Quantum Control Unit Calibration Through Hessian Eigenvector Reduction
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Solution Overview
Problem
Existing quantum control methods, such as Gradient Ascent Pulse Engineering (GRAPE) and neural networks, struggle with inefficiencies due to the need for exhaustive knowledge of the quantum system, uncontrollable external factors, and imprecise system characterization, leading to suboptimal control performance and high computational costs.
Innovation Solution
A device and method that utilize a memory to store initial values of operating parameters and a loss function, calculate eigenvectors of the Hessian matrix, and optimize these parameters using an optimizer to achieve target attributes by linearly combining eigenvectors, reducing the number of parameters needed for calibration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If GRAPE algorithm is used for quantum control optimization, then control performance can be improved, but the complexity of the system increases due to requiring exhaustive knowledge of the quantum system and large number of parameters
Solution Approach 1:
The patent extracts only the most relevant information from the quantum system by computing the Hessian matrix and selecting only the p eigenvectors corresponding to the largest absolute eigenvalues. This extraction approach allows the method to focus on the dominant modes of parameter interaction while ignoring less significant ones, thereby reducing complexity while maintaining control performance.
Solution Approach 2:
The patent transforms the control optimization problem by changing the parameter representation from the original n parameters to a reduced set of p parameters through eigenvector decomposition. This parameter transformation enables efficient optimization by working in a lower-dimensional space that captures the essential system behavior.
2Loss of time
If the number of operating parameters is reduced for online optimization, then calibration time is reduced, but the precision of control may deteriorate
Solution Approach 1:
The patent performs a parameter transformation by decomposing the Hessian matrix and selecting the p eigenvectors corresponding to the largest absolute eigenvalues. This transformation identifies and retains only the most influential parameter directions, enabling reduced-dimensional optimization that maintains control precision while significantly reducing calibration time.
Solution Approach 2:
The patent applies partial action by optimizing only along the p dominant eigenvector directions rather than all n parameter directions. This partial optimization approach is sufficient to achieve the desired control performance while avoiding the computational burden of full-parameter optimization.
3Reliability
If robustness to perturbations is improved through offline optimization, then reliability increases, but computational resources and time are significantly consumed
Solution Approach 1:
The patent extracts the essential system characteristics by computing the Hessian matrix at the initial parameter values and selecting only the p eigenvectors with the largest absolute eigenvalues. This extraction creates a reduced-order model that captures the dominant system behavior, enabling robust control design with significantly reduced computational resources compared to full-system optimization.
Data Source
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AI summary
The invention relates to a device (1) and a method for performing an online calibration of the control unit of a quantum system. The device (1) is arranged to receive data representing a set of respective initial values of n operating parameters of the control unit on which the dynamics of the quantum system depends, a loss function and a non-zero natural number p less than n. A calculator (7) is arranged to determine the p eigenvectors corresponding respectively to the p largest absolute eigenvalues of the Hessian of the loss function at the initial values of the n operating parameters, and an optimizer (9) is arranged to determine a set of respective final values of the n operating parameters by optimizing the loss function in a vicinity of the set of initial values explored by linearly combining the p eigenvectors.