Skip to main content
Problem List
Q7.Inverse Phase Operation (S† from S & Z)Easy

Q7.Inverse Phase Operation (S† from S & Z)

Single-Qubit OperationsQubits: 1Q
Synthesize the adjoint phase gate S†=(100−i)S^\dagger = \begin{pmatrix}1 & 0 \\ 0 & -i\end{pmatrix} using only S and Z gates.
Target Objective:
Starting from equal superposition ∣+⟩|+\rangle, apply S and Z to transform it to ∣i−⟩=12(∣0⟩−i∣1⟩)|i-\rangle = \frac{1}{\sqrt{2}}(|0\rangle - i|1\rangle).
Judge Acceptance Criteria:

Statevector fidelity must reach ≥ 99.9% with the target unitary solution.

Gates:
q[0]|0⟩
S0
S1
S2
S3
S4
S5
S6
S7
Live Python / Qiskit Code (Edit to Update Circuit)
 
Type Qiskit Python code above to update gates on wires automatically0 gates · 1Q
0 gates placed1 Qubits · 8 Steps
State Measurement Distribution:2 non-zero basis states
|0⟩100.0%
|1⟩0.0%