Variational LOCC-assisted quantum circuits for long-range entangled states

• URL: http://arxiv.org/abs/2409.07281v1
• Date: Wed, 11 Sep 2024 14:08:33 GMT
• Title: Variational LOCC-assisted quantum circuits for long-range entangled states
• Authors: Yuxuan Yan, Muzhou Ma, You Zhou, Xiongfeng Ma,
• Abstract summary: Long-range entanglement is an important quantum resource, especially for topological orders and quantum error correction. A promising avenue is offered by replacing some quantum resources with local operations and classical communication (LOCC) Here, we propose a quantum-classical hybrid algorithm to find ground states of given Hamiltonians based on parameterized LOCC protocols.
• Score: 1.6258326496071918
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Long-range entanglement is an important quantum resource, especially for topological orders and quantum error correction. In reality, preparing long-range entangled states requires a deep unitary circuit, which poses significant experimental challenges. A promising avenue is offered by replacing some quantum resources with local operations and classical communication (LOCC). With these classical components, one can communicate information from mid-circuit measurements in distant parts of the system, which results in a substantial reduction of circuit depth in many important cases. However, to prepare general long-range entangled states, finding LOCC-assisted circuits of a short depth remains an open question. Here, we address such a challenge by proposing a quantum-classical hybrid algorithm to find ground states of given Hamiltonians based on parameterized LOCC protocols. We introduce an efficient protocol for estimating parameter gradients and use such gradients for variational optimization. Theoretically, we establish the conditions for the absence of barren plateaus, ensuring trainability at a large system size. Numerically, the algorithm accurately solves the ground state of long-range entangled models, such as the perturbed GHZ state and surface code. Our results clearly demonstrate the practical advantage of our algorithm in the accuracy of estimated ground state energy over conventional unitary variational circuits, as well as the theoretical advantage in creating long-range entanglement.

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