuits using different noise models to investigate Hamiltonian simulation on NISQ devices.
Related papers
- 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) - Photonic quantum simulations of coupled $PT$-symmetric Hamiltonians [0.0]
We use a programmable integrated photonic chip to simulate a model comprised of twin pairs of $PT$-symmetric Hamiltonians, with each the time reverse of its twin.
We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behaviour that arises due to interference between subsystems undergoing time-reversed evolutions.
arXiv Detail & Related papers (2022-02-01T11:54:10Z) - 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) - Parallel Quantum Algorithm for Hamiltonian Simulation [9.680246554758343]
A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians.
The running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence.
We show that the total gate depth of our algorithm has a $operatornamepolyloglog (1/epsilon)$ dependence in the parallel setting.
arXiv Detail & Related papers (2021-05-25T12:46:33Z) - 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) - Engineering analog quantum chemistry Hamiltonians using cold atoms in
optical lattices [69.50862982117127]
We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups.
We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
arXiv Detail & Related papers (2020-11-28T11:23:06Z) - Digital-Analog Quantum Simulations Using The Cross-Resonance Effect [0.0]
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing.
We consider superconducting architectures and extend the cross-resonance effect, up to first order in theory, from a two-qubit interaction to an analog Hamiltonian acting on 1D chains and 2D square lattices.
arXiv Detail & Related papers (2020-11-20T17:07:28Z) - Stoquasticity in circuit QED [78.980148137396]
We show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems.
We corroborate the recent finding that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits.
arXiv Detail & Related papers (2020-11-02T16:41:28Z) - Dynamical Self-energy Mapping (DSEM) for quantum computing [0.0]
For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available.
We present how to bypass this challenge in practical molecular chemistry simulations on NISQ devices by employing a classical-quantum hybrid algorithm.
arXiv Detail & Related papers (2020-10-12T04:12:21Z)
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.