Transversal Logical T Gate in Triply Even Quantum Codes
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Solution Overview
Problem
Triorthogonal quantum codes, specifically triply orthogonal codes, are not fault-tolerant for implementing the logical T gate due to error propagation from controlled Z gates, which hinders efficient fault-tolerant quantum computations.
Innovation Solution
Constructing triply even quantum codes and quantum polar codes that allow for a transversal implementation of the logical T gate, ensuring that errors do not propagate across qubits, by using a triply even matrix and puncturing procedure to create a triorthogonal matrix with odd-weight rows, enabling efficient fault-tolerant quantum computing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If triorthogonal quantum codes are used for quantum computation, then quantum error correction is achieved, but the logical T gate cannot be implemented fault-tolerantly due to error propagation from controlled Z gates
Solution Approach 1:
The patent changes the code parameters by transitioning from general triorthogonal codes to triply even quantum codes, which have specific parity constraints on their codewords. This parameter change modifies the code structure to allow transversal T gate implementation while maintaining error correction capabilities, thereby achieving fault-tolerance without error propagation.
Solution Approach 2:
The patent applies transversal operations where the logical T gate is implemented by applying T gates independently to each physical qubit in the code block. This segmentation of the gate operation across individual qubits prevents error propagation, as each qubit's error remains isolated rather than spreading through the code structure.
2Reliability
If transversal logical T gate is implemented in triply even quantum codes, then fault-tolerance is achieved, but code construction complexity increases due to triply even matrix requirements
Solution Approach 1:
The patent uses preliminary action by pre-constraining the code to be triply even before implementing the T gate. The code is designed with specific parity properties built-in, which simplifies the subsequent T gate implementation and ensures fault-tolerance without requiring complex error correction procedures during gate operation.
Solution Approach 2:
The patent relates triply even quantum codes to classical triply even codes through a copying approach, where the quantum code structure is derived from classical code properties. This allows leveraging well-studied classical coding theory to guide quantum code construction, reducing the complexity of creating new quantum codes with desired fault-tolerance properties.
Data Source
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AI summary
The present invention concerns a quantum processing system (1) configured to implement a transversal action of a logical T gate on a triply even quantum code (Q1) or a triply even quantum polar code (Q2) encoding K logical qubits into N physical qubits wherein the logical T gate is a tensorproduct of K elementary logical gates acting on the corresponding K logical qubits.