New Lower-bounds for Quantum Computation with Non-Collapsing Measurements
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915688937947136 |
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| author | Miloschewsky, David Podder, Supartha |
| author_facet | Miloschewsky, David Podder, Supartha |
| contents | Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without collapsing them. Although PDQP contains SZK, it still requires $Ω(N^{1/4})$ queries to solve unstructured search. We formulate an alternative equivalent definition of PDQP, which we use to prove the positive weighted adversary lower-bounding method, establishing multiple tighter bounds and a trade-off between queries and non-collapsing measurements. We utilize the technique in order to analyze the query complexity of the well-studied majority and element distinctness problems. Additionally, we prove a tight $Θ(N^{1/3})$ bound on search. Furthermore, we use the lower-bound to explore PDQP under query restrictions, finding that when combined with non-adaptive queries, we limit the speed-up in several cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Lower-bounds for Quantum Computation with Non-Collapsing Measurements Miloschewsky, David Podder, Supartha Quantum Physics Computational Complexity Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without collapsing them. Although PDQP contains SZK, it still requires $Ω(N^{1/4})$ queries to solve unstructured search. We formulate an alternative equivalent definition of PDQP, which we use to prove the positive weighted adversary lower-bounding method, establishing multiple tighter bounds and a trade-off between queries and non-collapsing measurements. We utilize the technique in order to analyze the query complexity of the well-studied majority and element distinctness problems. Additionally, we prove a tight $Θ(N^{1/3})$ bound on search. Furthermore, we use the lower-bound to explore PDQP under query restrictions, finding that when combined with non-adaptive queries, we limit the speed-up in several cases. |
| title | New Lower-bounds for Quantum Computation with Non-Collapsing Measurements |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2411.04085 |