Preparing valence-bond-solid states on noisy intermediate-scale quantum computers
Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS s...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-03-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.013190 |
| _version_ | 1797210518371434496 |
|---|---|
| author | Bruno Murta Pedro M. Q. Cruz J. Fernández-Rossier |
| author_facet | Bruno Murta Pedro M. Q. Cruz J. Fernández-Rossier |
| author_sort | Bruno Murta |
| collection | DOAJ |
| description | Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb, and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general nondeterministic method herein proposed to the preparation of the spin-1 and spin-3/2 VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. The probabilistic nature of the proposed routine translates into an average number of repetitions to successfully prepare the VBS state that scales exponentially with the number of lattice sites N. However, two strategies to quadratically reduce this repetition overhead for any bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future. |
| first_indexed | 2024-04-24T10:11:52Z |
| format | Article |
| id | doaj.art-823db52992c84daa8360f14499925be2 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:11:52Z |
| publishDate | 2023-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-823db52992c84daa8360f14499925be22024-04-12T17:29:24ZengAmerican Physical SocietyPhysical Review Research2643-15642023-03-015101319010.1103/PhysRevResearch.5.013190Preparing valence-bond-solid states on noisy intermediate-scale quantum computersBruno MurtaPedro M. Q. CruzJ. Fernández-RossierQuantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb, and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general nondeterministic method herein proposed to the preparation of the spin-1 and spin-3/2 VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. The probabilistic nature of the proposed routine translates into an average number of repetitions to successfully prepare the VBS state that scales exponentially with the number of lattice sites N. However, two strategies to quadratically reduce this repetition overhead for any bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future.http://doi.org/10.1103/PhysRevResearch.5.013190 |
| spellingShingle | Bruno Murta Pedro M. Q. Cruz J. Fernández-Rossier Preparing valence-bond-solid states on noisy intermediate-scale quantum computers Physical Review Research |
| title | Preparing valence-bond-solid states on noisy intermediate-scale quantum computers |
| title_full | Preparing valence-bond-solid states on noisy intermediate-scale quantum computers |
| title_fullStr | Preparing valence-bond-solid states on noisy intermediate-scale quantum computers |
| title_full_unstemmed | Preparing valence-bond-solid states on noisy intermediate-scale quantum computers |
| title_short | Preparing valence-bond-solid states on noisy intermediate-scale quantum computers |
| title_sort | preparing valence bond solid states on noisy intermediate scale quantum computers |
| url | http://doi.org/10.1103/PhysRevResearch.5.013190 |
| work_keys_str_mv | AT brunomurta preparingvalencebondsolidstatesonnoisyintermediatescalequantumcomputers AT pedromqcruz preparingvalencebondsolidstatesonnoisyintermediatescalequantumcomputers AT jfernandezrossier preparingvalencebondsolidstatesonnoisyintermediatescalequantumcomputers |