Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.12305 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908278685958144 |
|---|---|
| author | Singh, Harshdeep Majumder, Sonjoy Mishra, Sabyashachi |
| author_facet | Singh, Harshdeep Majumder, Sonjoy Mishra, Sabyashachi |
| contents | The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the Partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from $O(\frac{N^4}{ε^2})$ to $O(\frac{1}{ε^2})$ for a system of $N$ qubits and accuracy $ε$, while the overall cost of VQE can be reduced from $O(\frac{N^7}{ε^2})$ to $O(\frac{N^3}{ε^2})$. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20-40% to 5-10% without any additional error correction or mitigation technique. Additionally, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation Singh, Harshdeep Majumder, Sonjoy Mishra, Sabyashachi Quantum Physics The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the Partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from $O(\frac{N^4}{ε^2})$ to $O(\frac{1}{ε^2})$ for a system of $N$ qubits and accuracy $ε$, while the overall cost of VQE can be reduced from $O(\frac{N^7}{ε^2})$ to $O(\frac{N^3}{ε^2})$. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20-40% to 5-10% without any additional error correction or mitigation technique. Additionally, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem. |
| title | SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.12305 |