QuTiP example: Quantum Gates and their usage¶
Author: Anubhav Vardhan (anubhavvardhan@gmail.com)
User-defined gate added by: Boxi Li (etamin1201@gmail.com)
For more information about QuTiP see http://qutip.org
Installation:¶
The circuit image visualization requires LaTeX and ImageMagick for display. The module automatically process the LaTeX code for plotting the circuit, generate the pdf and convert it to the png format.
On Mac and Linux, ImageMagick can be easily installed with the command conda install imagemagick if you have conda installed.
Otherwise, please follow the installation instructions on the ImageMagick documentation.
On windows, you need to download and install ImageMagick installer. In addition, you also need perl (for pdfcrop) and Ghostscript (additional dependency of ImageMagick for png conversion).
To test if the installation is complete, try the following three commands working correctly in Command Prompt: pdflatex, pdfcrop and magick anypdf.pdf antpdf.png, where anypdf.pdf is any pdf file you have.
In [1]:
import numpy as np
from numpy import pi
from qutip import Qobj, about
from qutip_qip.circuit import QubitCircuit
from qutip_qip.operations import (Gate, berkeley, cnot, cphase, csign, fredkin,
gate_sequence_product, globalphase, iswap,
molmer_sorensen, phasegate, qrot, rx, ry, rz,
snot, sqrtiswap, sqrtnot, sqrtswap, swap,
swapalpha, toffoli)
%matplotlib inline
Introduction¶
Gates in QuTiP and their representation¶
Controlled-PHASE¶
In [2]:
cphase(pi / 2)
Out[2]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1j\end{array}\right)$$
In [3]:
q = QubitCircuit(2, reverse_states=False)
q.add_gate("CSIGN", controls=[0], targets=[1])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[3]:
Rotation about X-axis¶
In [4]:
rx(pi / 2)
Out[4]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}0.707 & -0.707j\\-0.707j & 0.707\end{array}\right)$$
In [5]:
q = QubitCircuit(1, reverse_states=False)
q.add_gate("RX", targets=[0], arg_value=pi / 2, arg_label=r"\frac{\pi}{2}")
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[5]:
Rotation about Y-axis¶
In [6]:
ry(pi / 2)
Out[6]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}0.707 & -0.707\\0.707 & 0.707\end{array}\right)$$
In [7]:
q = QubitCircuit(1, reverse_states=False)
q.add_gate("RY", targets=[0], arg_value=pi / 2, arg_label=r"\frac{\pi}{2}")
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[7]:
Rotation about Z-axis¶
In [8]:
rz(pi / 2)
Out[8]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}(0.707-0.707j) & 0\\0 & (0.707+0.707j)\end{array}\right)$$
In [9]:
q = QubitCircuit(1, reverse_states=False)
q.add_gate("RZ", targets=[0], arg_value=pi / 2, arg_label=r"\frac{\pi}{2}")
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[9]:
CNOT¶
In [10]:
cnot()
Out[10]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 0 & 1\\0 & 0 & 1 & 0\end{array}\right)$$
In [11]:
q = QubitCircuit(2, reverse_states=False)
q.add_gate("CNOT", controls=[0], targets=[1])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[11]:
CSIGN¶
In [12]:
csign()
Out[12]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & -1\end{array}\right)$$
In [13]:
q = QubitCircuit(2, reverse_states=False)
q.add_gate("CSIGN", controls=[0], targets=[1])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[13]:
Berkeley¶
In [14]:
berkeley()
Out[14]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}0.924 & 0 & 0 & 0.383j\\0 & 0.383 & 0.924j & 0\\0 & 0.924j & 0.383 & 0\\0.383j & 0 & 0 & 0.924\end{array}\right)$$
In [15]:
q = QubitCircuit(2, reverse_states=False)
q.add_gate("BERKELEY", targets=[0, 1])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[15]:
SWAPalpha¶
In [16]:
swapalpha(pi / 2)
Out[16]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & (0.610-0.488j) & (0.390+0.488j) & 0\\0 & (0.390+0.488j) & (0.610-0.488j) & 0\\0 & 0 & 0 & 1\end{array}\right)$$
FREDKIN¶
In [17]:
fredkin()
Out[17]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=Dense, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{array}\right)$$
