Seven qubits, q0 to q6, make up the Quantum Bellagio Circuit. The primary qubits are q0, q2, q3 and q4. The Haadamard gates put these into superposition producing 24 = 16 parts in the mega qubit. Consequently, the rest of the qubits are dependent qubits. Each part from 1 to 16 of the mega qubit represents a different possible state of the multipart qubit and so every possible combination of Kimmel and Maher working at the Bellagio. The goal is to find those parts that meet the constraints.
Note that jv represents true and j^ represents false. In the short form used they are v and ^ to make it easier to view.
Changes to Mega Qubit by Haadamard Gates
| The initial state of the mega qubit with 7 qubits is: |^^^^^^^> | |
| H 0 | |^^^^^^^>+ |v^^^^^^> |
| q0 is the first state in each of the parts of the mega qubit and it represents k. The Haadmard Gate H 0 puts q0 into superposition. As a result, the initial mega qubit becomes two parts with states as above. This represents all combinations of k. q0 has bits of j^ and jv in the parts 1 and 2 of the mega qubit. The jv parts represent Kimmel at the Bellagio on Day1 (true) whereas the j^ parts represent Kimmel not being at the Bellagio on Day 1 (false). | |
| H 1 | |^^^^^^^> + |^v^^^^^>+ |v^^^^^^> + |vv^^^^^> |
| q1 is the second state in each of the parts of the mega qubit and it represents k‾ . The Haadmard Gate H 1 puts q1 into superposition. As a result, the two-part mega qubit turns into the combination of four parts as above. This represents all combinations of k and k‾. q1 has bits of j^, jv, j^ and jv, in parts 1, 2, 3 and 4 of the mega qubit. The jv parts represent Kimmel at the Aladdin on Day1 (true) whereas the j^ parts represent Kimmel not being at the Aladdin on Day 1 (false). | |
| H 2 | |^^^^^^^>+|^^v^^^^>+|^v^^^^^>+|^vv^^^^>+|v^^^^^^>+|v^v^^^^>+ |vv^^^^>+ |vvv^^^^> |
| q2 is the third state in each of the parts of the mega qubit and it represents m. The Haadmard Gate H 2 puts q2 into superposition. As a result, the four-part mega qubit turns into the combination of eight parts as above. This represents all combinations of k, k‾ and m. q2 has bits of j^ and jv in parts 1 to 8 of the mega qubit. The jv parts represent Maher at the Bellagio on Day1 (true) whereas the j^ parts represent Maher not being at the Bellagio on Day 1 (false). | |
| H 3 | |^^^^^^^>+|^^^v^^^>+|^^v^^^^>+|^^vv^^^>+|^v^^^^^>+|^v^v^^^>+|^vv^^^^>+|^vvv^^^>+|v^^^^^^>++|v^^v^^^>+|v^v^^^^>+|v^vv^^^>+ |vv^^^^^> |vv^v^^^>|vvv^^^>|vvvv^^^> |
| q3 is the fourth state in each of the parts of the mega qubit and it represents m‾. The Haadmard Gate H 3 puts q3 into superposition. As a result, the eight-part mega qubit turns into the combination of sixteen parts as above. This represents all combinations of k, k‾, m and m‾. q3 has bits of j^ and jv in parts 1 to 16 of the mega qubit. The jv parts represent Maher at Caesar’s on Day1 (true) whereas the j^ parts represent Maher not being at the Caesar’s on Day 1 (false). |
Quantum Simulators vs Quantum Computers
The 4 Haadamard gates of the Quantum Bellagio Circuit produced 16 combinations of the qubits k, k‾ ,m and m‾. This is 24 multipart states in the mega qubit. A program that puts more qubits into superposition quickly generates huge levels of computation because the number of mega qubit parts grows exponentially. Digital computers can simulate Quantum Computers. However when there are many primary qubits then the computational load on the simulators becomes too great. For instance passing 50 primary qubits through Haadamard gates will result in 250 mega qubit parts.
Quantum simulators are more available on line and are very useful for smaller projects. They can easily measure qubits at different stages of the circuit which is also an advantage.
In conclusion, this post shows how the Haadamard gates set up a quantum circuit with all possible combinations of attendance at the Bellagio for days 1 and 2 by Kimmel and Maher.
Next: Bellagio Circuit Part 1 Continued
Previous: Bellagio Circuit Setup