MicroAlgo Inc. (NASDAQ: MLGO) announced development of a quantum query algorithm framework based on sum-of-squares representation of Boolean functions, according to a company statement.

The framework consists of three steps: finding sum-of-squares representations of Boolean functions and their negations, constructing quantum states for the algorithm's final state, and identifying unitary operators within the algorithm.

The approach uses multilinear polynomials to represent Boolean functions as sums of squares, which the company states provides mathematical foundation for quantum algorithm design. The method aims to leverage quantum superposition and entanglement properties to improve query efficiency compared to classical algorithms.

In the first step, the company uses algebraic tools and computer algebra systems to derive sum-of-squares representations. The second step involves constructing quantum states through qubit initialization, phase modulation, and gate operations using rotation gates and CNOT gates. The final step requires finding optimal unitary operators through mathematical optimization and machine learning methods.

The company acknowledges the framework faces challenges in certain practical applications and may be infeasible in specific situations. However, MicroAlgo states the algorithm shows potential for problems with low complexity.

MicroAlgo, based in the Cayman Islands, develops central processing algorithms and provides solutions integrating algorithms with software and hardware. The company's services include algorithm optimization, computing power acceleration, and data intelligence services.