Kaustuvi / 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.

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:

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

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

1. 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.

2. 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:

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

modules/gd_tools.py:

1. cost_func(x) : a cost function that returns the value of a gradient at x
2. 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
3. bell_cost_func(x): a cost function that returns the value of a gradient at x for finding Bell state
4. 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