TOFFOLI¶
In [18]:
toffoli()
Out[18]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=Dense, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\end{array}\right)$$
SWAP¶
In [19]:
swap()
q = QubitCircuit(2, reverse_states=False)
q.add_gate("SWAP", targets=[0, 1])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[19]:
ISWAP¶
In [20]:
iswap()
q = QubitCircuit(2, reverse_states=False)
q.add_gate("ISWAP", targets=[0, 1])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[20]:
SQRTiSWAP¶
In [21]:
sqrtiswap()
Out[21]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 0.707 & 0.707j & 0\\0 & 0.707j & 0.707 & 0\\0 & 0 & 0 & 1\end{array}\right)$$
SQRTSWAP¶
In [22]:
sqrtswap()
Out[22]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & (0.500+0.500j) & (0.500-0.500j) & 0\\0 & (0.500-0.500j) & (0.500+0.500j) & 0\\0 & 0 & 0 & 1\end{array}\right)$$
SQRTNOT¶
In [23]:
sqrtnot()
Out[23]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}(0.500+0.500j) & (0.500-0.500j)\\(0.500-0.500j) & (0.500+0.500j)\end{array}\right)$$
HADAMARD¶
In [24]:
snot()
Out[24]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=True$$\left(\begin{array}{cc}0.707 & 0.707\\0.707 & -0.707\end{array}\right)$$
PHASEGATE¶
In [25]:
phasegate(pi / 2)
Out[25]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}1 & 0\\0 & 1j\end{array}\right)$$
GLOBALPHASE¶
In [26]:
globalphase(pi / 2)
Out[26]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}1j & 0\\0 & 1j\end{array}\right)$$
Mølmer–Sørensen gate¶
In [27]:
molmer_sorensen(pi / 2)
Out[27]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}0.707 & 0 & 0 & -0.707j\\0 & 0.707 & -0.707j & 0\\0 & -0.707j & 0.707 & 0\\-0.707j & 0 & 0 & 0.707\end{array}\right)$$
Qubit rotation gate¶
In [28]:
qrot(pi / 2, pi / 4)
Out[28]:
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=False$$\left(\begin{array}{cc}0.707 & (-0.500-0.500j)\\(0.500-0.500j) & 0.707\end{array}\right)$$
Expanding gates to larger qubit registers¶
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:
In [29]:
cnot(N=3)
Out[29]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\end{array}\right)$$
In [30]:
q = QubitCircuit(3, reverse_states=False)
q.add_gate("CNOT", controls=[1], targets=[2])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[30]:
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):
In [31]:
cnot(N=3, control=2, target=0)
Out[31]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{array}\right)$$
In [32]:
q = QubitCircuit(3, reverse_states=False)
q.add_gate("CNOT", controls=[0], targets=[2])
q.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[32]:
Setup of a Qubit Circuit¶
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.
In [33]:
N = 2
qc0 = QubitCircuit(N)
qc0.add_gate("ISWAP", [0, 1], None)
qc0.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[33]:
In [34]:
U_list0 = qc0.propagators()
U0 = gate_sequence_product(U_list0)
U0
Out[34]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 0 & 1j & 0\\0 & 1j & 0 & 0\\0 & 0 & 0 & 1\end{array}\right)$$
In [35]:
qc1 = QubitCircuit(N)
qc1.add_gate("CNOT", 0, 1)
qc1.add_gate("CNOT", 1, 0)
qc1.add_gate("CNOT", 0, 1)
qc1.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[35]:
In [36]:
U_list1 = qc1.propagators()
U1 = gate_sequence_product(U_list1)
U1
Out[36]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=CSR, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 0 & 1 & 0\\0 & 1 & 0 & 0\\0 & 0 & 0 & 1\end{array}\right)$$
In place of manually converting the SWAP gate to CNOTs, it can be automatically converted using an inbuilt function in QubitCircuit
In [37]:
qc2 = qc0.resolve_gates("CNOT")
qc2.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[37]:
In [38]:
U_list2 = qc2.propagators()
U2 = gate_sequence_product(U_list2)
U2
Out[38]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 0 & 1j & 0\\0 & 1j & 0 & 0\\0 & 0 & 0 & 1\end{array}\right)$$
From QuTiP 4.4, we can also add gate at arbitrary position in a circuit.
