qcpython 1.0.2

QCpy is a lightweight quantum circuit simulator and visualization of quantum computing.

README.md

QCpy - A Quantum Computing Library for Python

QCpy is an open source python library and collaborative project for flexible simulations and visualizations of quantum circuits. Designed by college students with students in mind, this library contains a powerful set of tools to teach computer scientists about the emerging discipline of quantum computing (QC).

Recommended Resources on Quantum Computing:

• Microsoft’s Linear Algebra for Quantum Computing
• IBM’s Quantum Computing: a field guide
• Wikipedia: Quantum Computing

---

Qubits

class QC.Qubit.Qubit(initial_state=’z’)

Object representation of a qubit.

Parameters:

initial_state (chr) - Character input for starting direction in the x, y, or z axis.

Attributes:

state (numpy.ndarray) - current state of qubit in matrix representation.

---

Quantum Gates

class QC.QuantumGate.Identity()

Gate that does not modify the quantum state.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of Identity gate.

Identity.matrix = [1+0j, 0+0j], 
	          [0+0j, 1+0j]

class QC.QuantumGate.PauliX()

Quantum equivalent of the NOT gate in classical computing with respect to the standard basis |0>, |1>.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of Pauli-X gate.

PauliX.matrix = [0+0j, 1+0j], 
	        [1+0j, 0+0j]

class QC.QuantumGate.PauliY()

Rotation around y-axis of the bloch sphere by π radiains, mapping |0> to i|1> and |1> to -i|0>.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of Pauli-Y gate.

PauliY.matrix = [0+0j, 0-1j],
                [0+1j, 0+0j]

class QC.QuantumGate.PauliZ()

Rotation around z-axis of the bloch sphere by π radiains, mapping |1> to -|1>; known as the phase-flip.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of Pauli-Z gate.

PauliY.matrix = [1+0j, 0+0j], 
                [0+0j, -1+0j]

class QC.QuantumGate.Hadamard()

Maps the basis states |0> to |+> and |1> to |->, creating a superposition state if given a computation basis state.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of Hadamard gate.

Hadamard.matrix = ([1,  1] 
                   [1, -1]) * (1/sqrt(2))

class QC.QuantumGate.CNot(inverse=False)

Controlled gate acts on two or more qubits, performing the NOT operation of the target qubit only if the control qubits are |1>, can act as a quantum regiester and is used to entangle and disentangle Bell states.

Parameters:

inverse (bool) - if the gate is an inverse, with the target being above the control.

Attributes:

matrix (np.ndarray) - matrix representation of CNOT gate.

# regular
CNot.matrix = [1+0j, 0+0j, 0+0j, 0+0j],
              [0+0j, 1+0j, 0+0j, 0+0j],
              [0+0j, 0+0j, 0+0j, 1+0j],
              [0+0j, 0+0j, 1+0j, 0+0j]
# inverse
CNot.matrix = [1+0j, 0+0j, 0+0j, 0+0j],
              [0+0j, 0+0j, 0+0j, 1+0j],
              [0+0j, 0+0j, 1+0j, 0+0j],
              [0+0j, 1+0j, 0+0j, 0+0j] 

class QC.QuantumGate.Swap()

Swaps two qubits, with respect to the basis |00>, |01>, |10>, and |11>.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of SWAP gate.

Swap.matrix = [1+0j, 0+0j, 0+0j, 0+0j],
              [0+0j, 0+0j, 1+0j, 0+0j],
              [0+0j, 1+0j, 0+0j, 0+0j],
              [0+0j, 0+0j, 0+0j, 1+0j]

class QC.QuantumGate.Toffoli()

Universal reversible logic gate, known as the “controlled-controlled-NOT” gate; if the two control bits are set to 1, it will invert the target.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of Toffoli gate.

Toffoli.matrix = [1+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j],
                 [0+0j, 1+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j],
                 [0+0j, 0+0j, 1+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j],
                 [0+0j, 0+0j, 0+0j, 1+0j, 0+0j, 0+0j, 0+0j, 0+0j],
                 [0+0j, 0+0j, 0+0j, 0+0j, 1+0j, 0+0j, 0+0j, 0+0j],
                 [0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 1+0j, 0+0j, 0+0j],
                 [0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 1+0j],
                 [0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 0+0j, 1+0j, 0+0j]

class QC.QuantumGate.Phase(theta=numpy.pi/2)

Applies a rotation of theta around the z-axis.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation around z-axis.

