Quantum Control Synthesis Using Bandwidth-Limited Basis Functions
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Solution Overview
Problem
Conventional techniques for determining quantum controls for quantum computing are complex and do not effectively account for real-world hardware limitations, making it cumbersome to define and generate control fields for quantum systems.
Innovation Solution
The use of discrete prolate spheroidal sequences as basis functions in a gradient-based optimization approach to synthesize quantum controls, reducing the dimensionality of the optimization problem and incorporating bandwidth constraints to generate accurate control fields efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional techniques are used to determine quantum controls, then the control fields can be generated, but the process becomes complex and does not effectively account for hardware limitations
Solution Approach 1:
The patent transforms the quantum control synthesis problem by changing the parameterization approach - using discrete prolate spheroidal sequences as basis functions to represent control fields. This parameterization inherently incorporates bandwidth constraints and reduces the dimensionality of the optimization space, making the synthesis both accurate and computationally tractable while respecting hardware limitations
Solution Approach 2:
The control field is segmented into a weighted sum of discrete prolate spheroidal sequences, allowing the optimization to operate on a reduced set of coefficients rather than the full control field. This segmentation maintains accuracy while reducing complexity by focusing optimization on essential parameters
2Device complexity
If the dimensionality of optimization problem is reduced using basis functions, then the synthesis complexity decreases, but the bandwidth constraints must be properly incorporated
Solution Approach 1:
By selecting discrete prolate spheroidal sequences as basis functions, the patent changes the parameter space such that bandwidth constraints are naturally embedded in the basis function properties. This allows reduced dimensionality optimization while maintaining precise adherence to bandwidth requirements, as these sequences are specifically designed to concentrate energy within specified frequency bands
3Productivity
If gradient based optimization is applied to coefficients of basis functions, then accurate control fields can be synthesized efficiently, but the computational complexity of gradient determination increases
Solution Approach 1:
The patent replaces direct gradient computation on the full control field with gradient computation on the coefficients of the discrete prolate spheroidal sequence expansion. This substitution leverages the mathematical properties of these sequences to simplify the gradient determination process, achieving efficient synthesis with reduced computational complexity
Data Source
AI summary
An example method for facilitating the generation of a control field for a quantum system is provided. The example method may include receiving quantum system experiment input parameters and generating a set of coefficients defining a plurality of controls. The plurality of controls may be provided as a weighted sum of basis functions that include discrete prolate spheroidal sequences. The example method may further include applying a gradient based optimization, synthesizing the plurality of controls, and configuring a waveform generator with the plurality of controls to enable the waveform generator to generate the control field.