Precision of quantum simulation of all-to-all coupling in a local architecture

• URL: http://arxiv.org/abs/2302.02458v1
• Date: Sun, 5 Feb 2023 18:54:28 GMT
• Title: Precision of quantum simulation of all-to-all coupling in a local architecture
• Authors: Evgeny Mozgunov
• Abstract summary: We find an analytic relation between the values $J_ij$ of the desired interaction and the parameters of the 2d circuit. For the relative error to be a constant $epsilon$, one requires an energy scale growing as $n6$ in the number of qubits. Our proof is based on the Schrieffer-Wolff transformation and generalizes to any hardware.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a simple 2d local circuit that implements all-to-all interactions via perturbative gadgets. We find an analytic relation between the values $J_{ij}$ of the desired interaction and the parameters of the 2d circuit, as well as the expression for the error in the quantum spectrum. For the relative error to be a constant $\epsilon$, one requires an energy scale growing as $n^6$ in the number of qubits, or equivalently a control precision up to $ n^{-6}$. Our proof is based on the Schrieffer-Wolff transformation and generalizes to any hardware. In the architectures available today, $5$ digits of control precision are sufficient for $n=40,~ \epsilon =0.1$. Comparing our construction, known as paramagnetic trees, to ferromagnetic chains used in minor embedding, we find that at chain length $>3$ the performance of minor embedding degrades exponentially with the length of the chain, while our construction experiences only a polynomial decrease.

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