Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve meaningful quantum advantage. In this work, we present an appro...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-02-01
|
| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-02-06-1624/pdf/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832086546686148608 |
|---|---|
| author | Erenay Karacan Yanbin Chen Christian B. Mendl |
| author_facet | Erenay Karacan Yanbin Chen Christian B. Mendl |
| author_sort | Erenay Karacan |
| collection | DOAJ |
| description | Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve meaningful quantum advantage. In this work, we present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian. Our method aims to tackle limitations introduced by a small spectral gap and high degeneracy of low energy states. It is based on an adaptive sequence of eigenspace filtering through Quantum Eigenvalue Transformation of Unitary Matrices (QETU) combined with spectrum profiling. By combining our proposed algorithm with state-of-the-art phase estimation methods, we achieved good approximations for the ground state energy with local, two-qubit gate depolarizing probability up to $10^{-4}$. To demonstrate the key results in this work, we ran simulations with the transverse-field Ising Model on classical computers using $\texttt{Qiskit}$. We compare the performance of our approach with the static implementation of QETU and show that we can consistently achieve three to four orders of magnitude improvement in the absolute error rate. |
| format | Article |
| id | doaj-art-ebaecf08f4e544328875eae2fbd7c7bf |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-ebaecf08f4e544328875eae2fbd7c7bf2025-02-06T14:43:32ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-02-019162410.22331/q-2025-02-06-162410.22331/q-2025-02-06-1624Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer FilteringErenay KaracanYanbin ChenChristian B. MendlHamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve meaningful quantum advantage. In this work, we present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian. Our method aims to tackle limitations introduced by a small spectral gap and high degeneracy of low energy states. It is based on an adaptive sequence of eigenspace filtering through Quantum Eigenvalue Transformation of Unitary Matrices (QETU) combined with spectrum profiling. By combining our proposed algorithm with state-of-the-art phase estimation methods, we achieved good approximations for the ground state energy with local, two-qubit gate depolarizing probability up to $10^{-4}$. To demonstrate the key results in this work, we ran simulations with the transverse-field Ising Model on classical computers using $\texttt{Qiskit}$. We compare the performance of our approach with the static implementation of QETU and show that we can consistently achieve three to four orders of magnitude improvement in the absolute error rate.https://quantum-journal.org/papers/q-2025-02-06-1624/pdf/ |
| spellingShingle | Erenay Karacan Yanbin Chen Christian B. Mendl Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering Quantum |
| title | Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering |
| title_full | Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering |
| title_fullStr | Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering |
| title_full_unstemmed | Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering |
| title_short | Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering |
| title_sort | enhancing scalability of quantum eigenvalue transformation of unitary matrices for ground state preparation through adaptive finer filtering |
| url | https://quantum-journal.org/papers/q-2025-02-06-1624/pdf/ |
| work_keys_str_mv | AT erenaykaracan enhancingscalabilityofquantumeigenvaluetransformationofunitarymatricesforgroundstatepreparationthroughadaptivefinerfiltering AT yanbinchen enhancingscalabilityofquantumeigenvaluetransformationofunitarymatricesforgroundstatepreparationthroughadaptivefinerfiltering AT christianbmendl enhancingscalabilityofquantumeigenvaluetransformationofunitarymatricesforgroundstatepreparationthroughadaptivefinerfiltering |