Classical certification of quantum gates under the dimension assumption

• URL: http://arxiv.org/abs/2401.17006v3
• Date: Fri, 3 May 2024 17:23:37 GMT
• Title: Classical certification of quantum gates under the dimension assumption
• Authors: Jan Nöller, Nikolai Miklin, Martin Kliesch, Mariami Gachechiladze,
• Abstract summary: We develop an efficient method for certifying single-qubit quantum gates in a black-box scenario. We prove that the method's sample complexity grows as $mathrmO(varepsilon-1)$. We show that the proposed method can be used to certify a gate set universal for single-qubit quantum computation.
• Score: 0.1874930567916036
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop an efficient method for certifying single-qubit quantum gates in a black-box scenario, assuming only the dimension of the quantum system is known. The method is based on testing the outcomes of exact quantum computations on a single qubit, with no auxiliary systems required. We prove that the method's sample complexity grows as $\mathrm{O}(\varepsilon^{-1})$ with respect to the average gate infidelity $\varepsilon$ for the certification of a relevant single-qubit gate, which experimentally corresponds to a $\pi/2$-pulse. Furthermore, we show that the proposed method can be used to certify a gate set universal for single-qubit quantum computation. Our approach takes a first step in bridging the gap between strong notions of certification from self-testing and practically highly relevant approaches from quantum system characterization.

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