In [39]:
qc1.add_gate("CSIGN", index=[1], targets=[0], controls=[1])
qc1.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[39]:
Example of basis transformation¶
In [40]:
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
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[40]:
In [41]:
U3 = gate_sequence_product(qc3.propagators())
U3
Out[41]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}(0.354-0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0\\(0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0\\0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354+0.354j)\\0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j)\\(-0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0\\(0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0\\0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354+0.354j)\\0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j)\end{array}\right)$$
The transformation can either be only in terms of 2-qubit gates:¶
In [42]:
qc4 = qc3.resolve_gates("CNOT")
qc4.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[42]:
In [43]:
U4 = gate_sequence_product(qc4.propagators())
U4
Out[43]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}(0.354-0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0\\(0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0\\0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354+0.354j)\\0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j)\\(-0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0\\(0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0\\0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354+0.354j)\\0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j)\end{array}\right)$$
In [44]:
qc5 = qc3.resolve_gates("ISWAP")
qc5.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[44]:
In [45]:
U5 = gate_sequence_product(qc5.propagators())
U5
Out[45]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}(0.354-0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0\\(0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0\\0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354+0.354j)\\0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j)\\(-0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0\\(0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0\\0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354+0.354j)\\0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j)\end{array}\right)$$
Or the transformation can be in terms of any 2 single qubit rotation gates along with the 2-qubit gate.¶
In [46]:
qc6 = qc3.resolve_gates(["ISWAP", "RX", "RY"])
qc6.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[46]:
In [47]:
U6 = gate_sequence_product(qc6.propagators())
U6
Out[47]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}(0.354-0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0\\(0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0\\0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354+0.354j)\\0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j)\\(-0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0\\(0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0\\0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354+0.354j)\\0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j)\end{array}\right)$$
In [48]:
qc7 = qc3.resolve_gates(["CNOT", "RZ", "RX"])
qc7.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[48]:
In [49]:
U7 = gate_sequence_product(qc7.propagators())
U7
Out[49]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}(0.354-0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0\\(0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0\\0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354+0.354j)\\0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0 & (0.354-0.354j) & 0 & (0.354-0.354j)\\(-0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (-0.354+0.354j) & 0 & (0.354-0.354j) & 0\\(0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j) & 0\\0 & (0.354+0.354j) & 0 & (-0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (-0.354+0.354j)\\0 & (0.354-0.354j) & 0 & (0.354-0.354j) & 0 & (0.354+0.354j) & 0 & (0.354+0.354j)\end{array}\right)$$
Resolving non-adjacent interactions¶
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.
In [50]:
qc8 = QubitCircuit(3)
qc8.add_gate("CNOT", 2, 0)
qc8.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[50]:
In [51]:
U8 = gate_sequence_product(qc8.propagators())
U8
Out[51]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\end{array}\right)$$
In [52]:
qc9 = qc8.adjacent_gates()
qc9.gates
Out[52]:
[Gate(SWAP, targets=[0, 1], controls=None, classical controls=None, control_value=None, classical_control_value=None), Gate(CNOT, targets=[2], controls=[1], classical controls=None, control_value=None, classical_control_value=None), Gate(SWAP, targets=[0, 1], controls=None, classical controls=None, control_value=None, classical_control_value=None)]
In [53]:
U9 = gate_sequence_product(qc9.propagators())
U9
Out[53]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\end{array}\right)$$
In [54]:
qc10 = qc9.resolve_gates("CNOT")
qc10.png
/usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip_qip/circuit/circuit_latex.py:95: UserWarning: Could not locate system 'pdfcrop': image output may have additional margins. warnings.warn(
Out[54]:
In [55]:
U10 = gate_sequence_product(qc10.propagators())
U10
Out[55]:
Quantum object: dims=[[2, 2, 2], [2, 2, 2]], shape=(8, 8), type='oper', dtype=CSR, isherm=True$$\left(\begin{array}{cc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\end{array}\right)$$
Adding gate in the middle of a circuit¶
From QuTiP 4.4 one can add a gate at an arbitrary position of a circuit. All one needs to do is to specify the parameter index. With this, we can also add the same gate at multiple positions at the same time.
