Author: Anubhav Vardhan (anubhavvardhan@gmail.com)
For more information about QuTiP see http://qutip.org
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%matplotlib inline
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from IPython.display import Image
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from numpy import pi
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from qutip import *
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cphase(pi/2)
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Image(filename='images/cphase.png')
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rx(pi/2)
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Image(filename='images/rx.png')
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ry(pi/2)
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Image(filename='images/ry.png')
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rz(pi/2)
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Image(filename='images/rz.png')
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cnot()
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Image(filename='images/cnot.png')
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csign()
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Image(filename='images/csign.png')
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berkeley()
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Image(filename='images/berkeley.png')
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swapalpha(pi/2)
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Image(filename='images/swapalpha.png')
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fredkin()
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Image(filename='images/fredkin.png')
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toffoli()
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Image(filename='images/toffoli.png')
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swap()
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Image(filename='images/swap.png')
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iswap()
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Image(filename='images/iswap.png')
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sqrtiswap()
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Image(filename='images/sqrtiswap.png')
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sqrtswap()
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Image(filename='images/sqrtswap.png')
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sqrtnot()
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Image(filename='images/sqrtnot.png')
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snot()
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Image(filename='images/snot.png')
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phasegate(pi/2)
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Image(filename='images/phasegate.png')
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globalphase(pi/2)
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Image(filename='images/globalphase.png')
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molmer_sorensen(pi/2)
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qrot(pi/2, pi/4)
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The example above show how to generate matrice representations of the gates implemented in QuTiP, in their minimal qubit requirements. If the same gates is to be represented in a qubit register of size $N$, the optional keywork argument N can be specified when calling the gate function. For example, to generate the matrix for the CNOT gate for a $N=3$ bit register:
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cnot(N=3)
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Image(filename='images/cnot310.png')
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Furthermore, the control and target qubits (when applicable) can also be similarly specified using keyword arguments control and target (or in some cases controls or targets):
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cnot(N=3, control=2, target=0)
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Image(filename='images/cnot302.png')
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The gates implemented in QuTiP can be used to build any qubit circuit using the class QubitCircuit. The output can be obtained in the form of a unitary matrix or a latex representation.
In the following example, we take a SWAP gate. It is known that a swap gate is equivalent to three CNOT gates applied in the given format.
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N = 2
qc0 = QubitCircuit(N)
qc0.add_gate("SWAP", [0, 1], None)
qc0.png
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U_list0 = qc0.propagators()
U0 = gate_sequence_product(U_list0)
U0
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qc1 = QubitCircuit(N)
qc1.add_gate("CNOT", 0, 1)
qc1.add_gate("CNOT", 1, 0)
qc1.add_gate("CNOT", 0, 1)
qc1.png
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U_list1 = qc1.propagators()
U1 = gate_sequence_product(U_list1)
U1
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In place of manually converting the SWAP gate to CNOTs, it can be automatically converted using an inbuilt function in QubitCircuit
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qc2 = qc0.resolve_gates("CNOT")
qc2.png
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U_list2 = qc2.propagators()
U2 = gate_sequence_product(U_list2)
U2
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qc3 = QubitCircuit(3)
qc3.add_gate("CNOT", 1, 0)
qc3.add_gate("RX", 0, None, pi/2, r"\pi/2")
qc3.add_gate("RY", 1, None, pi/2, r"\pi/2")
qc3.add_gate("RZ", 2, None, pi/2, r"\pi/2")
qc3.add_gate("ISWAP", [1, 2])
qc3.png
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U3 = gate_sequence_product(qc3.propagators())
U3
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qc4 = qc3.resolve_gates("CNOT")
qc4.png
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U4 = gate_sequence_product(qc4.propagators())
U4
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qc5 = qc3.resolve_gates("ISWAP")
qc5.png
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U5 = gate_sequence_product(qc5.propagators())
U5
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qc6 = qc3.resolve_gates(["ISWAP", "RX", "RY"])
qc6.png
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U6 = gate_sequence_product(qc6.propagators())
U6
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qc7 = qc3.resolve_gates(["CNOT", "RZ", "RX"])
qc7.png
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U7 = gate_sequence_product(qc7.propagators())
U7
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Interactions between non-adjacent qubits can be resolved by QubitCircuit to a series of adjacent interactions, which is useful for systems such as spin chain models.
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qc8 = QubitCircuit(3)
qc8.add_gate("CNOT", 2, 0)
qc8.png
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U8 = gate_sequence_product(qc8.propagators())
U8
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qc9 = qc8.adjacent_gates()
qc9.png
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U9 = gate_sequence_product(qc9.propagators())
U9
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qc10 = qc9.resolve_gates("CNOT")
qc10.png
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U10 = gate_sequence_product(qc10.propagators())
U10
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import numpy as np
def user_gate1(arg_value):
# controlled rotation X
mat = np.zeros((4, 4), dtype=np.complex)
mat[0, 0] = mat[1, 1] = 1.
mat[2:4, 2:4] = rx(arg_value)
return Qobj(mat, dims=[[2, 2], [2, 2]])
def user_gate2():
# S gate
mat = np.array([[1., 0],
[0., 1.j]])
return Qobj(mat, dims=[[2], [2]])
To let the QubitCircuit process those gates, one can modify its the attributes QubitCircuit.user_gates, which is a python dictionary in the form {name: gate_function}.
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qc = QubitCircuit(2)
qc.user_gates = {"CTRLRX": user_gate1,
"S" : user_gate2}
When calling the add_gate method, the targets qubits and the argument need to be given.
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# qubit 0 controlls qubit 1
qc.add_gate("CTRLRX", targets=[0,1], arg_value=pi/2)
# qubit 1 controlls qutbi 0
qc.add_gate("CTRLRX", targets=[1,0], arg_value=pi/2)
# a gate can also be added using the Gate class
g_T = Gate("S", targets=[1])
qc.add_gate("S", targets=[1])
props = qc.propagators()
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props[0] # qubit 0 controlls qubit 1
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props[1] # qubit 1 controlls qutbi 0
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props[2] # S gate acts on qubit 1
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from qutip.ipynbtools import version_table
version_table()
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