Efficient Circuit-Based Quantum State Tomography via Sparse Entry Optimization

We propose an efficient circuit-based quantum state tomography (QST) scheme to reconstruct n-qubit states with k nonzero entries using measurements of |ψ and U₁|ψ, , U₂ₘ|ψ, where m ≤ k. Each Uⱼ involves CNOT gates followed by a single-qubit gate, either Hadamard H or $HD$, where D = diag(1,i), targeting a specific qubit. We provide an upper limit on the number of CNOT gates based on the nonzero entries' positions in |ψ. This approach, applied to both state and process tomography, was tested using the Qiskit simulator.