Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912377889357824 |
|---|---|
| author | Kökcü, Efekan Camps, Daan Oftelie, Lindsay Bassman de Jong, Wibe A. Van Beeumen, Roel Kemper, A. F. |
| author_facet | Kökcü, Efekan Camps, Daan Oftelie, Lindsay Bassman de Jong, Wibe A. Van Beeumen, Roel Kemper, A. F. |
| contents | Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales linearly in the number of qubits, has a depth independent of evolution time and compresses time-dependent Hamiltonians. The algorithm is limited to simple nearest-neighbor spin interactions and fermionic hopping. In this work, we extend our methods to compress evolution with long-range fermionic hopping, thereby enabling the embedding of arbitrary lattices onto a chain of qubits for fermion models. Moreover, we show that controlled time evolution, as well as fermion creation and annihilation operators can also be compressed. We demonstrate our results by adiabatically preparing the ground state for a half-filled fermionic chain, simulating a $4 \times 4$ tight binding model on ibmq washington, and calculating the topological Zak phase on a Quantinuum H1-1 trapped-ion quantum computer. With these new developments, our results enable the simulation of a wider range of models of interest and the efficient compression of subcircuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09538 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution Kökcü, Efekan Camps, Daan Oftelie, Lindsay Bassman de Jong, Wibe A. Van Beeumen, Roel Kemper, A. F. Quantum Physics Strongly Correlated Electrons Mathematical Physics Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales linearly in the number of qubits, has a depth independent of evolution time and compresses time-dependent Hamiltonians. The algorithm is limited to simple nearest-neighbor spin interactions and fermionic hopping. In this work, we extend our methods to compress evolution with long-range fermionic hopping, thereby enabling the embedding of arbitrary lattices onto a chain of qubits for fermion models. Moreover, we show that controlled time evolution, as well as fermion creation and annihilation operators can also be compressed. We demonstrate our results by adiabatically preparing the ground state for a half-filled fermionic chain, simulating a $4 \times 4$ tight binding model on ibmq washington, and calculating the topological Zak phase on a Quantinuum H1-1 trapped-ion quantum computer. With these new developments, our results enable the simulation of a wider range of models of interest and the efficient compression of subcircuits. |
| title | Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2303.09538 |