TY - JOUR
T1 - Adiabatic quantum algorithm for artificial graphene
AU - Pérez-Obiol, Axel
AU - Pérez-Salinas, Adrián
AU - Sánchez-Ramírez, Sergio
AU - Araújo, Bruna G.M.
AU - Garcia-Saez, Artur
N1 - Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/11
Y1 - 2022/11
N2 - We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic, spin-orbit, and Coulomb terms. The initial state is obtained efficiently using Gaussian-state preparation, while the readout of the ground energy is organized into seventeen sets of measurements, irrespective of the size of the problem. The total depth of the corresponding quantum circuit scales polynomially with the size of the system. A full simulation of the algorithm is performed and ground energies are obtained for lattices with up to four hexagons. Our results are benchmarked with exact diagonalization for systems with one and two hexagons. For larger systems we use the exact state vector and approximate matrix product state simulation techniques. The latter allows us to systematically trade off precision with memory and therefore to tackle larger systems. We analyze adiabatic and Trotterization errors, providing estimates for optimal periods and time discretizations given a finite accuracy. In the case of large systems we also study approximation errors.
AB - We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic, spin-orbit, and Coulomb terms. The initial state is obtained efficiently using Gaussian-state preparation, while the readout of the ground energy is organized into seventeen sets of measurements, irrespective of the size of the problem. The total depth of the corresponding quantum circuit scales polynomially with the size of the system. A full simulation of the algorithm is performed and ground energies are obtained for lattices with up to four hexagons. Our results are benchmarked with exact diagonalization for systems with one and two hexagons. For larger systems we use the exact state vector and approximate matrix product state simulation techniques. The latter allows us to systematically trade off precision with memory and therefore to tackle larger systems. We analyze adiabatic and Trotterization errors, providing estimates for optimal periods and time discretizations given a finite accuracy. In the case of large systems we also study approximation errors.
UR - http://www.scopus.com/inward/record.url?scp=85142044842&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.106.052408
DO - 10.1103/PhysRevA.106.052408
M3 - Article
AN - SCOPUS:85142044842
SN - 2469-9926
VL - 106
JO - Physical Review A
JF - Physical Review A
IS - 5
M1 - 052408
ER -