# How to implement a quantum_and() gate

I have encoder() and decoder() functions as follows:

def encoder(x: int=0, y: int=0, n=4):
"""
An encoder to convert two n-bit nonnegative integers (uint) x and y to a 2n-qubit QuantumCircuit.
This encoder will be used by autograder.
"""
assert x >= 0 and x < 2**n and isinstance(n,int), f"Your input x must be an integer in the range [0,{(2**n)-1}]."
assert y >= 0 and y < 2**n and isinstance(n,int), f"Your input y must be an integer in the range [0,{(2**n)-1}]."

qc = QuantumCircuit(n*2)

for i in range(n):
if x >= 2**(n-i-1):
qc.x(n-i-1)
x -= 2**(n-i-1)

for i in range(n):
if y >= 2**(n-i-1):
qc.x(2*n-i-1)
y -= 2**(n-i-1)

return qc

def decoder(qc: QuantumCircuit, n=4):
"""
A decoder to convert a QuantumCircuit to an n-bit nonnegative integer from the simulation histogram
by measuring the first n qubits in the quantum circuit.
The result should be deterministic on a noise-free machine, hence shot=1 is used for simulation.
This decoder will be used by autograder.
"""
assert n >= 1
assert isinstance(qc, QuantumCircuit)
assert qc.num_qubits >= n

n_qubits = qc.num_qubits
n_clbits = max(n, qc.num_clbits)

qr = QuantumRegister(n_qubits)
cr = ClassicalRegister(n_clbits)
qc_base = QuantumCircuit(qr, cr)
qc = qc_base.compose(qc)

simulator = QasmSimulator()
qc.measure(list(range(n)), list(range(n)))
cc = transpile(qc, simulator)
job = simulator.run(cc, shots=1)
result = list(job.result().get_counts(cc).keys())[0]

z = 0
for i in range(n):
z += int(result[i])*2**(n-i-1)

return z


How to implement the quantum_and gate? Any suggestions and clues would be helpful.

def quantum_and():
"""
An N-qubit quantum circuit which calculates the AND result of input1 on [q0] and input2 on [q1],
The output will be measured on [q0].
You need to decide the amount of additional qubits needed to implement the function.
The function must be compatible with the provided encoder(n=1) and decoder(n=1).
N must be either 2 or 3.
Args:
None
Return:

• Have a look at Toffoli gate. It behaves like AND provided target qubit is initialized to state $|0\rangle$. See more here en.m.wikipedia.org/wiki/Toffoli_gate Jan 30 at 7:41