Quantum Error Correction: Graph Theoretical Decoders and Benchmarking Quantum Computers using Decoders

Singh, Rahul Pratap (2021) Quantum Error Correction: Graph Theoretical Decoders and Benchmarking Quantum Computers using Decoders. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Rahul Pratap Singh (16MS064)) 16MS064_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

The best available quantum computers are Noisy Intermediate Scale Quantum(NISQ) devices. These quantum computers have a significant amount of error, making them impossible to use for universal quantum computation. Hardware and software improvements in quantum computers in the past decade had improved it by a large margin. These improvements are indeed required to reduce error bounds but cannot eliminate the need for Quantum Error Correction in future quantum devices. Quantum Error Correction in NISQ devices is not very resourceful as the error bounds are still higher than what is required for Quantum Error Correction to work. However, this does not eliminate the use of Quantum Error Correction on NISQ devices. It can also be used for benchmarking quantum computers, as it is done in this thesis. Quantum Error Correction requires encoding the state and then decoding it to preserve the encoded state from errors. However, Encoding, Measurement, and then using classical decoder will be used in this thesis as decoding inside a quantum circuit might not be suitable in NISQ as gates also contribute to the errors. The classical decoder used here is a Graph Theoretical Decoder and is theorized by James Robin Wootton[1]. In this, the noisy outcome is converted into a graph and then decoded using graph-theoretical methods. The decoder uses clustering with two parameters, Manhattan distance and the Epsilon ( distance between two samples to be considered neighbors), and then matches nodes inside v ABSTRACT vi each cluster, reducing the complexity compared to minimum weight matching in the entire graph. Finding a perfect epsilon is also essential in order to create a clustering decoder that decodes perfectly, and an analysis of different Epsilon is also done in this thesis at the end. The benchmarking is done on the IBMQ Manhattan quantum processor, which is a 65 qubit quantum computer. QISKIT, an IBM open-source python library for quantum computing, is used for performing this benchmarking scheme and all the protocols used here for this thesis are compatible with QISKIT. And a new quantum error code is created for decoherence error and bit flip error.

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