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Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: New bounds on the TSC of binary signature sets are derived for any number of signatures K and any signature length L and for almost all K, L in {1,2,...,256}, and the design procedure is based on simple transformations of Hadamard matrices.
Abstract: The Welch lower bound (see Welch, R.L., IEEE Trans. Inform. Theory, vol.IT-20, p.397-9, 1974) on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. We derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L. Then, for almost all K, L in {1,2,...,256}, we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.
171 citations
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TL;DR: In this article, Shi proved that Toffoli and Hadamard are universal for quantum computation and showed that one only needs to add the Hadamaard gate to make a 'classical' set of gates quantum universal.
Abstract: Recently Shi proved that Toffoli and Hadamard are universal for quantum computation This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only needs to add the Hadamard gate to make a 'classical' set of gates quantum universal In this note we give a few lines proof of this fact relying on Kitaev's universal set of gates, and discuss the meaning of the result
169 citations
07 Oct 2018
TL;DR: This work presents the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation by constructing a measurement protocol, which enables a classical verifier to use a quantum prover as a trusted measurement device.
Abstract: We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum prover as a trusted measurement device. The protocol forces the prover to behave as follows: the prover must construct an n qubit state of his choice, measure each qubit in the Hadamard or standard basis as directed by the verifier, and report the measurement results to the verifier. The soundness of this protocol is enforced based on the assumption that the learning with errors problem is computationally intractable for efficient quantum machines.
168 citations
TL;DR: The experimental and numerical simulation results show that the reconstruction time of GIFWHT is greatly reduced, the quality of the recovered image is noticeably improved, and it is robust against interference from environmental illumination and could save memory.
Abstract: In this paper, we propose a ghost imaging scheme with fast Walsh–Hadamard transform, named GIFWHT. In the scheme, Walsh–Hadamard pattern pairs are used to illuminate an object to generate pairs of detection results, and the corresponding differential detection result is used as the result as that from the conventional bucket detector. By performing the fast Walsh–Hadamard transform on 2k (k is a positive integer) differential detection results, the image of the object can be recovered. The experimental and numerical simulation results show that the reconstruction time of GIFWHT is greatly reduced, and the quality of the recovered image is noticeably improved. In addition, GIFWHT is robust against interference from environmental illumination and could save memory.
167 citations
TL;DR: In this article, the Hermite-Hadamard and Hermite Hadamard-Fejer type inequalities for fractional integrals were obtained, which generalize the Riemann-Liouville equivalence.
163 citations