Simon's algorithm is run for qubits

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms

Quantum Information and Technology, Ch Oracles, quantum parallelism and the first algorithms

Problem

Simon's algorithm is run for n=4n=4 qubits. Three runs return the strings y(1)=0100y^{(1)}=0100, y(2)=1010y^{(2)}=1010 and y(3)=0011y^{(3)}=0011 on the input register. ((a)) Write the three equations y(i)⋅s=0(mod2)y^{(i)}\cdot s=0\pmod2 in the unknown bits s=s1s2s3s4s=s_1s_2s_3s_4, solve them by elimination, and list every candidate string ss consistent with all three. ((b)) State the two classical queries that settle, with certainty, which candidate is the true hidden string, and the rule that decides it.

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