Modifications of Quantum Computation and Adaptive Queries to PP
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arXiv
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| Format: | Preprint |
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2025
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| author | Miloschewsky, David Podder, Supartha |
| author_facet | Miloschewsky, David Podder, Supartha |
| contents | In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first, $\mathsf{CorrBQP}$, is a modification of $\mathsf{BQP}$ which has the power to perform correlated measurements, i.e. measurements that output the same value across a partition of registers. The second, $\mathsf{MajBQP}$, augments $\mathsf{BQP}$ with the ability to collapse a register to its most likely measurement outcome. Specifically, we consider two variants, $\mathsf{MajBQP}$ and $\mathsf{AdMajBQP}$, where the latter may perform intermediate measurements. We exactly characterize the computational power of the models, $\mathsf{CorrBQP} = \mathsf{AdMajBQP} = \mathsf{BPP}^{\mathsf{PP}}$ and $\mathsf{MajBQP} = \mathsf{P}^{\mathsf{PP}}$. In fact, we show that other metaphysical modifications of $\mathsf{BQP}$, such as $\mathsf{CBQP}$ (i.e. $\mathsf{BQP}$ with the ability to clone arbitrary quantum states), are also equal to $\mathsf{BPP}^{\mathsf{PP}}$. We show that $\mathsf{CorrBQP}$ and $\mathsf{MajBQP}$ are self-low with respect to classically-accessible queries. In contrast, if they were self-low under quantumly-accessible queries, the counting hierarchy would collapse. Furthermore, we introduce a variant of rational degree that lower-bounds the query complexity of $\mathsf{BPP}^{\mathsf{PP}}$. Lastly, we extend the adversary lower-bounding technique to $\mathsf{AdPDQP}$, $\mathsf{BQP}$ with the ability to sample the current state of an algorithm with collapsing it and adapt the computation based on the samples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modifications of Quantum Computation and Adaptive Queries to PP Miloschewsky, David Podder, Supartha Computational Complexity Quantum Physics In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first, $\mathsf{CorrBQP}$, is a modification of $\mathsf{BQP}$ which has the power to perform correlated measurements, i.e. measurements that output the same value across a partition of registers. The second, $\mathsf{MajBQP}$, augments $\mathsf{BQP}$ with the ability to collapse a register to its most likely measurement outcome. Specifically, we consider two variants, $\mathsf{MajBQP}$ and $\mathsf{AdMajBQP}$, where the latter may perform intermediate measurements. We exactly characterize the computational power of the models, $\mathsf{CorrBQP} = \mathsf{AdMajBQP} = \mathsf{BPP}^{\mathsf{PP}}$ and $\mathsf{MajBQP} = \mathsf{P}^{\mathsf{PP}}$. In fact, we show that other metaphysical modifications of $\mathsf{BQP}$, such as $\mathsf{CBQP}$ (i.e. $\mathsf{BQP}$ with the ability to clone arbitrary quantum states), are also equal to $\mathsf{BPP}^{\mathsf{PP}}$. We show that $\mathsf{CorrBQP}$ and $\mathsf{MajBQP}$ are self-low with respect to classically-accessible queries. In contrast, if they were self-low under quantumly-accessible queries, the counting hierarchy would collapse. Furthermore, we introduce a variant of rational degree that lower-bounds the query complexity of $\mathsf{BPP}^{\mathsf{PP}}$. Lastly, we extend the adversary lower-bounding technique to $\mathsf{AdPDQP}$, $\mathsf{BQP}$ with the ability to sample the current state of an algorithm with collapsing it and adapt the computation based on the samples. |
| title | Modifications of Quantum Computation and Adaptive Queries to PP |
| topic | Computational Complexity Quantum Physics |
| url | https://arxiv.org/abs/2507.03692 |