Attributes:

matrix (np.ndarray) - matrix representation of Phase gate.

Phase.matrix = [1+0j, 0+0j],
	       [0+0j, numpy.exp(0+1j * theta)]

class QC.QuantumGate.S()

Equivalent to a pi/2 rotation around the z-axis.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of S gate.

S.matrix = [1+0j, 0+0j],
           [0+0j, 0+1j]

class QC.QuantumGate.Sdg()

Inverse of S gate; a -pi/2 rotation around the z-axis.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of an inverse S gate.

Sdg.matrix = [1+0j, 0+0j],
             [0+0j, 0-1j]

class QC.QuantumGate.T()

Square of S gate; where T = S^2.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of a T gate.

T.matrix = [1+0j, 0+0j],
           [0+0j, numpy.exp((0+1j * numpy.pi) / 4)]

class QC.QuantumGate.Tdg()

Inverse of T gate.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of a inverse of T gate.

Tdg.matrix = [1+0j, 0+0j],
             [0+0j, numpy.exp((0-1j * numpy.pi) / 4)]

class QC.QuantumGate.Rz(theta=numpy.pi/2)

Rotation of qubit around the z-axis.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation around z-axis.

Attributes:

matrix (np.ndarray) - matrix representation of an Rz gate.

Rz.matrix = [numpy.exp((0-1j * (theta / 2))), 0+0j],
            [0+0j, numpy.exp(0+1j * (theta / 2))]

class QC.QuantumGate.Rx(theta=numpy.pi/2)

Rotation of qubit around the x-axis.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation around x-axis.

Attributes:

matrix (np.ndarray) - matrix representation of an Rx gate.

Rx.matrix = [numpy.cos(theta / 2), 0-1j * numpy.sin(theta / 2)],
            [0-1j * numpy.sin(theta / 2), numpy.cos(theta / 2)]

class QC.QuantumGate.Ry(theta=numpy.pi/2)

Rotation of qubit around the y-axis.

Parameters:

theta (float)default: numpy.pi/2 - angle of rotation around y-axis.

Attributes:

matrix (np.ndarray) - matrix representation of an Ry gate.

Ry.matrix = [numpy.cos(theta / 2), -1 * numpy.sin(theta / 2)],
            [numpy.sin(theta / 2), numpy.cos(theta / 2)]

class QC.QuantumGate.Sx()

Rotation around the x-axis by 90 degrees in the counter-clockwise direction. Also known as the “square-root X gate” due to the fact that applying the SX gate twice results in an X gate.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of an Sx gate.

Sx.matrix = [1+1j, 1-1j], 
            [1-1j, 1+1j]]) * (1 / 2)

class QC.QuantumGate.Sxdg()

Inverse of the Sx gate.

Parameters:

None

Attributes:

matrix (np.ndarray) - matrix representation of an inverse Sx gate.

Sxdg.matrix = [1-1j, 1+1j], 
              [1+1j, 1-1j]]) * (1 / 2)

class QC.QuantumGate.U(theta=numpy.pi/2, phi=numpy.pi/2, lmbda=numpy.pi/2)

Rotation of qubit with respect to theta, phi, and lambda, in Euler angles.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation around Euler angle theta.

phi (float) default: numpy.pi/2 - angle of rotation around Euler angle phi.

lmbda (float) default: numpy.pi/2 - angle of rotation around Eulear angle lambda.

Attributes:

matrix (np.ndarray) - matrix representation of a U gate.

U.matrix = [numpy.cos(theta / 2), -1 * numpy.exp(0+1j * lmbda) * numpy.sin(theta / 2)], 
           [numpy.exp(0+1j * phi) * numpy.sin(theta / 2), numpy.exp(0+1j * (lmbda + phi)) * numpy.cos(theta / 2)]]

class QC.QuantumGate.Rxx(theta=numpy.pi/2)

Rotation about XX, maximally entangling at theta = pi/2.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation around XX.

