(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

F_4\big[(|0\rangle+|2\rangle)/\sqrt2\big]

, writing the result as a normalised sum of

|0\rangle,\dots,|3\rangle

. (b) An eigenphase is to be resolved to

m=3

bits with failure probability below

\epsilon=0.05

. Using the rule

t = m + \lceil\log_2(2+1/(2\epsilon))\rceil

, find

t

. (c) A phase gate

R=\mathrm{diag}(1,e^{2\pi i\cdot 3/8})

has eigenstates

|0\rangle

(eigenvalue

1

) and

|1\rangle

(eigenvalue

e^{2\pi i\cdot3/8}

). Phase estimation with

t=3

control qubits is run on the input

\sqrt{1/3}\,|0\rangle + \sqrt{2/3}\,|1\rangle

for this target qubit. List the possible outputs and their probabilities.

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