Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond

Abstract

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.

Generation of Accessible Sets in the Dynamical Modeling of Quantum Network Systems

“…For an N-qubit system, the number of operators in Λ is 3 N . The generation rule (14) indicates that, finding an accessible set involves finding all of the operators coupled with the measurement operators in (12).…”

“…) where is the Hamiltonian set given in (11) and M is the measurement set given in (12), we aim to develop an economic method to simplify the generation of the accessible set G with a good ordering according to generation rules (13) and (14).…”

Identification of Time-Varying Decoherence Rates for Open Quantum Systems

“…whereŷ(k) are the outputs generated by the estimated decoherence rate r(t) from the dynamical equation (11).…”

“…For a given time-varying r(t), there is generally no analytical method to solve (11). To obtain numerical solutions, we use piecewise constant function to approximate r(t).…”

“…[9] utilizes the time traces of observable measurements to identify Hamiltonian parameters, and the corresponding identifiability problem is then studied in Refs. [10], [11]. The work in Ref.…”