Two-Particle Scattering on Non-Translation Invariant Line Lattices
Quantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line lattice is sufficient to perform universal quantum computati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-04-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-04-04-1308/pdf/ |
| _version_ | 1797222462583209984 |
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| author | Luna Lima e Silva Daniel Jost Brod |
| author_facet | Luna Lima e Silva Daniel Jost Brod |
| author_sort | Luna Lima e Silva |
| collection | DOAJ |
| description | Quantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line lattice is sufficient to perform universal quantum computation. In this work we solve the problem of two-particle scattering on the line lattice for a family of interactions without translation invariance, recovering the Bose-Hubbard interaction as the limiting case. Due to its generality, our systematic approach lays the groundwork to solve the more general problem of multi-particle scattering on general graphs, which in turn can enable design of different or simpler quantum gates and gadgets. As a consequence of this work, we show that a CPHASE gate can be achieved with high fidelity when the interaction acts only on a small portion of the line graph. |
| first_indexed | 2024-04-24T13:21:43Z |
| format | Article |
| id | doaj.art-9b6d9f9505124129b4160d97380c78b0 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-24T13:21:43Z |
| publishDate | 2024-04-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-9b6d9f9505124129b4160d97380c78b02024-04-04T13:49:14ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-04-018130810.22331/q-2024-04-04-130810.22331/q-2024-04-04-1308Two-Particle Scattering on Non-Translation Invariant Line LatticesLuna Lima e SilvaDaniel Jost BrodQuantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line lattice is sufficient to perform universal quantum computation. In this work we solve the problem of two-particle scattering on the line lattice for a family of interactions without translation invariance, recovering the Bose-Hubbard interaction as the limiting case. Due to its generality, our systematic approach lays the groundwork to solve the more general problem of multi-particle scattering on general graphs, which in turn can enable design of different or simpler quantum gates and gadgets. As a consequence of this work, we show that a CPHASE gate can be achieved with high fidelity when the interaction acts only on a small portion of the line graph.https://quantum-journal.org/papers/q-2024-04-04-1308/pdf/ |
| spellingShingle | Luna Lima e Silva Daniel Jost Brod Two-Particle Scattering on Non-Translation Invariant Line Lattices Quantum |
| title | Two-Particle Scattering on Non-Translation Invariant Line Lattices |
| title_full | Two-Particle Scattering on Non-Translation Invariant Line Lattices |
| title_fullStr | Two-Particle Scattering on Non-Translation Invariant Line Lattices |
| title_full_unstemmed | Two-Particle Scattering on Non-Translation Invariant Line Lattices |
| title_short | Two-Particle Scattering on Non-Translation Invariant Line Lattices |
| title_sort | two particle scattering on non translation invariant line lattices |
| url | https://quantum-journal.org/papers/q-2024-04-04-1308/pdf/ |
| work_keys_str_mv | AT lunalimaesilva twoparticlescatteringonnontranslationinvariantlinelattices AT danieljostbrod twoparticlescatteringonnontranslationinvariantlinelattices |