Three qubits start in

PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Open quantum systems, decoherence and error correction

Quantum Information and Technology, Ch The stabilizer formalism

Problem

Three qubits start in ∣000⟩|000\rangle, stabilized by {Z1,Z2,Z3}\{Z_1, Z_2, Z_3\}. The following circuit is applied, in this order: a Hadamard HH on qubit 2; a CNOT with qubit 2 as control and qubit 1 as target; a CNOT with qubit 2 as control and qubit 3 as target. Use the conjugation rules H:X↔ZH: X \leftrightarrow Z (on the qubit it acts on) and, for CNOTc→t\mathrm{CNOT}_{c\to t}: Xc→XcXtX_c \to X_cX_t, Zt→ZcZtZ_t \to Z_cZ_t, with XtX_t and ZcZ_c unchanged, to track the stabilizer generators through the circuit step by step. Give the three generators of the final state and identify that state.

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