Quantum Speedup for Inferring the Value of Each Bit of a Solution State in Unsorted Databases Using a Bio-Molecular...

Area of Science:

• Computational Biology
• Quantum Computing
• Bio-molecular Algorithms

Background:

• Inferring specific data bits from large, unsorted databases presents significant computational challenges.
• Existing algorithms often struggle with the exponential complexity inherent in such problems.

Purpose of the Study:

• To propose a novel bio-molecular algorithm for efficient bit inference in unsorted databases.
• To explore the connection between bio-molecular computation and quantum algorithms for enhanced data processing.

Main Methods:

• Development of a bio-molecular algorithm with specific operational and resource complexity (O(n^2) operations, O(2^(n-1)) DNA strands).
• Representation of bio-molecular solution spaces as eigenvectors for quantum analysis.
• Extension of quantum phase estimation and quantum counting algorithms for bio-molecular data.

Main Results:

• The proposed bio-molecular algorithm determines each output bit by running n times.
• Quantum algorithms successfully compute unitary operators and eigenvalues from the bio-molecular solution space.
• Verification through graph clique problems and modular arithmetic on IBM Quantum's backend.

Conclusions:

• The bio-molecular algorithm offers an efficient approach to bit inference in unsorted databases.
• Integration with quantum algorithms provides a powerful framework for complex computational tasks.
• The study demonstrates the practical application of these hybrid computational models.