Consider the three-qubit product state

PHYSICS · Multi-part · 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

Consider the three-qubit product state ∣ψ⟩=∣+⟩1⊗∣1⟩2⊗∣−i⟩3|\psi\rangle = |{+}\rangle_1 \otimes |1\rangle_2 \otimes |{-i}\rangle_3, where ∣+⟩|{+}\rangle is the +1+1 eigenstate of XX, ∣1⟩|1\rangle is the −1-1 eigenstate of ZZ, and ∣−i⟩|{-i}\rangle is the −1-1 eigenstate of YY. ((a)) Write three independent generators, one acting nontrivially on each qubit, that stabilize ∣ψ⟩|\psi\rangle. ((b)) Check that they commute and are independent. ((c)) State the dimension of the fixed space and confirm ∣ψ⟩|\psi\rangle is the unique state they stabilize.

Browse the problem library