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arXiv:2303.07966 · Pramana

Universality in quantum measurements

Avijit Lahiri

Published Dec 12, 2023• 0 citations
arXivHTMLPDF
DOI
10.1007/s12043-023-02661-7

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Measurement-based quantum computing is one of the most promising quantum computing models. Although various universal resource states have been proposed so far, it was open whether only two Pauli bases are enough for both of universal measurement-based quantum computing and its verification. In this paper, we construct a universal hypergraph state that only requires X and Z-basis measurements for universal measurement-based quantum computing. We also show that universal measurement-based quantum computing on our hypergraph state can be verified in polynomial time using only X and Z-basis measurements. Furthermore, in order to demonstrate an advantage of our hypergraph state, we construct a verifiable blind quantum computing protocol that requires only X and Z-basis measurements for the client.
We show that any jointly measurable pair of quantum observables can be obtained in a sequential measurement scheme, even if the second observable will be decided after the first measurement. This means that it is possible to perform a measurement of any quantum observable in a way that does not disturb the subsequent measurements more than is dictated by joint measurability. Only measurements with a specific structure have this universality feature. As a supplementing result, we provide a characterization of all possible joint measurements obtained from a sequential measurement lacking universality.
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In order to formalize these other forms of computation, while pointing out the role and the necessity of classical control in measurement-based computation, and for establishing a new upper bound of the minimal resources needed to quantum universality, a formal model is introduced by means of Measurement-based Quantum Turing Machines.