Quantum Gate Error Evaluation Using Linearized Matrix Exponentials
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Solution Overview
Problem
Existing quantum gate error evaluation methods face challenges due to nonlinear amplification in error amplification circuits, leading to complex data analysis and low numerical stability, with potential singularities complicating error estimation.
Innovation Solution
A method involving linear approximation of error amplification using matrices to represent quantum gate sequences, avoiding singularities by defining errors as the product of unitary matrices and their exponentials, and formulating error estimation as a quadratic programming problem with positive semidefinite constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If error amplification circuit with nonlinear amplification action is used, then measurement precision of quantum gate errors is improved, but device complexity and computational load increase
Solution Approach 1:
The patent transforms the nonlinear amplification problem into a linear one by changing the parameter representation. Instead of directly analyzing nonlinear amplification effects, the patent represents quantum gate errors using exponential forms and applies linear approximation methods, thereby simplifying the measurement analysis while maintaining accuracy.
Solution Approach 2:
The patent introduces an intermediary mathematical framework (exponential representation and linear approximation) between the nonlinear amplification circuit and the error measurement process. This intermediary approach allows the system to benefit from error amplification while avoiding the computational complexity of direct nonlinear analysis.
2Measurement precision
If error amplification circuit with nonlinear amplification action is used, then measurement precision of quantum gate errors is improved, but productivity of error evaluation decreases
Solution Approach 1:
By changing the mathematical parameters from nonlinear to linear representation, the patent significantly reduces computational load and accelerates the error evaluation process while preserving measurement precision.
Solution Approach 2:
The patent substitutes complex nonlinear computational mechanics with simpler linear approximation methods, replacing heavy computational processing with more efficient mathematical operations that yield the same measurement results.
3Device complexity
If simple approximation method is used, then device complexity is reduced, but measurement precision decreases due to singularities
Solution Approach 1:
The patent changes the parameter representation to exponential forms that inherently avoid singularity problems. By representing errors as exponentials rather than using simple linear approximations, the method maintains measurement precision across all quantum gate types including those with singularities.
Data Source
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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.