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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Counting the Ground State Degeneracy by Evolution Methods.

Zhen Guo¹, Li You^1,2,3,4

¹Tsinghua University, State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Beijing 100084, China.

Physical Review Letters

|October 25, 2025

Summary

This summary is machine-generated.

Counting ground state degeneracy, a complex physics problem, is now more accessible. This study introduces a novel algorithm that transforms degeneracy counting into finding a special ground state in an enlarged system, enabling broader application of existing methods.

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Area of Science:

Quantum Physics
Computational Complexity
Condensed Matter Physics

Background:

Counting ground state degeneracy of k-local Hamiltonians is crucial in physics.
This problem is computationally harder than finding a single ground state.
Existing methods for degeneracy counting are limited.

Purpose of the Study:

To develop an efficient algorithm for counting ground state degeneracy.
To map the degeneracy counting problem to finding a special ground state in a modified system.
To enable the use of established ground state finding methods for degeneracy counting.

Main Methods:

Proposing a novel algorithm to map degeneracy counting to a ground state finding problem.
Enlarging the system by doubling the number of qubits or spins.
Constructing a k-local super Hamiltonian for the enlarged system.
Utilizing traditional ground state finding methods (power, Lanczos, quantum imaginary time evolution) on the super Hamiltonian.

Main Results:

Demonstrated that traditional ground state finding algorithms can solve the mapped problem.
Successfully applied the algorithm with power, Lanczos, and quantum imaginary time evolution methods.
Illustrated applications in detecting phase boundaries and analyzing frustration vs. quantum fluctuation competition.
Showcased potential for implementation using quantum circuits.

Conclusions:

The proposed algorithm effectively transforms ground state degeneracy counting into a solvable ground state finding problem.
This approach broadens the applicability of existing computational physics techniques.
The method offers a viable path for studying complex quantum systems and their properties, with potential quantum circuit implementations.