In [56]:
qc = QubitCircuit(1)
qc.add_gate("RX", targets=1, arg_value=np.pi / 2)
qc.add_gate("RX", targets=1, arg_value=np.pi / 2)
qc.add_gate("RY", targets=1, arg_value=np.pi / 2, index=[0])
qc.gates
Out[56]:
[Gate(RY, targets=[1], controls=None, classical controls=None, control_value=None, classical_control_value=None), Gate(RX, targets=[1], controls=None, classical controls=None, control_value=None, classical_control_value=None), Gate(RX, targets=[1], controls=None, classical controls=None, control_value=None, classical_control_value=None)]
User defined gates¶
From QuTiP 4.4 on, user defined gates can be defined by a python function that takes at most one parameter and return a Qobj, the dimension of the Qobj has to match the qubit system.
In [57]:
def user_gate1(arg_value):
# controlled rotation X
mat = np.zeros((4, 4), dtype=complex)
mat[0, 0] = mat[1, 1] = 1.0
mat[2:4, 2:4] = rx(arg_value).full()
return Qobj(mat, dims=[[2, 2], [2, 2]])
def user_gate2():
# S gate
mat = np.array([[1.0, 0], [0.0, 1.0j]])
return Qobj(mat, dims=[[2], [2]])
To let the QubitCircuit process those gates, we need to modify its attribute QubitCircuit.user_gates, which is a python dictionary in the form {name: gate_function}.
In [58]:
qc = QubitCircuit(2)
qc.user_gates = {"CTRLRX": user_gate1, "S": user_gate2}
When calling the add_gate method, the target qubits and the argument need to be given.
In [59]:
# qubit 0 controls qubit 1
qc.add_gate("CTRLRX", targets=[0, 1], arg_value=pi / 2)
# qubit 1 controls qubit 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()
In [60]:
props[0] # qubit 0 controls qubit 1
Out[60]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 0.707 & -0.707j\\0 & 0 & -0.707j & 0.707\end{array}\right)$$
In [61]:
props[1] # qubit 1 controls qubit 0
Out[61]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 0.707 & 0 & -0.707j\\0 & 0 & 1 & 0\\0 & -0.707j & 0 & 0.707\end{array}\right)$$
In [62]:
props[2] # S gate acts on qubit 1
Out[62]:
Quantum object: dims=[[2, 2], [2, 2]], shape=(4, 4), type='oper', dtype=CSR, isherm=False$$\left(\begin{array}{cc}1 & 0 & 0 & 0\\0 & 1j & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1j\end{array}\right)$$
Software versions¶
In [63]:
about()
QuTiP: Quantum Toolbox in Python ================================ Copyright (c) QuTiP team 2011 and later. Current admin team: Alexander Pitchford, Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, Eric Giguère, Boxi Li, Jake Lishman, Simon Cross, Asier Galicia, Paul Menczel, and Patrick Hopf. Board members: Daniel Burgarth, Robert Johansson, Anton F. Kockum, Franco Nori and Will Zeng. Original developers: R. J. Johansson & P. D. Nation. Previous lead developers: Chris Granade & A. Grimsmo. Currently developed through wide collaboration. See https://github.com/qutip for details. QuTiP Version: 5.1.0.dev0+c874c4a Numpy Version: 1.22.4 Scipy Version: 1.13.1 Cython Version: 3.0.10 Matplotlib Version: 3.5.2 Python Version: 3.10.4 Number of CPUs: 4 BLAS Info: Generic INTEL MKL Ext: False Platform Info: Linux (x86_64) Installation path: /usr/share/miniconda3/envs/test-environment/lib/python3.10/site-packages/qutip ================================================================================ Please cite QuTiP in your publication. ================================================================================ For your convenience a bibtex reference can be easily generated using `qutip.cite()`