We propose an efficient circuit-based quantum state tomography (QST) scheme to reconstruct n -qubit states with k nonzero entries using measurements of |\psi⟩ and U₁|\psi⟩, …, U₂ₘ|\psi⟩, 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 |\psi⟩ . This approach, applied to both state and process tomography, was tested using the Qiskit simulator.

This is joint work with Kevin Yipu Wu and Zherui Zhang, College of William & Mary.

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