Quantum-Kernel Regression via Hybrid Classical-Quantum Optimization
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Solution Overview
Problem
Current quantum computers, particularly Noisy, Intermediate-Scale Quantum (NISQ) devices, face limitations in the number of qubits and lack of error correction, making it challenging to efficiently solve regression problems and differential equations.
Innovation Solution
A hybrid computer system combining a quantum computer and a classical computer uses quantum kernels to solve regression problems. This system determines kernel values and derivatives using the quantum computer and optimizes kernel coefficients with a classical optimizer, minimizing the computational load on the quantum device.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum computers are used to solve regression problems using kernel methods, then feature richness and expressibility are improved, but computational cost and time increase
Solution Approach 1:
The patent pre-computes and stores kernel values for kernel points before solving the regression problem. This preliminary action separates the expensive quantum computation (kernel evaluation) from the optimization process, allowing the quantum computer to be used only once to generate the kernel matrix, while subsequent optimization iterations use pre-computed values, significantly reducing total computational time
Solution Approach 2:
The patent divides the computational task into two distinct parts: (1) quantum computation for evaluating kernel values at predetermined kernel points, and (2) classical optimization for determining optimal kernel coefficients. This segmentation allows each part to be solved by the most suitable system, reducing overall computational burden
2Adaptability or versatility
If variational methods with parameterized quantum circuits are used, then optimization capability is improved, but quantum circuit depth requirements increase
Solution Approach 1:
The patent extracts the optimization parameters (kernel coefficients) from the quantum circuit and handles them classically. The quantum circuit is simplified to only evaluate kernel values without optimization parameters, reducing circuit depth and noise accumulation, while the classical optimizer handles the parameter optimization externally
Solution Approach 2:
The patent introduces a classical optimizer as an intermediary between the quantum kernel evaluation and the final solution. The classical optimizer receives kernel values from the quantum computer and computes optimal coefficients, avoiding the need for complex parameterized quantum circuits and their associated depth requirements
3Measurement precision
If quantum kernels are used for regression problems, then solution accuracy is improved, but the computational burden on the quantum system increases
Solution Approach 1:
The patent performs preliminary quantum computation to evaluate all kernel values before the optimization process begins. This single quantum computation step produces all necessary kernel information, minimizing repeated quantum computations and reducing the total computational burden on the quantum system while maintaining high solution accuracy
Solution Approach 2:
The patent evaluates kernels at a fixed set of predetermined kernel points that may be more than strictly necessary for the final solution. This excessive action ensures sufficient feature coverage and accuracy while allowing the classical optimizer to select only the most relevant kernel coefficients, balancing quantum computational effort with solution quality
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The approach allows for efficient solving of regression problems and differential equations by leveraging the high-dimensional feature space of quantum computers while reducing the computational burden on the quantum system, thereby enhancing accuracy and reducing computational costs.
Implementation Method 1
The quantum kernel may be based on an overlap of two wave functions
Data Source
AI summary
Methods and systems are disclosed for solving a regression problem, for example a data regression and/or a differential equation problem, over a problem domain. The method comprises: receiving or determining, by a classical computer, a regression problem description and a set of kernel points in the problem domain; receiving or determining, by the classical computer, a trial function associated with the regression problem, the trial function being based on a quantum kernel and being parameterized by kernel coefficient(s); determining, using a quantum computer, for each of the kernel points, a kernel value of the quantum kernel and/or a kernel derivative value of a derivative of the quantum kernel; determining, by the classical computer, a set of optimal kernel coefficients based on the kernel value and/or kernel derivative value and determining, by the classical computer, a solution function based on the trial function and the set of optimal kernel coefficients.