Quantum Gate Error Evaluation With Linearized Matrix Models
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Solution Overview
Problem
Existing quantum tomography methods face challenges in accurately evaluating errors in quantum operations due to the nonlinear amplification of errors in quantum gates, leading to high computational load and instability in data analysis, particularly when singularities occur.
Innovation Solution
A method that approximates the error amplification process linearly by representing quantum gates as a product of ideal matrices and matrix exponentials of error matrices, using a linear approximation function to estimate errors, thereby avoiding singularities and reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum tomography is used to evaluate errors in quantum operations, then measurement precision is improved, but device complexity increases due to the need to repeatedly obtain measurement values while changing quantum operation combinations
Solution Approach 1:
The patent extracts the essential error information by representing quantum gates as products of ideal matrices and error matrices, separating the error component from the ideal operation. This allows error evaluation without requiring complex quantum tomography experiments with multiple operation combinations.
Solution Approach 2:
The patent changes the parameter representation by using matrix exponential forms to describe error accumulation, transforming the error model from a complex experimental parameter set to a manageable mathematical parameter space that can be evaluated with simpler measurements.
2Measurement precision
If nonlinear error amplification is used in quantum gate sequences, then error detection capability is improved, but reliability decreases due to computational instability and singularities
Solution Approach 1:
The patent segments the quantum gate into ideal operation and error components, representing it as a product of an ideal matrix and an error matrix. This segmentation allows linear approximation of error effects without the computational instability of full nonlinear amplification.
Solution Approach 2:
The patent introduces an intermediary linear approximation function that mediates between the quantum operation and error evaluation. This intermediary avoids direct computation with nonlinear error amplification and its associated singularities while still capturing essential error information.
3Manufacturing precision
If full quantum tomography analysis is performed, then manufacturing precision is improved, but loss of time increases due to repeated experiments with changing quantum operation combinations
Solution Approach 1:
The patent performs preliminary error characterization by representing quantum gates in a standardized matrix form with explicit error components. This preliminary representation enables faster calibration iterations without requiring full quantum tomography analysis each time.
Solution Approach 2:
The patent uses simplified error models that can be quickly evaluated and discarded, replacing the need for time-consuming full tomography analysis. These lightweight error representations enable rapid calibration iterations.
Data Source
AI summary
An information processing apparatus obtains measurement data representing measurement values measured after a quantum gate sequence including first and second quantum gates is executed a plurality of times, defines, in representing the first quantum gate as the product of a first matrix representing an ideal value of the first matrix and a matrix exponential of a second matrix representing an error, a variable representing the second matrix, generates a function that linearly approximates an effect of the error on the measurement values, by approximating a composite quantum gate that is a combination of the first and second quantum gates by the product of the first matrix, a third matrix representing an ideal value of the second quantum gate, and a matrix exponential of a transformation result of transforming a value of the variable using the third matrix, and estimates the error using the function and measurement data.