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Focus: Landmarks—Correcting Quantum Computer Errors

David Lindley

Published Jun 10, 2016• 0 citations
OpenAlex

Abstract

In the mid-1990s, researchers proposed methods to preserve the integrity of quantum bits—techniques that may become the key to practical quantum computing on a large scale.

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Saumo, Masuk Ridwan, Faisal, Nafis, Md. Saifur Rahman

This thesis titled, “Performance Analysis of Extension of 3- and 5-bit Quantum Repetition Codes”, submitted by the group as mentioned below has been accepted as satisfactory in partial fulfillment of the requirements for the degree B.Sc. in EEE in March 2025. This is to certify that the work presented in this thesis is the outcome of the investigation and research carried out by us under the supervision of Dr Md Saifur Rahman. Group Members:Masuk Ridwan Saumo, ID: S201906106Nafis Faisal, ID: S201906033 Supervisor:Dr Md Saifur RahmanProfessorDepartment of Electrical and Electronic EngineeringBangladesh University of Engineering and Technology Abstract: Quantum computers are becoming an engineer's reality from a physicist's dream. Microsoft, IBM, Google are some of the key players who are pushing the quantum boundaries and bringing us closer to actual quantum computers. Although research in Quantum Computing is focused mostly on creating viable Qubits, a large portion of research is also dedicated to reducing errors due to decoherence, noise and errors from various sources so that the calculations done using Qubits are not flawed. Transmitting Quantum Information from one place to another is what Quantum Communication is about. Here too, the channel induces errors in the transmitted Qubits leading to loss in quantum information. Quantum Error Correction came as an analogue to classical error correction to solve the same problems of bit errors in quantum computation and communication. This work investigates a type of error correction code, the repetition code, common to both classical and quantum domain. In this work, extended 3-bit and 5-bit quantum repetition codes (QRC) in tripartite and pentapartite GHZ states were investigated to probe their efficacy in error correction. 3- and 5-bit QRC can completely protect the Ideal GHZ state, i.e. resulting fidelity remains at one at all conditions. The research indicates that, in case of generalized GHZ states, all of them performed better than their conventional counterparts, especially extension of 5-bit QRC showing the highest fidelity. Modified 5 bit quantum repetition code in pentapartite GHZ state displayed a fidelity margin of 0.075-0.1 over traditional 3-bit QRC on a single state. However small this margin may seem, this fidelity increase is quite remarkable in large-scale quantum computations and practical implementations.

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Study of quantum error correction and fault tolerant quantum computing

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•Jul 1, 2017•0 citations
The Intelligence Community, DOD, financial, and commercial entities rely on encryption to protect its most sensitive information. Public Key Encryption (PKE) method is used to encrypt information using the principle that it is difficult to factor a very large number into its primes unless one has access to a private key that was used to encrypt the information. Using this technology, decrypting a message using a 128-bit long key would take a classical supercomputer about 1 billion billion years to decrypt. However, in the mid-1990s, mathematicians Shor and Grover developed algorithms that have proved to be efficient in factoring large numbers into primes using a quantum computer. The development of quantum hardware and algorithms therefore threaten encryption protection. In 2019, Google announced that it established quantum supremacy, meaning that its quantum computer solved a problem that no classical computer could. The authors of this paper conducted a study to describe the latest encryption research and development, methods used, and the potential vulnerability due to quantum computing. The authors further established the timeframes in which pre-quantum encryption method will become vulnerable under three scenarios. All the research for this study was derived from unclassified open source materials.
This thesis titled, “Performance Analysis of Extension of 3- and 5-bit Quantum Repetition Codes”, submitted by the group as mentioned below has been accepted as satisfactory in partial fulfillment of the requirements for the degree B.Sc. in EEE in March 2025. This is to certify that the work presented in this thesis is the outcome of the investigation and research carried out by us under the supervision of Dr Md Saifur Rahman. Group Members:Masuk Ridwan Saumo, ID: S201906106Nafis Faisal, ID: S201906033 Supervisor:Dr Md Saifur RahmanProfessorDepartment of Electrical and Electronic EngineeringBangladesh University of Engineering and Technology Abstract: Quantum computers are becoming an engineer's reality from a physicist's dream. Microsoft, IBM, Google are some of the key players who are pushing the quantum boundaries and bringing us closer to actual quantum computers. Although research in Quantum Computing is focused mostly on creating viable Qubits, a large portion of research is also dedicated to reducing errors due to decoherence, noise and errors from various sources so that the calculations done using Qubits are not flawed. Transmitting Quantum Information from one place to another is what Quantum Communication is about. Here too, the channel induces errors in the transmitted Qubits leading to loss in quantum information. Quantum Error Correction came as an analogue to classical error correction to solve the same problems of bit errors in quantum computation and communication. This work investigates a type of error correction code, the repetition code, common to both classical and quantum domain. In this work, extended 3-bit and 5-bit quantum repetition codes (QRC) in tripartite and pentapartite GHZ states were investigated to probe their efficacy in error correction. 3- and 5-bit QRC can completely protect the Ideal GHZ state, i.e. resulting fidelity remains at one at all conditions. The research indicates that, in case of generalized GHZ states, all of them performed better than their conventional counterparts, especially extension of 5-bit QRC showing the highest fidelity. Modified 5 bit quantum repetition code in pentapartite GHZ state displayed a fidelity margin of 0.075-0.1 over traditional 3-bit QRC on a single state. However small this margin may seem, this fidelity increase is quite remarkable in large-scale quantum computations and practical implementations.