Qubit-efficient encoding scheme for quantum simulations of electronic structure
Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of N spin-orbitals into an N-qubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.023154 |
| _version_ | 1797210710358360064 |
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| author | Yu Shee Pei-Kai Tsai Cheng-Lin Hong Hao-Chung Cheng Hsi-Sheng Goan |
| author_facet | Yu Shee Pei-Kai Tsai Cheng-Lin Hong Hao-Chung Cheng Hsi-Sheng Goan |
| author_sort | Yu Shee |
| collection | DOAJ |
| description | Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of N spin-orbitals into an N-qubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of the system so the qubit Hilbert space in this case may have unphysical states and thus cannot be fully utilized. We propose a generalized qubit-efficient encoding (QEE) scheme that requires the qubit number to be only logarithmic in the number of configurations that satisfy the required conditions and symmetries. For the case of considering only the particle-conserving and singlet configurations, we reduce the qubit count to an upper bound of O(mlog_{2}N), where m is the number of particles. This QEE scheme is demonstrated on an H_{2} molecule in the 6-31G basis set and a LiH molecule in the STO-3G basis set using fewer qubits than the common encoding methods. We calculate the ground-state energy surfaces using a variational quantum eigensolver algorithm with a hardware-efficient ansatz circuit. We choose to use a hardware-efficient ansatz since most of the Hilbert space in our scheme is spanned by desired configurations so a heuristic search for an eigenstate is sensible. The simulations are performed on IBM Quantum machines and the Qiskit simulator with a noise model implemented from a IBM Quantum machine. Using the methods of measurement error mitigation and error-free linear extrapolation, we demonstrate that most of the distributions of the extrapolated energies using our QEE scheme agree with the exact results obtained by Hamiltonian diagonalization in the given basis sets within chemical accuracy. Our proposed scheme and results show the feasibility of quantum simulations for larger molecular systems in the noisy intermediate-scale quantum (NISQ) era. The number of terms in the Hamiltonian has an upper bound of O(N^{2m+1}/(m−1)!m!) for the QEE scheme while it scales as O(N^{4}) for the Jordan-Wigner encoding scheme. Nevertheless, we present several cases where QEE is useful. |
| first_indexed | 2024-04-24T10:14:55Z |
| format | Article |
| id | doaj.art-2d932dff397d45c9b661250368bdf315 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:14:55Z |
| publishDate | 2022-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-2d932dff397d45c9b661250368bdf3152024-04-12T17:21:15ZengAmerican Physical SocietyPhysical Review Research2643-15642022-05-014202315410.1103/PhysRevResearch.4.023154Qubit-efficient encoding scheme for quantum simulations of electronic structureYu SheePei-Kai TsaiCheng-Lin HongHao-Chung ChengHsi-Sheng GoanSimulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of N spin-orbitals into an N-qubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of the system so the qubit Hilbert space in this case may have unphysical states and thus cannot be fully utilized. We propose a generalized qubit-efficient encoding (QEE) scheme that requires the qubit number to be only logarithmic in the number of configurations that satisfy the required conditions and symmetries. For the case of considering only the particle-conserving and singlet configurations, we reduce the qubit count to an upper bound of O(mlog_{2}N), where m is the number of particles. This QEE scheme is demonstrated on an H_{2} molecule in the 6-31G basis set and a LiH molecule in the STO-3G basis set using fewer qubits than the common encoding methods. We calculate the ground-state energy surfaces using a variational quantum eigensolver algorithm with a hardware-efficient ansatz circuit. We choose to use a hardware-efficient ansatz since most of the Hilbert space in our scheme is spanned by desired configurations so a heuristic search for an eigenstate is sensible. The simulations are performed on IBM Quantum machines and the Qiskit simulator with a noise model implemented from a IBM Quantum machine. Using the methods of measurement error mitigation and error-free linear extrapolation, we demonstrate that most of the distributions of the extrapolated energies using our QEE scheme agree with the exact results obtained by Hamiltonian diagonalization in the given basis sets within chemical accuracy. Our proposed scheme and results show the feasibility of quantum simulations for larger molecular systems in the noisy intermediate-scale quantum (NISQ) era. The number of terms in the Hamiltonian has an upper bound of O(N^{2m+1}/(m−1)!m!) for the QEE scheme while it scales as O(N^{4}) for the Jordan-Wigner encoding scheme. Nevertheless, we present several cases where QEE is useful.http://doi.org/10.1103/PhysRevResearch.4.023154 |
| spellingShingle | Yu Shee Pei-Kai Tsai Cheng-Lin Hong Hao-Chung Cheng Hsi-Sheng Goan Qubit-efficient encoding scheme for quantum simulations of electronic structure Physical Review Research |
| title | Qubit-efficient encoding scheme for quantum simulations of electronic structure |
| title_full | Qubit-efficient encoding scheme for quantum simulations of electronic structure |
| title_fullStr | Qubit-efficient encoding scheme for quantum simulations of electronic structure |
| title_full_unstemmed | Qubit-efficient encoding scheme for quantum simulations of electronic structure |
| title_short | Qubit-efficient encoding scheme for quantum simulations of electronic structure |
| title_sort | qubit efficient encoding scheme for quantum simulations of electronic structure |
| url | http://doi.org/10.1103/PhysRevResearch.4.023154 |
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