Attributes:

matrix (np.ndarray) - matrix representation of an Rxx gate.

Rxx.matrix = [numpy.cos(theta / 2), 0+0j, 0+0j, 0-1j * numpy.sin(theta / 2)],
             [0+0j, numpy.cos(theta / 2), 0-1j * numpy.sin(theta / 2), 0+0j],
             [0+0j, 0-1j * numpy.sin(theta / 2), numpy.cos(theta / 2), 0+0j],
             [0-1j * numpy.sin(theta / 2), 0+0j, 0+0j, numpy.cos(theta / 2)]

class QC.QuantumGate.Rzz(theta=numpy.pi/2)

Rotation about ZZ, maximally entangling at theta = pi/2.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation around ZZ.

Attributes:

matrix (np.ndarray) - matrix representation of an Rzz gate.

Rzz.matrix = [numpy.exp(0-1j * (theta / 2)), 0+0j, 0+0j, 0+0j],
             [0+0j, numpy.exp(0+1j * (theta / 2)), 0+0j, 0+0j],
             [0+0j, 0+0j, numpy.exp(0+1j * (theta / 2)), 0+0j],
             [0+0j, 0+0j, 0+0j, numpy.exp(0-1j * (theta / 2))]

class QC.QuantumGate.Cr(theta=numpy.pi/2)

Controlled phase shift rotation in theta radians; generalization of Cz gate.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation in theta radians.

Attributes:

matrix (np.ndarray) - matrix representation of an Cr gate.

Cz.matrix = [1+0j, 0+0j, 0+0j, 0+0j],
            [0+0j, 1+0j, 0+0j, 0+0j],
            [0+0j, 0+0j, 1+0j, 0+0j],
            [0+0j, 0+0j, 0+0j, numpy.exp(theta * 0+1j)]

class QC.QuantumGate.Cz(theta=numpy.pi/2)

Controlled phase shift rotation in theta radians.

Parameters:

theta (float) default: numpy.pi/2 - angle of rotation in theta radians.

Attributes:

matrix (np.ndarray) - matrix representation of an Cz gate.

Cz.matrix = [1+0j, 0+0j, 0+0j, 0+0j],
            [0+0j, 1+0j, 0+0j, 0+0j],
            [0+0j, 0+0j, 1+0j, 0+0j],
            [0+0j, 0+0j, 0+0j, -1+0j]

---

Quantum Circuit

class QC.QuantumCircuit.QuantumCircuit(qubits, little_endian=False, prep='z')

Quantum circuit that represents the state of a quantum system and performs operations on select qubits.

Parameters:

qubits (int) - number of qubits in the circuit.

little_endian (bool) default: False - order of qubits and tensor products.

prep (char) options: [z, y, x] - initial direction of the qubits' phase angle.

Attributes:

None

QuantumCircuit.circuit()

Dictionary representation of the circuit

Parameters:

None

Returns:

circuit (dict[int, list[str]]) - key: qubit; value: name of gate.

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)
qc.cnot(0, 1)
qc.hadamard(0)

print(qc.circuit())

# {0: ['hadamard', 'cnot_control', 'hadamard'], 
#  1: ['cnot_target']}

QuantumCircuit.amplitude(round=3)

Returns vector of all possible amplitudes for the quantum circuit

Parameters:

round (int) - rounding the amplitude to the nearest round

Returns:

amplitude (numpy.ndarray[float16]) - amplitude of the quantum circuit.

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)
qc.cnot(0, 1)
qc.hadamard(0)

print(qc.amplitude())

# [[0.5]
# [0.5]
# [0.5]
# [0.5]]

QuantumCircuit.phaseAngle(round=2, radian=True)

Calculates possible phase angles for the quantum circuit

Parameters:

round (int) - rounding the amplitude to the nearest round

radian (bool) - whether or not the values are in radians or degrees.

Returns:

phase_angle (numpy.ndarray) - array of qubit's phase angle.

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)
qc.cnot(0, 1)
qc.hadamard(0)

print(qc.phaseAngle())

# [[0.        ]
# [0.         ]
# [0.         ]
# [3.14159265]]

QuantumCircuit.state(round=3)

Returns state of the quantum circuit.

