Running a Quantum Circuit
Quantum computers are analogue computers. In effect, this means that they are subject to physical errors each time a quantum circuit runs. As a result, quantum programs are run many times to ensure accurate results. Measurement of the qubits causes the qubits in the mega qubit to collapse to one of the possible 16 parts. The diagram above shows the measurements of the primary qubits q0, q1, q2 and q3 for each run that has been tagged by q6 as a valid solution.
In practice, it is only necessary to measure q0 and q2 because q1 is the complement of q0 and q3 is the complement of q2. i.e. If q0 is true then q1 must be false and vice versa. The same applies to q2 and q3.
Solutions Found
The solution above, after 8192 circuit runs or shots using IBM Qiskit, shows counts of the tagged results for each combination of q0 – q3. The qubit results are in reverse order with the result 1011 representing q0 = 1, q1 = 1, q2 = 0 and q3 = 1. The results show that 2,992 of the tagged results were for the qubits represented by 1011, 3038 for 1110 and 1234 for 1111. The other results were for less than 300 or less than 4% of the results.
First Solution 1011
This part represents the 14th part of the mega qubit starting with vv^v in the final diagram of the mega qubit. It meets the logic requirements (k‾ ∨ m‾) ∧ (k ∨ m) because:
- q0 = v – k true – Kimmel at the Bellagio on Day 1 and at the Aladdin on Day 2
- q3 = v – m‾ true – Maher at Caesars on Day 1 and at the Bellagio on Day 2
Note that q1 = v also. This does not make logical sense as q0 = v represents k as true and q1 = v represents k as not true. The tagging of the solutions took place when the q0 and q1 were entangled. This means that if q0 had been measured before tagging and found to = v, then q1 would = ^ due to entanglement. The qubits would have measured v^^v and not the vv^v. However they were not measured at this stage. The mega qubit was untangled and when finally measured it had the value vv^v.
Interestingly, the 10th part with the value v^^v has not been tagged as a solution. During the entanglement of q2 and q3 by the cnot 2,3 and X 3 gates, the part is set to v^^^. In this configuration the constraint (k‾ ∨ m‾) is not met when checked by the ccnot 1,3,4 gate as both q1 and q3 are false.
This shows the subtlety of the entanglement and superposition effect on the program.
Second Solution 1110
This part represents the 15th part of the mega qubit starting with vvv^ in the final diagram of the mega qubit. It meets the logic requirements (k‾ ∨ m‾) ∧ (k ∨ m) because:
- q1 = v – k‾ true – Kimmel at the Aladdin on Day 1 and at the Bellagio on Day 2
- q2 = v – m true – Maher at the Bellagio on Day 1 and at Caesars on Day 2
Again, q0 = v and q1 = v does not make logical sense. This is put down to the tagging taking place when the qubits were entangled as in the first solution above.
Third Solution 1111
This part represents the 16th part of the mega qubit starting with vvvv in the final diagram of the mega qubit. It meets the logic requirements (k‾ ∨ m‾) ∧ (k ∨ m) because:
- q0 = v – k true – Kimmel at the Bellagio on Day 1 and at the Aladdin on Day 2
- q3 = v – m‾ true – Maher at Caesars on Day 1 and at the Bellagio on Day 2
Again, q0 = v and q1 = v does not make logical sense. Neither does q2 = v and q3 = v make logical sense. These results are put down to the tagging taking place when the qubits were entangled as in the first solution above.
Just Measuring q0 and q2
The circuit can be run with the measurement of q0 and q2 only. This gives a clearer result as above that shows that the 01 and 10 solutions are optimum.
The 01 solution represents: q0 = v and q2 = ^. i.e.
- q0 = v – k true – Kimmel at the Bellagio on Day 1 and at the Aladdin on Day 2
- q2 = ^ – m false – Maher at Caesars on Day 1 and at the Bellagio on Day 2
The 10 solution represents: q0 = ^ and q2 = v. i.e.
- q0 = ^ – k false – Kimmel at the Aladdin on Day 1 and at the Bellagio on Day 2
- q2 = v – m true – Maher at the Bellagio on Day 1 and at Caesars on Day 2
However it misses out on the more subtle effects of entanglement as shown above when the 4 qubits are measured.
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