Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond
For quantum system identification, this work provides a theoretical framework and efficient algorithm to determine parameter identifiability, reducing computational cost in practical quantum experiments.
The paper extends the classical Similarity Transformation Approach (STA) to quantum Hamiltonian identifiability, proving identifiability of spin-1/2 chain systems with arbitrary dimension using single-qubit probes. It also introduces a Structure Preserving Transformation (SPT) method for non-minimal systems, enabling an economic identification algorithm with computational complexity dependent on the number of unknown parameters rather than system dimension.
The identifiability of a system is concerned with whether the unknown parameters in the system can be uniquely determined with all the possible data generated by a certain experimental setting. A test of quantum Hamiltonian identifiability is an important tool to save time and cost when exploring the identification capability of quantum probes and experimentally implementing quantum identification schemes. In this paper, we generalize the identifiability test based on the Similarity Transformation Approach (STA) in classical control theory and extend it to the domain of quantum Hamiltonian identification. We employ STA to prove the identifiability of spin-1/2 chain systems with arbitrary dimension assisted by single-qubit probes. We further extend the traditional STA method by proposing a Structure Preserving Transformation (SPT) method for non-minimal systems. We use the SPT method to introduce an indicator for the existence of economic quantum Hamiltonian identification algorithms, whose computational complexity directly depends on the number of unknown parameters (which could be much smaller than the system dimension). Finally, we give an example of such an economic Hamiltonian identification algorithm and perform simulations to demonstrate its effectiveness.