Parameters:

round (int) - rounding the state to the nearest round

Returns:

_state (numpy.ndarray) - array of quantum circuit's state.

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)
qc.cnot(0, 1)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.   +0.j]
# [0.707+0.j]]

QuantumCircuit.probabilities(round=3)

Returns probabilitiy of the qubits within the quantum circuit.

Parameters:

round (int) - rounding the probabilities to the nearest round

Returns:

prob_matrix (numpy.ndarray) - array of quantum circuit's probabilities.

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.cnot(0, 1)

print(qc.probabilities())

# [0.5 0.  0.  0.5]

QuantumCircuit.measure()

Collapses the state based on the quantum circuit's probabilities.

Parameters:

None

Returns:

final_state (numpy.ndarray) - array of quantum circuit's measurement.

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)
qc.cnot(0, 1)

print(qc.measure())

# ~Results may vary~
# 00

QuantumCircuit.reverse()

Reverses the quantum circuit's values.

Parameters:

None

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

print(qc.state())

qc.reverse()

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.707+0.j]
# [0.   +0.j]]
 
# [[0.   +0.j]
# [0.707+0.j]
# [0.   +0.j]
# [0.707+0.j]]

QuantumCircuit.toffoli(control_1, control_2, target)

A 3-qubit quantum gate that takes in two control qubits and one target qubit.

Parameters:

control_1 (int) - first control qubit.

control_2 (int) - second control qubit.

target (int) - target qubit.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(3)

qc.hadamard(0)

qc.hadamard(1)

qc.toffoli(0,1,2)

print(qc.state())

# [[0.5+0.j]
# [0. +0.j]
# [0.5+0.j]
# [0. +0.j]
# [0.5+0.j]
# [0. +0.j]
# [0. +0.j]
# [0.5+0.j]]

QuantumCircuit.rccx(control_1, control_2, target)

A 3-qubit quantum gate that takes in two control qubits and one target qubit.

Parameters:

control_1 (int) - first control qubit.

control_2 (int) - second control qubit.

target (int) - target qubit.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(3)

qc.hadamard(0)

qc.hadamard(1)

qc.rccx(0,1,2)

print(qc.state())

# [[ 0.5-0.j ]
# [ 0. +0.j ]
# [ 0.5-0.j ]
# [ 0. +0.j ]
# [ 0.5-0.j ]
# [ 0. +0.j ]
# [-0. +0.j ]
# [ 0. +0.5j]]

QuantumCircuit.rc3x(a, b, c, d)

A 4-qubit quantum gate that takes in 4 unique qubits.

Parameters:

a (int) - first input qubit.

b (int) - second input qubit.

c (int) - third input qubit.

d (int) - fourth input qubit.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(4)

qc.hadamard(0)

qc.hadamard(1)

qc.hadamard(2)

qc.rc3x(0,1,2)

print(qc.state())

# [[ 0.354-0.j   ]
# [ 0.   +0.j   ]
# [ 0.354-0.j   ]
# [ 0.   +0.j   ]
# [ 0.354-0.j   ]
# [ 0.   +0.j   ]
# [ 0.354-0.j   ]
# [ 0.   +0.j   ]
# [ 0.354-0.j   ]
# [ 0.   +0.j   ]
# [ 0.354-0.j   ]
# [ 0.   +0.j   ]
# [ 0.   +0.354j]
# [-0.   +0.j   ]
# [ 0.   -0.j   ]
# [-0.354+0.j   ]]

QuantumCircuit.cnot(control, target)

A 2-qubit quantum gate that takes in a control qubit and one target qubit.

Parameters:

control (int) - control qubit.

target (int) - target qubit.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(2)

qc.hadamard(0)

qc.cnot(0,1)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.   +0.j]
# [0.707+0.j]]

QuantumCircuit.cr(control, target)

A 2-qubit quantum gate that takes in a control qubit and one target qubit.

