(a) Compute , writing the result as a normalised sum of . (b) An eigenphase is to be…

PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms · The quantum circuit model and quantum algorithms

Quantum Information and Technology, Ch The quantum Fourier transform and phase estimation

Problem

(a) Compute F8∣4⟩F_8|4\rangle, writing the result as a normalised sum of ∣0⟩,…,∣7⟩|0\rangle,\dots,|7\rangle. (b) An eigenphase is to be resolved to m=10m=10 bits with failure probability below ϵ=0.001\epsilon = 0.001. Using the rule t=m+⌈log⁡2(2+1/(2ϵ))⌉t = m + \lceil\log_2(2+1/(2\epsilon))\rceil, find tt. (c) The Pauli ZZ gate has eigenstates ∣0⟩|0\rangle (eigenvalue +1+1) and ∣1⟩|1\rangle (eigenvalue −1-1). Phase estimation with t=2t=2 control qubits is run on the input 0.9 ∣0⟩+0.1 ∣1⟩\sqrt{0.9}\,|0\rangle + \sqrt{0.1}\,|1\rangle for this target qubit. List the possible two-bit outputs and their probabilities.

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