Quantum Computing Fourier Component Transformation
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Solution Overview
Problem
Current quantum computing systems face inefficiencies in processing arithmetic functions, particularly when dealing with functions of single or multiple variables, as they often require significant quantum arithmetic and circuit depth, leading to increased computation time and error rates.
Innovation Solution
A quantum computing system is configured with a classical computer and quantum computer combination, where arithmetic functions are transformed into executable Fourier components using rotation gates on qubits, allowing for efficient processing without the need for extensive quantum arithmetic, thereby reducing circuit depth and computation time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum arithmetic is used to compute arithmetic functions, then computation accuracy is improved, but circuit depth and computation time increase
Solution Approach 1:
The patent segments the arithmetic function computation into two parts: (1) transformation of the arithmetic function into Fourier components using classical computation, and (2) evaluation of Fourier components using quantum computation with rotation gates. This segmentation allows the quantum computer to focus only on evaluating simple rotational operations rather than performing complex quantum arithmetic, thereby reducing circuit depth while maintaining computation accuracy.
Solution Approach 2:
The patent introduces Fourier components as an intermediary representation between the original arithmetic function and the quantum computation. By transforming the arithmetic function into Fourier components classically and then evaluating these components quantum mechanically using rotation gates, the system avoids direct quantum arithmetic while preserving computational accuracy through the Fourier transformation bridge.
2Measurement precision
If quantum arithmetic is used to compute arithmetic functions, then computation accuracy is improved, but device complexity increases
Solution Approach 1:
The computation is segmented such that complex function transformation is performed classically while the quantum computer handles only simple rotation gate operations on Fourier components. This segmentation dramatically reduces the quantum circuit depth from what would be required for full quantum arithmetic to just the depth needed for rotational operations.
Solution Approach 2:
The patent substitutes complex quantum arithmetic operations with simpler rotational operations on qubits. Instead of using quantum circuits to perform addition, multiplication, and other arithmetic operations, the system uses rotation gates that are inherently simpler and require less circuit depth, while maintaining computational accuracy through the Fourier transformation approach.
3Device complexity
If Fourier components are used instead of quantum arithmetic, then circuit depth is reduced, but the number of quantum queries increases
Solution Approach 1:
The patent changes the parameter representation from direct arithmetic function evaluation to Fourier component evaluation. By transforming the function into the frequency domain and evaluating Fourier components, the system trades off the number of queries against the simplicity of each individual quantum operation, achieving shallower circuits that can be executed more efficiently on near-term quantum hardware.
Data Source
AI summary
A quantum computing system includes a classical computer coupled in combination with a quantum computer, wherein the quantum computing system is configurable to execute program instructions to process input data to generate corresponding output data. The program instructions include one or more arithmetic functions to be executed using the quantum computer. The quantum computing system is configured to apply a transformation to transform the one or more arithmetic functions into a series of Fourier components that are executable using the quantum computer by using one or more quantum circuits utilizing rotation gates acting on qubits representing the Fourier components, and to process outputs from the one or more quantum circuits to generate results of the one or more arithmetic functions, wherein the results are used to generate the corresponding output data.