Quantum Circuit Construction for Linear and Piecewise Linear Functions
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Solution Overview
Problem
Current methods for option valuation in quantum computation, such as the classical Monte Carlo method, require a large number of samples, leading to increased computation and reduced efficiency, and there is a lack of effective implementation of linear functions in quantum computation.
Innovation Solution
A method and apparatus for constructing a quantum circuit corresponding to a linear function by adding an independent variable to a qubit, obtaining a second qubit, adding a parametric quantum logic gate, and determining its parameter value based on the target linear function, as well as constructing a quantum circuit for piecewise linear functions by comparing the independent variable with breakpoints and applying parametric quantum logic gates accordingly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the classical Monte Carlo method is used for option valuation, then the method can perform price prediction of underlying assets, but it requires a large quantity of samples which increases computation amount and reduces efficiency
Solution Approach 1:
The patent replaces the classical Monte Carlo method (mechanical sampling process) with a quantum circuit-based approach. The quantum circuit uses qubits, quantum logic gates, and quantum operations to directly compute option valuation results, eliminating the need for extensive classical sampling while maintaining or improving accuracy and efficiency.
Solution Approach 2:
The patent changes the fundamental parameters of the computation system by transitioning from classical bits to quantum bits (qubits). This parameter change enables the system to process option valuation problems with fewer computational resources, as quantum states can represent multiple possibilities simultaneously through superposition, thereby reducing the number of samples needed.
2Productivity
If linear functions are implemented in quantum computation, then quantum computers can process mathematical problems more efficiently, but the implementation of linear functions in quantum computation is still an urgent problem to be resolved
Solution Approach 1:
The patent segments the implementation of linear functions into discrete quantum circuit components. It breaks down the linear function f(x) = ax + b into specific quantum logic gate operations (such as rotation gates R(θ) where θ is determined by the linear function parameters). This segmentation makes the implementation systematic and manageable, resolving the difficulty of implementing linear functions in quantum computation.
Solution Approach 2:
The patent establishes a direct mapping between linear function parameters (slope and intercept) and quantum circuit parameters (gate rotation angles and qubit states). By changing the parameters of quantum logic gates based on the linear function coefficients, the patent enables efficient implementation of linear functions, allowing quantum computers to process such mathematical problems with high efficiency.
Data Source
AI summary
Disclosed are a method and an apparatus for constructing a quantum circuit corresponding to a linear function. The method includes: adding an independent variable of a target linear function on a first qubit; obtaining a second qubit for outputting the target linear function, adding a parametric quantum logic gate acting on the second qubit, and controlling the parametric quantum logic gate by using the first qubit; and determining a parameter value of the parametric quantum logic gate based on the target linear function, to obtain a quantum circuit corresponding to the target linear function.