Parameters:

control (int) - control qubit.

target (int) - target qubit.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(2)

qc.hadamard(0)

qc.cr(0,1)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.707+0.j]
# [0.   +0.j]]

QuantumCircuit.cz(control, target)

A 2-qubit quantum gate that takes in a control qubit and one target qubit.

Parameters:

control (int) - control qubit.

target (int) - target qubit.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(2)

qc.hadamard(0)

qc.cz(0,1)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.707+0.j]
# [0.   +0.j]]

QuantumCircuit.swap(qubit_1, qubit_2)

A 2-qubit quantum gate that takes in 2 qubits to swap there properties.

Parameters:

qubit_1 (int) - first qubit to swap.

qubit_2 (int) - second qubit to swap.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(2)

qc.hadamard(0)

qc.swap(0,1)

print(qc.state())

# [[0.707+0.j]
# [0.707+0.j]
# [0.   +0.j]
# [0.   +0.j]]

QuantumCircuit.rxx(qubit_1, qubit_2, theta=numpy.pi/2)

A 2-qubit quantum gate that takes in two qubits and a representation of theta to initialize in the quantum state.

Parameters:

qubit_1 (int) - first qubit input.

qubit_2 (int) - second qubit input.

theta (float) default: numpy.pi/2 - angle of rotation around z-axis.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(2)

qc.hadamard(0)

qc.rxx(0,1)

print(qc.state())

# [[0.5+0.j ]
# [0. -0.5j]
# [0.5+0.j ]
# [0. -0.5j]]

QuantumCircuit.rzz(qubit_1, qubit_2, theta=numpy.pi/2)

A 2-qubit quantum gate that takes in two qubits and a representation of theta to initialize in the quantum state.

Parameters:

qubit_1 (int) - first qubit input.

qubit_2 (int) - second qubit input.

theta (float) default: numpy.pi/2 - angle of rotation around z-axis.

Returns:

None

Example:

from QCpy import QuantumCircuit
qc = QuantumCircuit(2)

qc.hadamard(0)

qc.rxx(0,1)

print(qc.state())

# [[0.5+0.j ]
# [0. -0.5j]
# [0.5+0.j ]
# [0. -0.5j]]

QuantumCircuit.customControlPhase(control, target, custom_matrix)

Used to insert single qubit based quantum gates to have a control qubit apart of it and committing to the quantum state.

Parameters:

control (int) - control qubit for given matrix.

target (int) - target qubit for given matrix.

custom_matrix (np.array) - matrix to be applied to the quantum circuit.

Returns:

None

Example:

from QCpy import QuantumCircuit

from QCpy.QuantumGate import PauliX

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.customControlPhase(0,1, PauliX().matrix)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.   +0.j]
# [0.707+0.j]]

QuantumCircuit.identity(qubit)

Used to confirm value that a qubit is representing and does nothing to manipulate the value of such qubit.

Parameters:

qubit (int) - the qubit to have the identity gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.identity(0)

print(qc.state())

# [[1.+0.j]
# [0.+0.j]
# [0.+0.j]
# [0.+0.j]]

QuantumCircuit.x(qubit)

Used to invert the value of what a qubit is representing.

Parameters:

qubit (int) - the qubit to have the Pauli-X gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.x(0)

print(qc.state())

# [[0.+0.j]
# [0.+0.j]
# [1.+0.j]
# [0.+0.j]]

QuantumCircuit.hadmard(qubit)

Used to put a given qubit into superposition.

Parameters:

qubit (int) - the qubit to have the Hadamard gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.707+0.j]
# [0.   +0.j]]

QuantumCircuit.y(qubit)

Changes the state of a qubit by pi around the y-axis of a Bloch Sphere.

Parameters:

qubit (int) - the qubit to have the Pauli-Y gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.y(0)

print(qc.state())

# [[0.+0.j]
# [0.+0.j]
# [0.+1.j]
# [0.+0.j]]

QuantumCircuit.z(qubit)

Changes the state of a qubit by pi around the z-axis of a Bloch Sphere.

Parameters:

qubit (int) - the qubit to have the Pauli-Z gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.z(0)

print(qc.state())

# [[ 0.707+0.j]
# [ 0.   +0.j]
# [-0.707+0.j]
# [ 0.   +0.j]]

QuantumCircuit.phase(qubit, theta=numpy.pi/2)

Commits to a rotation around the z-axis based off of the inputted theta value.

