Scalable estimation of pure multi-qubit states

• URL: http://arxiv.org/abs/2107.05691v1
• Date: Mon, 12 Jul 2021 19:02:56 GMT
• Title: Scalable estimation of pure multi-qubit states
• Authors: L. Pereira, L. Zambrano, and A. Delgado
• Abstract summary: We introduce an inductive $n$-qubit pure-state estimation method. The proposed method exhibits a very favorable scaling in the number of qubits when compared to other estimation methods. We experimentally demonstrate the proposed method in one of IBM's quantum processors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce an inductive $n$-qubit pure-state estimation method. This is based on projective measurements on states of $2n+1$ separable bases or $2$ entangled bases plus the computational basis. Thus, the total number of measurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the proposed method exhibits a very favorable scaling in the number of qubits when compared to other estimation methods. Monte Carlo numerical experiments show that the method can achieve a high estimation fidelity. For instance, an average fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with $21$ separable bases. The use of separable bases makes our estimation method particularly well suited for applications in noisy intermediate-scale quantum computers, where entangling gates are much less accurate than local gates. We experimentally demonstrate the proposed method in one of IBM's quantum processors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a fidelity close to $0.875$ via separable bases. Other $10$-qubit separable and entangled states achieve an estimation fidelity in the order of $0.85$ and $0.7$, respectively.

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