Quantum Graph-State Synthesis with SAT

• URL: http://arxiv.org/abs/2309.03593v2
• Date: Fri, 25 Oct 2024 11:50:27 GMT
• Title: Quantum Graph-State Synthesis with SAT
• Authors: Sebastiaan Brand, Tim Coopmans, Alfons Laarman,
• Abstract summary: We present a CNF encoding for both local and non-local graph state operations. We use this encoding in a bounded-model-checking set-up to synthesize the desired transformation. We find that the approach is able to synthesize transformations for graphs up to 17 qubits in under 30 minutes.
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• Abstract: 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.

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