Singular-value decomposition using quantum annealing

Area of Science:

• Quantum Computing
• Linear Algebra
• Data Analysis

Background:

• Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) are fundamental linear algebra techniques.
• These methods are crucial for dimensionality reduction and data analysis in various scientific fields.
• Traditional computation of SVD and PCA can be resource-intensive for large datasets.

Purpose of the Study:

• To demonstrate the application of quantum annealing for performing SVD.
• To show how quantum annealing can be utilized for PCA.
• To adapt quantum annealing for finding maximum eigenstates, essential for SVD.

Main Methods:

• Utilizing quantum annealing to find the ground state of a system.
• Transforming the sign of the final Hamiltonian to target the maximum eigenstate.
• Employing an approximation focusing on the maximum eigenvalue to determine the adiabatic timescale.

Main Results:

• Successfully adapted quantum annealing to perform singular value decomposition.
• Demonstrated the feasibility of using quantum annealing for principal component analysis.
• Developed a method to obtain maximum eigenstates using quantum annealing by Hamiltonian sign transformation.

Conclusions:

• Quantum annealing offers a novel approach for SVD and PCA.
• The proposed method provides a pathway for quantum-enhanced data analysis.
• Further research can explore the scalability and efficiency of this quantum approach.