Quantum Graph-State Synthesis with SAT
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913563117879296 |
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| author | Brand, Sebastiaan Coopmans, Tim Laarman, Alfons |
| author_facet | Brand, Sebastiaan Coopmans, Tim Laarman, Alfons |
| contents | In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a given source graph state to a desired target graph state using only local operations. Recently it has been shown that deciding transformability is already NP-hard. In this paper, we present a CNF encoding for both local and non-local graph state operations, corresponding to one- and two-qubit Clifford gates and single-qubit Pauli measurements. We use this encoding in a bounded-model-checking set-up to synthesize the desired transformation. Additionally, for a completeness threshold on local transformations, we provide an upper bound on the length of the transformation if it exists. We evaluate the approach in two settings: the first is the synthesis of the ubiquitous GHZ state from a random graph state where we can vary the number of qubits, while the second is based on a proposed 14 node quantum network. We find that the approach is able to synthesize transformations for graphs up to 17 qubits in under 30 minutes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03593 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Graph-State Synthesis with SAT Brand, Sebastiaan Coopmans, Tim Laarman, Alfons Quantum Physics Data Structures and Algorithms In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a given source graph state to a desired target graph state using only local operations. Recently it has been shown that deciding transformability is already NP-hard. In this paper, we present a CNF encoding for both local and non-local graph state operations, corresponding to one- and two-qubit Clifford gates and single-qubit Pauli measurements. We use this encoding in a bounded-model-checking set-up to synthesize the desired transformation. Additionally, for a completeness threshold on local transformations, we provide an upper bound on the length of the transformation if it exists. We evaluate the approach in two settings: the first is the synthesis of the ubiquitous GHZ state from a random graph state where we can vary the number of qubits, while the second is based on a proposed 14 node quantum network. We find that the approach is able to synthesize transformations for graphs up to 17 qubits in under 30 minutes. |
| title | Quantum Graph-State Synthesis with SAT |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2309.03593 |