Automated error correction in superdense coding, with implementation on superconducting quantum computer

Abstract

Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoid-able noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of the algorithms, thereby decreasing any quantum advantage. Here we present a task-specific error-correction technique that provides a complete protection over a restricted set of quantum states. Specifically, we give an automated error correction in Superdense Coding algorithms utilizing n-qubit generalized Bell states. At its core, it is based on nondestructive discrimination method of Bell states involving measurements on ancilla qubits (phase and parity ancilla). The algorithm is shown to be distributable and can be distributed to any set of parties sharing orthogonal states. Automated refers to experimentally implementing the algorithm in a quantum computer by utilizing unitary operators with no measurements in between and thus without the need for outside intervention. We also experimentally realize our automated error correction technique for three different types of superdense coding algorithm on a 7-qubit superconducting IBM quantum computer and also on a 27-qubit quantum simulator in the presence of noise. Probability histograms are generated to show the high fidelity of our experimental results. Quantum state tomography is also carried out with the quantum computer to explicate the efficacy of our method. error correction techniques on this algorithm. We presented a step-by-step automated error correction protocol for the generalized superdense coding involving GBS. We primarily focused on three different kinds of errors, namely, arbitrary phase shift, phase flip, and bit-flip error, where we assumed errors to be independently distributed. We have also verified our results by implementing the protocol on a 7-qubit superconducting quantum computer named imbq_nairobi , which can be accessed as an open-source cloud computing system using Qiskit. We analyzed our experimental results using probability histogram and quantum state tomography, where we considered each type of error separately and also cases where all of them occurred simultaneously for three different scenarios. In one of these scenarios, we looked at the superdense coding algorithm that uses a mixture of different types of multipartite maximally entangled states. Our paper also raises an important question that should we focus more on developing general quantum error-correcting thereby increasing the complexity, or look for task-specific error-correcting codes that provide a significant advantage over the former? And for a extensive can we these task-specific error correction Specifically for our it will way, it shares many similarities with superdense And in quantum we and to these kinds of