Quantum Computing 3 qubit Grovers Algorithm On IBM

Quantum Computing: 3 -qubit Grover’s Algorithm On IBM Q Eric Li, Dr. Tzu-Chieh Wei, Maziar Farahzad

Quantum Computers which exploit quantum mechanics to do computations IBM Q Commercially available universal quantum computers Open to public access through IBM Composer and QISKit Multiple quantum computers available

qubit quantum superposition en. wikipedia. org/wiki/Schrödinger%27 s_cat

Bloch Sphere Equation for qubit X-axis en. wikipedia. org/wiki/Bloch_sphere Y-axis

entanglement. “a correlation between individually random behaviors of the two (IBM Q FAQ) particles” Along with superposition, these two quantum phenomena are the reason why quantum computers have so much potential

Quantum Logic Gates

Quantum Matrices The values correspond with the amplitudes of the corresponding basis

Grover’s Algorithm www. researchgate. net/figure/Geometricrepresentation-of-Grovers-searchalgorithm_fig 1_322243277 quantumexperience. ng. bluemix. net/proxy/tutorial/full-userguide/004 -Quantum_Algorithms/070 -

Oracle www. researchgate. net/figure/Geometricrepresentation-of-Grovers-searchalgorithm_fig 1_322243277 quantumexperience. ng. bluemix. net/proxy/tutorial/full-userguide/004 -Quantum_Algorithms/070 -

Inversion About Mean www. researchgate. net/figure/Geometricrepresentation-of-Grovers-searchalgorithm_fig 1_322243277 quantumexperience. ng. bluemix. net/proxy/tutorial/full-userguide/004 -Quantum_Algorithms/070 -

Number of Iterations ■ www. researchgate. net/figure/Geometricrepresentation-of-Grovers-searchalgorithm_fig 1_322243277 Formulas from the book: Quantum Computation and Quantum Information by Nielsen and Chuang

3 -qubit Implementation ■

Lucky Number: ■ 2

Simulation Results ■

Results on IBM Q 16 Rueschlikon ■

Initial Debugging ■ Ran the circuit multiple times on IBM Q – Each one just as bad ■ Posted the issue to Git. Hub – The Toffoli gate (CCX) is not native to QISKit (package to access IBM Q) ■ Implemented using 6 CX gates which have a decently high amount of error – I had four Toffoli gates total – Suggested that I reduce the number of 2 -qubit gates and run on IBM Q 5 Tenerife (lower error rates)

Resolving the Issue ■ Needed a better Toffoli gate ■ Decomposed CCZ gate (which I could replace the H-Toffoli-H) gate using 3 CU gates and 2 CX gates – But the CU gates (control unitary phase shift gates) are implemented using two-qubit gates – Would introduce more error as more two-qubit gates are being used ■ Lower the number of 1 -qubit gates – H-X-H = Z ■ Only run one iteration ■ Run on IBM Q 5 Tenerife

Results on IBM Q 5 Tenerife ■