Quantum Preprocessing for Linear Systems via Matrix Conditioning
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current quantum preprocessing technologies are inadequate for addressing the challenges of large condition numbers in linear systems, limiting the acceleration performance of quantum computing and failing to satisfy diverse linear systems.
Innovation Solution
A quantum preprocessing method that involves acquiring element information of a linear system, constructing new matrices and vectors, and encoding this information into quantum circuits to perform quantum state evolution operations, thereby reducing the condition number and enabling simulation across different linear systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum linear solvers are used to solve linear systems, then exponential acceleration is achieved, but the complexity is negatively influenced by large condition numbers
Solution Approach 1:
The patent applies preliminary conditioning actions to the linear system before applying the quantum linear solver. By preprocessing the matrix A through classical conditioning techniques that transform it into a better-conditioned matrix, the system reduces the condition number κ in advance, thereby eliminating the negative influence on quantum solver complexity and improving both solution speed and reliability.
2Adaptability or versatility
If existing quantum preprocessing technology is applied, then some linear systems can be processed, but the technology is too scarce and cannot satisfy different linear systems
Solution Approach 1:
The patent develops a universal quantum preprocessing framework that can handle different types of linear systems through a standardized approach. By creating a multi-functional preprocessing system that combines classical matrix conditioning with quantum state preparation, the technology achieves broad applicability across various linear systems while maintaining manageable complexity through modular design.
Solution Approach 2:
The patent introduces an intermediary classical preprocessing step that acts as a bridge between the input linear system and the quantum solver. This intermediary conditioning process transforms diverse linear systems into a standardized form suitable for quantum processing, thereby expanding adaptability without directly increasing quantum circuit complexity.
3Reliability
If quantum state evolution operations are performed on constructed quantum circuits, then the condition number is lowered, but the linking of classical data structures with quantum states is required
Solution Approach 1:
The patent replaces direct manipulation of classical data structures with quantum state representations. By encoding matrix elements and vectors into quantum states and using quantum operations to perform conditioning, the system lowers the condition number through quantum mechanical processes rather than classical computational methods, reducing the complexity of classical-prequantum interface requirements.
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
This approach effectively links classical data structures with quantum states, allowing for the realization of quantum preprocessing that can satisfy various linear systems, lowers condition numbers, and fills technical gaps in quantum computing, enhancing the simulation capabilities of quantum computing.
Implementation Method 1
Quantum computing uses quantum superposition, and has an exponential acceleration effect during solution of linear systems via quantum linear solvers
Implementation Method 2
constructing a computing framework with the theory of quantum mechanics
Data Source
AI summary
Quantum preprocessing methods, devices, storage medium are disclosed. An embodiment includes: acquiring element information of a first matrix A and a first vector b in a linear system Ax={right arrow over (b)}; constructing a new matrix M for linear system preprocessing; computing a second matrix A′ and a second vector b′ for constructing a quantum circuit, according to the new matrix M; and constructing, a first quantum circuit representing a quantum state evolution of a specific class of element in the second matrix A′, and a second quantum circuit representing a quantum state evolution of a specific class of element in the second vector b′, and executing a quantum state evolution operation respectively on the first quantum circuit and the second quantum circuit, to obtain an evolved quantum state of the first quantum circuit and an evolved quantum state of the second quantum circuit.