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qc - Quantum Computing

quantumteleportation.py

  • Quantum teleportation is a protocol where a sender transmits a qubit to a receiver by making use of a shared entangled quantum state along with two bits of classical communication.
  • The entanglement is lost in the process.

Circuit

            ┌─────────────────────┐            ┌───┐ ░ ┌─┐    ░
q3_0: ──────┤ Initialize(0.6,0.8) ├─────────■──┤ H ├─░─┤M├────░───────■─
      ┌─────┴─────────────────────┴──────┐┌─┴─┐└───┘ ░ └╥┘┌─┐ ░       │
q3_1: ┤0                                 ├┤ X ├──────░──╫─┤M├─░───■───┼─
      │  Initialize(0.70711,0,0,0.70711) │└───┘      ░  ║ └╥┘ ░ ┌─┴─┐ │
q3_2: ┤1                                 ├───────────░──╫──╫──░─┤ X ├─■─
      └──────────────────────────────────┘           ░  ║  ║  ░ └───┘
c0: 2/══════════════════════════════════════════════════╩══╩════════════
                                                        0  1

superdense_coding.py

  • Superdense Coding allows for the transmission of two classical bits using one qubit of quantum communication at the cost of one e-bit of entanglement.
  • Through superdense coding, shared entanglement effectively allows for the doubling of the classical information-carrying capacity of sending qubits.
  • Holevo's Threorom

Circuit

        ┌───┐      ░ ┌───┐┌───┐ ░      ┌───┐ ░  ░ ┌─┐   
     a: ┤ H ├──■───░─┤ Z ├┤ X ├─░───■──┤ H ├─░──░─┤M├───
        └───┘┌─┴─┐ ░ └───┘└───┘ ░ ┌─┴─┐└───┘ ░  ░ └╥┘┌─┐
     b: ─────┤ X ├─░────────────░─┤ X ├──────░──░──╫─┤M├
             └───┘ ░            ░ └───┘      ░  ░  ║ └╥┘
meas: 2/═══════════════════════════════════════════╩══╩═
                                                   0  1
  • Different circuits are generated based on the inputs, the above is for (c, d) = (1, 1)
  • Circuit between the first and second barrier changes based on the inputs. (The Z and X gate.)

Bell States

$$ |\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) $$ $$ |\Phi^-\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle) $$ $$ |\Psi^+\rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle) $$ $$ |\Psi^-\rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle) $$