Pauli

Pauli operators and states

class sympy.physics.quantum.pauli.SigmaMinus(*args, **hints)

Pauli sigma minus operator

Parameters:

name : str

An optional string that labels the operator. Pauli operators with different names commute.

Examples

>>> from sympy.physics.quantum import represent, Dagger
>>> from sympy.physics.quantum.pauli import SigmaMinus
>>> sm = SigmaMinus()
>>> sm
SigmaMinus()
>>> Dagger(sm)
SigmaPlus()
>>> represent(sm)
Matrix([
[0, 0],
[1, 0]])

class sympy.physics.quantum.pauli.SigmaPlus(*args, **hints)

Pauli sigma plus operator

Parameters:

name : str

An optional string that labels the operator. Pauli operators with different names commute.

Examples

>>> from sympy.physics.quantum import represent, Dagger
>>> from sympy.physics.quantum.pauli import SigmaPlus
>>> sp = SigmaPlus()
>>> sp
SigmaPlus()
>>> Dagger(sp)
SigmaMinus()
>>> represent(sp)
Matrix([
[0, 1],
[0, 0]])

class sympy.physics.quantum.pauli.SigmaX(*args, **hints)

Pauli sigma x operator

Parameters:

name : str

An optional string that labels the operator. Pauli operators with different names commute.

Examples

>>> from sympy.physics.quantum import represent
>>> from sympy.physics.quantum.pauli import SigmaX
>>> sx = SigmaX()
>>> sx
SigmaX()
>>> represent(sx)
Matrix([
[0, 1],
[1, 0]])

class sympy.physics.quantum.pauli.SigmaY(*args, **hints)

Pauli sigma y operator

Parameters:

name : str

An optional string that labels the operator. Pauli operators with different names commute.

Examples

>>> from sympy.physics.quantum import represent
>>> from sympy.physics.quantum.pauli import SigmaY
>>> sy = SigmaY()
>>> sy
SigmaY()
>>> represent(sy)
Matrix([
[0, -I],
[I,  0]])

class sympy.physics.quantum.pauli.SigmaZ(*args, **hints)

Pauli sigma z operator

Parameters:

name : str

An optional string that labels the operator. Pauli operators with different names commute.

Examples

>>> from sympy.physics.quantum import represent
>>> from sympy.physics.quantum.pauli import SigmaZ
>>> sz = SigmaZ()
>>> sz ** 3
SigmaZ()
>>> represent(sz)
Matrix([
[1,  0],
[0, -1]])

class sympy.physics.quantum.pauli.SigmaZBra(n)

Bra for a two-level quantum system.

Parameters:

n : Number

The state number (0 or 1).

class sympy.physics.quantum.pauli.SigmaZKet(n)

Ket for a two-level system quantum system.

Parameters:

n : Number

The state number (0 or 1).

sympy.physics.quantum.pauli.qsimplify_pauli(e)

Simplify an expression that includes products of pauli operators.

Parameters:

e : expression

An expression that contains products of Pauli operators that is to be simplified.

Examples

>>> from sympy.physics.quantum.pauli import SigmaX, SigmaY
>>> from sympy.physics.quantum.pauli import qsimplify_pauli
>>> sx, sy = SigmaX(), SigmaY()
>>> sx * sy
SigmaX()*SigmaY()
>>> qsimplify_pauli(sx * sy)
I*SigmaZ()