Vibration Analysis of Cyclic Symmetrical Systems by Quantum Algorithms

Algorithm 1

Simple vibrating system.

IN: , ,

OUT:

(i) Append to two qubits in state and prepare the state .

(ii) Apply the sequence of operations , and respectively to the prepared state, and produce

(iii) Measure the first two qubits in the standard basis, conditioned on seeing . The outcome is proportional to

(iv) Applying to log qubits in state , prepare .

(v) Append to the outcome of the measurement.

(vi) Apply to the new state and prepare .

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

(viii) Append a qubit to the output to get

(ix) Perform controlled rotation on .

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

(xi) Uncompute the eigenvalue estimation to get , which is proportional to the state encoding the solution.