Parameters:

qubit (int) - the qubit to have the Phase gate be applied to the quantum wire.

theta (float) default: numpy.pi/2 - angle of rotation around z-axis.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.phase(0)

print(qc.state())

# [[0.707+0.j   ]
# [0.   +0.j   ]
# [0.   +0.707j]
# [0.   +0.j   ]]

QuantumCircuit.s(qubit)

Is a Phase gate where the inputted theta value is given as a constant of theta = pi / 2.

Parameters:

qubit (int) - the qubit to have the Pauli-Z gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.s(0)

print(qc.state())

# [[0.707+0.j   ]
# [0.   +0.j   ]
# [0.   +0.707j]
# [0.   +0.j   ]]

QuantumCircuit.sdg(qubit)

Is a Phase gate and inverse of the S gate where the inputted theta value is given as a constant of theta = -pi / 2.

Parameters:

qubit (int) - the qubit to have the Sdg gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.sdg(0)

print(qc.state())

# [[0.707+0.j   ]
# [0.   +0.j   ]
# [0.   -0.707j]
# [0.   +0.j   ]]

QuantumCircuit.t(qubit)

T gate is a special use case gate that in implemented from the P Gate.

Parameters:

qubit (int) - the qubit to have the T gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.t(0)

print(qc.state())

# [[0.707+0.j ]
# [0.   +0.j ]
# [0.5  +0.5j]
# [0.   +0.j ]]

QuantumCircuit.tdg(qubit)

Tdg gate is a special use case gate that in implemented from the P Gate and is the inverse of the T gate.

Parameters:

qubit (int) - the qubit to have the Tdg gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.tdg(0)

print(qc.state())

# [[0.707+0.j ]
# [0.   +0.j ]
# [0.5  -0.5j]
# [0.   +0.j ]]

QuantumCircuit.rz(qubit, theta=numpy.pi/2)

RZ gate commits a rotation around the z-axis for a qubit.

Parameters:

qubit (int) - the qubit to have the Rz gate be applied to the quantum wire.

theta (float) default: numpy.pi/2 - angle of rotation around z-axis.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.hadamard(0)

qc.rz(0)

print(qc.state())

# [[0.5-0.5j]
# [0. +0.j ]
# [0.5+0.5j]
# [0. +0.j ]]

QuantumCircuit.ry(qubit, theta=numpy.pi/2)

RY gate commits a rotation around the y-axis for a qubit.

Parameters:

qubit (int) - the qubit to have the Ry gate be applied to the quantum wire.

theta (float) default: numpy.pi/2 - angle of rotation around y-axis.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.ry(0)

print(qc.state())

# [[0.707+0.j]
# [0.   +0.j]
# [0.707+0.j]
# [0.   +0.j]]

QuantumCircuit.rx(qubit, theta=numpy.pi/2)

RX gate commits a rotation around the x-axis for a qubit.

Parameters:

qubit (int) - the qubit to have the Ry gate be applied to the quantum wire.

theta (float) default: numpy.pi/2 - angle of rotation around x-axis.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.rx(0)

print(qc.state())

# [[0.707+0.j   ]
# [0.   +0.j   ]
# [0.   -0.707j]
# [0.   +0.j   ]]

QuantumCircuit.sx(qubit)

SX gate is the square root of the Inverse gate (X, PauliX Gate).

Parameters:

qubit (int) - the qubit to have the Sx gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.sx(0)

print(qc.state())

# [[0.5+0.5j]
# [0. +0.j ]
# [0.5-0.5j]
# [0. +0.j ]]

QuantumCircuit.sxdg(qubit)

SXDG gate is the negative square root of the Inverse gate (X, PauliX Gate) and inverse of the SX gate.

Parameters:

qubit (int) - the qubit to have the SXdg gate be applied to the quantum wire.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.sxdg(0)

print(qc.state())

# [[0.5-0.5j]
# [0. +0.j ]
# [0.5+0.5j]
# [0. +0.j ]]

QuantumCircuit.u(qubit, theta=numpy.pi/2, phi=numpy.pi/2, lmbda=numpy.pi/2)

U gate is given three inputs (theta, phi, and lambda) that allow the inputs to manipulate the base matrix to allow for the position of the enacted qubit around the bloch sphere representation.

