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Can someone please help me making these gates on CIRQ programming:

  1. Decrement Gate (-1)
  2. Splitter Gate (If possible)

I was having trouble implementing these and was not sure if it's possible either.

Thanks in advance.

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I'm not sure what a splitter operation is.

There is a class cirq.ArithmeticOperation which is a helper class for implementing arithmetic. You can implement an increment gate with it like this:

import cirq

class Increment(cirq.ArithmeticOperation):
    def __init__(self, target_register):
        self.target_register = target_register

    def registers(self):
        return [self.target_register]

    def with_registers(self, *new_registers):
        return Increment(*new_registers)

    def apply(self, target_value):
        return [target_value + 1]

The helper class will ensure that several useful methods are implemented, such as a reasonably efficient simulation method. Note that the new register value returned in apply automatically wraps modulo $2^n$ where $n$ is the size of the register. Also it is your responsibility to make sure the arithmetic operation is actually reversible.

Then you can use it like this:

register = cirq.LineQubit.range(2)
circuit = cirq.Circuit(Increment(register))

print(circuit)
# 0: ───<__main__.Increment object at 0x000002594B1F03C8>───
#       │
# 1: ───#2──────────────────────────────────────────────────


print(cirq.unitary(Increment(register)))
# [[0.+0.j 0.+0.j 0.+0.j 1.+0.j]
#  [1.+0.j 0.+0.j 0.+0.j 0.+0.j]
#  [0.+0.j 1.+0.j 0.+0.j 0.+0.j]
#  [0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
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