2022
Sopena, Alejandro; Gordon, Max Hunter; García-Martín, Diego; Sierra, Germán; López, Esperanza
Algebraic Bethe Circuits Journal Article
In: arXiv, 2022.
@article{https://doi.org/10.48550/arxiv.2202.04673,
title = {Algebraic Bethe Circuits},
author = {Alejandro Sopena and Max Hunter Gordon and Diego García-Martín and Germán Sierra and Esperanza López},
doi = {10.48550/ARXIV.2202.04673},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
journal = {arXiv},
publisher = {arXiv},
abstract = {The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA to unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method in the spin-1/2 XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run numerical simulations, preparing eigenstates of the XXZ model for systems of up to 24 qubits and 12 magnons. Furthermore, we run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models in 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA to unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method in the spin-1/2 XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run numerical simulations, preparing eigenstates of the XXZ model for systems of up to 24 qubits and 12 magnons. Furthermore, we run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models in 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.
2021
Sopena, Alejandro; Gordon, Max Hunter; Sierra, Germán; López, Esperanza
Simulating quench dynamics on a digital quantum computer with data-driven error mitigation Journal Article
In: Quantum Science and Technology, vol. 6, no. 4, pp. 045003, 2021.
@article{Sopena_2021,
title = {Simulating quench dynamics on a digital quantum computer with data-driven error mitigation},
author = {Alejandro Sopena and Max Hunter Gordon and Germán Sierra and Esperanza López},
url = {https://arxiv.org/abs/2103.12680},
doi = {10.1088/2058-9565/ac0e7a},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-01},
journal = {Quantum Science and Technology},
volume = {6},
number = {4},
pages = {045003},
publisher = {IOP Publishing},
abstract = {Error mitigation is likely to be key in obtaining near term quantum advantage. In this work we present one of the first implementations of several Clifford data regression based methods which are used to mitigate the effect of noise in real quantum data. We explore the dynamics of the 1-D Ising model with transverse and longitudinal magnetic fields, highlighting signatures of confinement. We find in general Clifford data regression based techniques are advantageous in comparison with zero-noise extrapolation and obtain quantitative agreement with exact results for systems of 9 qubits with circuit depths of up to 176, involving hundreds of CNOT gates. This is the largest systems investigated so far in a study of this type. We also investigate the two-point correlation function and find the effect of noise on this more complicated observable can be mitigated using Clifford quantum circuit data highlighting the utility of these methods.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Error mitigation is likely to be key in obtaining near term quantum advantage. In this work we present one of the first implementations of several Clifford data regression based methods which are used to mitigate the effect of noise in real quantum data. We explore the dynamics of the 1-D Ising model with transverse and longitudinal magnetic fields, highlighting signatures of confinement. We find in general Clifford data regression based techniques are advantageous in comparison with zero-noise extrapolation and obtain quantitative agreement with exact results for systems of 9 qubits with circuit depths of up to 176, involving hundreds of CNOT gates. This is the largest systems investigated so far in a study of this type. We also investigate the two-point correlation function and find the effect of noise on this more complicated observable can be mitigated using Clifford quantum circuit data highlighting the utility of these methods.