TY - JOUR

T1 - Resource estimations for the Hamiltonian simulation in correlated electron materials

AU - Kanno, Shu

AU - Endo, Suguru

AU - Utsumi, Takeru

AU - Tada, Tomofumi

N1 - Funding Information:
This work was partly supported by JSPS KAKENHI Grant No. 21H01742.
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/7

Y1 - 2022/7

N2 - Correlated electron materials, such as superconductors and magnetic materials, are regarded as fascinating targets in quantum computing. However, the quantitative resources, specifically the number of quantum gates and qubits, required to perform a quantum algorithm to simulate correlated electron materials remain unclear. In this study, we estimate the resources required for the Hamiltonian simulation algorithm for correlated electron materials, specifically for organic superconductors, iron-based superconductors, binary transition-metal oxides, and perovskite oxides, using the fermionic swap network. The effective Hamiltonian derived using the ab initio downfolding method is adopted for the Hamiltonian simulation, and a procedure for the resource estimation by using the fermionic swap network for the effective Hamiltonians including the exchange interactions is proposed. For example, in the system for the 102 unit cells, the estimated numbers of gates per Trotter step and qubits are approximately 107 and 103, respectively, on average for the correlated electron materials. Furthermore, our results show that the number of interaction terms in the effective Hamiltonian, especially for the Coulomb interaction terms, is dominant in the gate resources when the number of unit cells constituting the whole system is up to 102, whereas the number of fermionic swap operations is dominant when the number of unit cells is more than 103.

AB - Correlated electron materials, such as superconductors and magnetic materials, are regarded as fascinating targets in quantum computing. However, the quantitative resources, specifically the number of quantum gates and qubits, required to perform a quantum algorithm to simulate correlated electron materials remain unclear. In this study, we estimate the resources required for the Hamiltonian simulation algorithm for correlated electron materials, specifically for organic superconductors, iron-based superconductors, binary transition-metal oxides, and perovskite oxides, using the fermionic swap network. The effective Hamiltonian derived using the ab initio downfolding method is adopted for the Hamiltonian simulation, and a procedure for the resource estimation by using the fermionic swap network for the effective Hamiltonians including the exchange interactions is proposed. For example, in the system for the 102 unit cells, the estimated numbers of gates per Trotter step and qubits are approximately 107 and 103, respectively, on average for the correlated electron materials. Furthermore, our results show that the number of interaction terms in the effective Hamiltonian, especially for the Coulomb interaction terms, is dominant in the gate resources when the number of unit cells constituting the whole system is up to 102, whereas the number of fermionic swap operations is dominant when the number of unit cells is more than 103.

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U2 - 10.1103/PhysRevA.106.012612

DO - 10.1103/PhysRevA.106.012612

M3 - Article

AN - SCOPUS:85135588446

SN - 2469-9926

VL - 106

JO - Physical Review A

JF - Physical Review A

IS - 1

M1 - 012612

ER -