Parameters:

qubit (int) - the qubit to have the U gate be applied to the quantum wire.

theta (float) default: numpy.pi/2 - angle representation to rotate the qubit's representation.

phi (float) default: numpy.pi/2 - angle representation to rotate the qubit's representation.

lmbda (float) default: numpy.pi/2 - angle representation to rotate the qubit's representation.

Returns:

None

Example:

from QCpy import QuantumCircuit

qc = QuantumCircuit(2)

qc.u(0)

print(qc.state())

# [[0.5-0.5j]
# [0. +0.j ]
# [0.5+0.5j]
# [0. +0.j ]]

QuantumCircuit.custom(qubit, custom_matrix)

Will take in a custom single qubit quantum gate and implement it on a qubit.

Parameters:

qubit (int) - the qubit to have the U gate be applied to the quantum wire.

custom_matrix (np.array) - matrix to be applied to the quantum circuit.

Returns:

None

Example:

from QCpy import QuantumCircuit

from QCpy.QuantumGate import PauliX

qc = QuantumCircuit(2)

qc.custom(0, PauliX().matrix)

print(qc.state())

# [[0.+0.j]
# [0.+0.j]
# [1.+0.j]
# [0.+0.j]]

Visualizer

A collection of classes to visualize the quantum circuit

class QC.Visualizer.QSphere(circuit)

Visualizes the quantum circuit as a q-sphere

Parameters:

circuit - the quantum circuit

Attributes:

None

QSphere.makeSphere(path="qsphere.png", save=True, show=True, darkmode=True)

Returns a Q-Sphere that plots a global visualization of the quantum states in a 3D global view

Parameters:

path (str) - name of the image to be saved

save (bool) - pass True for the graph to be saved

show (bool) - pass True for the sphere to be shown instead of saved

darkmode (bool) - pass True for darkmode, false for lightmode

Returns:

None

Example:

from QCpy import QuantumCircuit
from QCpy.Visualizer import *

qc = QuantumCircuit(3)

qc.hadamard(0)
qc.hadamard(1)
qc.hadamard(2)

sphere_ex = QSphere(qc)
sphere_ex.makeSphere(save=False, show=True)

class QC.Visualizer.StateVector(circuit)

Visualizes the quantum circuit's quantum amplitutes using a bar graph

Parameters:

circuit - the quantum circuit

Attributes:

None

StateVector.makeGraph(path="statevector.png", save=True, show=True, darkmode=True)

Returns a graph that plots all the amplitudes of the qubits being measured

Parameters:

path (str) - name of the image to be saved

save (bool) - pass True for the graph to be saved

show (bool) - pass True for the graph to be shown instead of saved

darkmode (bool) - pass True for darkmode and false for lightmode

Returns:

None

Example:

from QCpy import QuantumCircuit
from QCpy.Visualizer import *

qc = QuantumCircuit(3)

qc.hadamard(0)
qc.hadamard(1)
qc.hadamard(2)

stateVector_ex = StateVector(qc)
stateVector_ex.makeGraph(save=False, show=True)

class QC.Visualizer.Probabilities(circuit)

Visualizes the quantum circuit's qubits probability of being measured using a bar graph

Parameters:

circuit - the quantum circuit

Attributes:

None

Probabilities.makeGraph(path="probabilities.png", save=True, show=True, darkmode=True)

Returns a graph that plots all the probabilities of the qubits being measured

Parameters:

path (str) - name of the image to be saved

save (bool) - pass True for the graph to be saved

show (bool) - pass True for the graph to be shown instead of saved

darkmode (bool) - pass True for darkmode and false for lightmode

Returns:

None

Example:

from QCpy import QuantumCircuit
from QCpy.Visualizer import *

qc = QuantumCircuit(3)

qc.hadamard(0)
qc.hadamard(1)
qc.hadamard(2)

probabilities_ex = Probabilities(qc)
probabilities_ex.makeGraph(save=False, show=True)