Transpile mct to cx without QuantumCircuit

Question

to convert my circuit mct instructions to cx I transpiled a Qiskit circuit, but I want to do it without a circuit, because I want more qubits than Qiskit can handle (50 or more).

This is because I'm training a BPN neural net to be a cx gate acting on bloch coordinates. It inputs are control and target qubits bloch coordinates before cx, and outputs the same but after cx.

So how can I change mct instructions to cx, transpiling or what?

Answer 1

I dont think your problem is related with QuantumCircuit, but with synthesis of such as big MCT. By default, the amount of resulting gates grows very quickly (it looks exponentially), as more qubits are involved

from qiskit import QuantumCircuit
from qiskit import transpile

cxs = []
for controlled in (range(3,20)):
    target = 0
    control = list(range(target+1,controlled))
    qc = QuantumCircuit(num)
    qc = QuantumCircuit(num+len(control))
    qc.mcx(control, target)
    result = transpile(qc, basis_gates=['rx','ry','rz','cx'])
    cxs.append(result.count_ops()['cx'])

import matplotlib.pyplot as plt
plt.plot(cxs)
plt.show()

With 20 qubits, the default synthesis results in 800K CXs gates.

However, this default synthesis method uses no ancillas. In the mct documentation, should would notice that there are several "modes". The v-chain mode is the most efficient in terms of the result, but uses the biggest amount of ancillas. The amount of resulting cnots grows linearly with the amount of controlled qubits:

from qiskit import QuantumCircuit
from qiskit import transpile

cxs = []
for controlled in (range(3,20)):
    target = 0
    control = list(range(target+1,controlled))
    ancilla = list(range(len(control)+1, 2*len(control)-1))
    qc = QuantumCircuit(num)
    qc = QuantumCircuit(num+len(control)+len(ancilla))
    qc.mcx(control, target, ancilla, mode='v-chain')  # <-
    result = transpile(qc, basis_gates=['rx','ry','rz','cx'])
    cxs.append(result.count_ops()['cx'])

import matplotlib.pyplot as plt
plt.plot(cxs)
plt.show()

So, you can create a quantum circuit that considers these ancillas, it would look something like this:

from qiskit import QuantumCircuit
from qiskit import transpile

target = 0 # <- qubit 0 as a target 
control = list(range(target+1,60)) # <- controlled qubits
ancilla = list(range(len(control)+1, 2*len(control)-1)) # <- ancilla qubits
print('target', target)
print('control', control)
print('ancilla', ancilla)

qc = QuantumCircuit(num)
qc = QuantumCircuit(num+len(control)+len(ancilla))
qc.mcx(control, target, ancilla, mode='v-chain')
result = transpile(qc, basis_gates=['rx','ry','rz','cx'])

print(result.count_ops())

target 0
control [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59]
ancilla [60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116]
OrderedDict([('rz', 463), ('cx', 348), ('ry', 230), ('rx', 1)])

Answer 2

Fist use cirq.decompose_multi_controlled_x with num free qubits = num controls -2 and then transpile each ccx( always 2) with qiskit (15 instructions each). That works fast for lot's of qubits and give much less instrucions than qiskit transpile