Quantum Speedups for Bayesian Network Structure Learning
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912406581542912 |
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| author | Harviainen, Juha Rychkova, Kseniya Koivisto, Mikko |
| author_facet | Harviainen, Juha Rychkova, Kseniya Koivisto, Mikko |
| contents | The Bayesian network structure learning (BNSL) problem asks for a directed acyclic graph that maximizes a given score function. For networks with $n$ nodes, the fastest known algorithms run in time $O(2^n n^2)$ in the worst case, with no improvement in the asymptotic bound for two decades. Inspired by recent advances in quantum computing, we ask whether BNSL admits a polynomial quantum speedup, that is, whether the problem can be solved by a quantum algorithm in time $O(c^n)$ for some constant $c$ less than $2$. We answer the question in the affirmative by giving two algorithms achieving $c \le 1.817$ and $c \le 1.982$ assuming the number of potential parent sets is, respectively, subexponential and $O(1.453^n)$. Both algorithms assume the availability of a quantum random access memory. We also prove that one presumably cannot lower the base $2$ for any classical algorithm, as that would refute the strong exponential time hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19673 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Speedups for Bayesian Network Structure Learning Harviainen, Juha Rychkova, Kseniya Koivisto, Mikko Data Structures and Algorithms Quantum Physics The Bayesian network structure learning (BNSL) problem asks for a directed acyclic graph that maximizes a given score function. For networks with $n$ nodes, the fastest known algorithms run in time $O(2^n n^2)$ in the worst case, with no improvement in the asymptotic bound for two decades. Inspired by recent advances in quantum computing, we ask whether BNSL admits a polynomial quantum speedup, that is, whether the problem can be solved by a quantum algorithm in time $O(c^n)$ for some constant $c$ less than $2$. We answer the question in the affirmative by giving two algorithms achieving $c \le 1.817$ and $c \le 1.982$ assuming the number of potential parent sets is, respectively, subexponential and $O(1.453^n)$. Both algorithms assume the availability of a quantum random access memory. We also prove that one presumably cannot lower the base $2$ for any classical algorithm, as that would refute the strong exponential time hypothesis. |
| title | Quantum Speedups for Bayesian Network Structure Learning |
| topic | Data Structures and Algorithms Quantum Physics |
| url | https://arxiv.org/abs/2305.19673 |