Repeated Quantum Gate Sequence Evaluation With Linearized Error Estimation
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Solution Overview
Problem
Existing quantum tomography methods for evaluating errors in quantum gates face challenges due to the complexity and instability of data analysis caused by nonlinear error amplification circuits, which can lead to singularities and increased computational load.
Innovation Solution
A computer program that uses a linear approximation function to estimate errors in quantum gates by repeating a quantum gate sequence, determining a period where the matrix power yields an identity matrix, and generating a linear approximation function to analyze the influence of errors on measurement data, thereby simplifying data analysis and avoiding singularities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If an error amplification circuit is used to amplify minute errors of quantum gates, then measurement precision is improved, but device complexity and data analysis complexity increase
Solution Approach 1:
The patent transforms the nonlinear error amplification problem into a linear approximation problem by changing the mathematical parameters used in analysis. Instead of directly analyzing the nonlinear amplified errors, the system uses linear approximation functions with transformed parameters (matrix exponential form) to simplify the data analysis while maintaining measurement precision.
Solution Approach 2:
The patent introduces an intermediary linear approximation function that mediates between the nonlinear error amplification circuit and the final error evaluation. This intermediary layer transforms the complex nonlinear relationships into manageable linear forms, reducing data analysis complexity while preserving the ability to detect minute errors.
2Ease of operation
If a linear approximation function is used to simplify data analysis, then ease of operation is improved, but measurement precision may be reduced due to approximation errors
Solution Approach 1:
The patent carefully selects and transforms parameters in the linear approximation function to minimize approximation errors. By using matrix exponential transformations and optimizing the linear approximation parameters, the system maintains high measurement precision while enjoying the computational simplicity of linear methods.
Solution Approach 2:
The patent replaces complex nonlinear mathematical analysis with a simplified linear mathematical model. This substitution transforms the difficult nonlinear data analysis problem into a tractable linear problem that can be solved efficiently while maintaining sufficient accuracy for practical quantum gate error evaluation.
3Reliability
If quantum tomography is performed by repeatedly obtaining measurement values while changing combinations of quantum operations, then reliability of error evaluation is improved, but loss of time and productivity decrease
Solution Approach 1:
The patent extracts and focuses specifically on the error components of quantum gates by using targeted linear approximation functions. Instead of performing comprehensive quantum tomography on all quantum operations, the system extracts only the relevant error information through the linear approximation framework, significantly reducing evaluation time while maintaining reliability.
Solution Approach 2:
The patent applies partial action by using linear approximation for specific error evaluation purposes rather than performing complete nonlinear analysis. This partial approach focuses computational resources on the most critical error components, achieving sufficient reliability with reduced time investment.
Data Source
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AI summary
A computer acquires measurement data representing an execution result of executing, on a quantum computer, a quantum circuit where a quantum gate sequence including a first quantum gate is repeated N times, determines, from a first matrix representing an ideal value of the quantum gate sequence, a period of k such that a k-th power of the first matrix yields an identity matrix, generates a linear approximation function that linearly approximates an influence of an error, which the quantum computer has with respect to the first quantum gate, on the measurement data by approximating repetition of the quantum gate sequence using a matrix exponential of a first transformation result obtained by transforming the error using the first matrix, the N, and the period, and estimates the error using the linear approximation function and the measurement data, where each of N and K is an integer of one or more.