Graph-State Quantum Error Correction With Entangled Qubit Extension
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Solution Overview
Problem
Current methods for extending the dimension of quantum error correction codes using entangled qubits are complex and require sophisticated techniques.
Innovation Solution
A method and apparatus for generating quantum error correction codes by adding entangled qubits to a graph state, involving the generation of stabilizer generators and logical operators to detect errors and extend code dimension, using adjacency matrices and Pauli operators to configure stabilizers and logical operators.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If entangled qubits are added to extend the dimension of quantum error correction code, then the code dimension is extended, but the complexity of the generation method increases
Solution Approach 1:
The patent segments the quantum error correction code generation into distinct components: graph state preparation, stabilizer generator identification, and logical operator determination. By dividing the complex generation process into manageable segments, the method extends code dimension using entangled qubits while reducing the overall complexity of the generation procedure.
Solution Approach 2:
The patent utilizes graph states as a dimensional framework where qubits are represented as vertices and entanglement as edges. By adding entangled qubits (ebits) to the graph state, the code dimension is extended in a structured dimensional space, transforming the complex problem of code generation into a more manageable graph-theoretic operation.
2Reliability
If entangled qubits are incorporated into graph state, then error correction capability is enhanced, but the method becomes more complex
Solution Approach 1:
The patent applies preliminary action by pre-establishing the graph state structure with entangled qubits before error correction is needed. The stabilizer generators and logical operators are predetermined based on the graph state configuration, allowing the system to leverage pre-computed structures that enhance error correction capability while avoiding the complexity of real-time generation.
Solution Approach 2:
The patent changes key parameters of the quantum code by incorporating entangled qubits into the graph state. This modifies the stabilizer generators and logical operators to achieve enhanced error correction capability. By systematically changing these parameters through the graph state framework, the method improves reliability while maintaining manageable complexity through structured parameter transformation.
Data Source
AI summary
Provided is a quantum error correction code generating method using a graph state. According to the exemplary embodiment of the present invention, a quantum error correction code generating method using a graph state: includes: generating a graph state representing an adjacency relationship between a plurality of qubits including at least one entangled qubit (ebit); generating a first stabilizer generator which corresponds to the graph state and is configured by a plurality of stabilizers for detecting errors of the plurality of qubits; and generating at least one logical Z operator used for a phase flip operation of a codeword, at least one logical X operator used for a bit flip operation of a codeword, and a second stabilizer generator which is a sub set of the first stabilizer generator, based on the first stabilizer generator and the at least one entangled qubit.