Vibration Analysis of Cyclic Symmetrical Systems by Quantum Algorithms

Algorithm 2

Damped elastic vibrating system.

IN: ,

OUT:

(i) Applying to qubits in state , prepare .

(ii) Apply to .

(iii) Append to .

(iv) Apply to the new state and prepare .

(v) Run the eigenvalue estimation of , letting be the input, and get the output .

(vi) Append a qubit to the output to get .

(vii) Perform controlled rotation on .

(viii) Measure the last qubit in the standard basis, conditioned on seeing 1.The outcome is proportional to

(ix) Uncompute the eigenvalue estimation to get , which is proportional to the state .

(x) Apply the permutation on the outcome of the previous step.

(xi) Apply . This produces a state which is proportional to an vector consisting of blocks, each block

has entries, where the th element in the th block gives .