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We first prove a no-go theorem that ZN topological order cannot survive on any fractal embedded in two spatial dimensions and with DH=2−δ.
Quantum error correction ramp code#
In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a quantum error-correcting code with a macroscopic code distance or the presence of macroscopic systoles in systolic geometry. We consider the n-dimensional lattice with holes at all length scales the corresponding fractal (Hausdorff) dimension of which is DH=n−δ. We investigate topological order on fractal geometries embedded in n dimensions. Technology but discusses topics that will be relevant for various quantum The review does not focus on a particular We discuss the complexity of decoding and the notion of passive Two-dimensional (topological) codes, in particular the surface codeĪrchitecture. Review is focused on providing an overview of quantum error correction using Towards fault-tolerant universal quantum computation. Noise threshold, the special role played by Clifford gates and the route We review the theory ofįault-tolerance and quantum error-correction, discuss examples of various codesĪnd code constructions, the general quantum error correction conditions, the Stabilizer and subsystem stabilizer codes and their possible use in protecting
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In this review we consider the formalism of qubit Promising, but experimentally challenging, engineering program for building a Our quantum mutual information result quantifies the leakage of the ramp quantum secret-sharing schemes.Active quantum error correction using qubit stabilizer codes has emerged as a We solve by converting the Tyc-Rowe-Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for continuous-variable quantum mutual information to obtain quantum mutual information in terms of squeezing. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc-Rowe-Sanders continuous-variable quantum secret-sharing scheme. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. AbstractOur aim is to formulate continuous-variable quantum secret-sharing as a continuous-variable ramp quantum secret-sharing protocol, provide a certification procedure for it and explain the criteria for the certification.
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