bqresearcher_task_2

bqResearcher-Task 2: circuit for producing |00> and |11> with equal probabilities. Parameters are found using gradient descent. Circuit is modified for producing any of the 4 Bell states.

Run code as follows:

Open two terminals and run qvm -S and quilc -S in each of the terminals
Open another terminal and run main.py as python main.py

main.py: (all qubits are initially at state |0>)

Circuit for producing |00> and |11> with equal probabilties:
- A parametric circuit is called that uses only native gates ( http://docs.rigetti.com/en/stable/apidocs/gates.html?highlight=native#native-gates-for-rigetti-qpus).
- A superposition of |0> and |1> on qubit-1 is produced as follows:
  - Apply RX gate on qubit-1 with angle pi/2
  - Apply RZ gate on qubit-1 with angle theta
  - Apply RX gate on qubit-1 with angle -pi/2
- qubit-0 is changed to |1> state by applying RX and RZ gates on qubit-0 with angle pi
- A superposition of |0> and |1> on qubit-0 is produced as follows:
  - Apply RX gate on qubit-0 with angle pi/2
  - Apply RZ gate on qubit-0 with angle theta
  - Apply RX gate on qubit-0 with angle -pi/2
- The code uses an instance of a QuantumComputer which then compiles the parametric program to produce an executable that is scanned over for theta using gradient descent.
Modification for producing any of the 4 Bell states:
- An equal superposition of |0> and |1> on qubit-1 is produced as follws:
  - Apply RX gate on qubit-1 with angle pi/2
  - Apply RZ gate on qubit-1 with angle pi/2
  - Apply RX gate on qubit-1 with angle -pi/2
- qubit-0 is changed to |1> state by applying RX and RZ gates on qubit-0 with angle pi
- CNOT gate is implemented with qubit-1 as control and qubit-0 as target as follows:
  - Apply RX gate on qubit-0 with angle pi/2
  - Apply RZ gate on qubit-0 with angle pi/2
  - Apply RX gate on qubit-0 with angle -pi/2
  - Apply CZ gate with qubit-1 as control and qubit-0 as target
  - Apply RX gate on qubit-0 with angle pi/2
  - Apply RZ gate on qubit-0 with angle -pi/2
  - Apply RX gate on qubit-0 with angle -pi/2 - Note: The above steps are illustrated for producing the Bell state (|01> - |10>)/sqrt(2). The code produces all of the 4 Bell states by changing thetas and rotating qubit-0 by pi to produce |1> as appropriate.

bell_main.py: An attempt to find a Bell state using Gradient Descent.

modules/ckt_tools.py:

gen_ckt() : function that returns a program for producing |00> and |11> with equal probabilties.
bell_ckt() : function that returns a program for producing any of the 4 Bell states
init_qc_exec(ckt_program): function that returns an instance of a QuantumComputer and an executable after compiling ckt_program
bell_ckt_gd(): function that returns a program for producing any of the 4 Bell states using Gradient Descent

modules/gd_tools.py:

cost_func(x) : a cost function that returns the value of a gradient at x
find_optimal_theta(qc, executable): function that returns an optimal value of theta for the input executable using an intance of the QuantumComputer qc using gradient descent
bell_cost_func(x): a cost function that returns the value of a gradient at x for finding Bell state
bell_find_optimal_theta(qc, executable): function that returns an optimal value of theta for the input executable using an intance of the QuantumComputer qc using gradient descent for finding Bell State

Kaustuvi/bqresearcher_task_2

bqresearcher_task_2