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Use the doit() method, as in:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

Use The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method, as in:method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

sage: from sympy.physics.quantum import qapply
sage: from sympy.physics.quantum.gate import H
sage: [e0r, e1r] = [qapply(H(0)*ei) for ei in [e0, e1]]
sage: e0r, e1r
(sqrt(2)*|0>/2 + sqrt(2)*|1>/2, sqrt(2)*|0>/2 - sqrt(2)*|1>/2)

sage: qapply(Dagger(e0r)*e0r)
1
sage: qapply(Dagger(e0r)*e1r) 
0
sage: qapply(Dagger(e1r)*e0r) 
0
sage: qapply(Dagger(e1r)*e1r) 
1

sage: from sympy import Symbol, cos, sin, exp, I
sage: theta = Symbol('theta', real=True); phi = Symbol('varphi', real=True)
sage: Q = cos(theta)*e0 + exp(I*phi)*sin(theta)*e1; Q
exp(I*phi)*sin(theta)*|1> + cos(theta)*|0>
sage: simplify(qapply(Dagger(Q)*Q))
1

The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

Edit: The functionality actually exists, but it requires a systematic application of the qapply method.

First, suppose that we want to just rotate the qubit. We can apply the Hadamard coin as follows:

sage: from sympy.physics.quantum import qapply
sage: from sympy.physics.quantum.gate import H
sage: [e0r, e1r] = [qapply(H(0)*ei) for ei in [e0, e1]]
sage: e0r, e1r
(sqrt(2)*|0>/2 + sqrt(2)*|1>/2, sqrt(2)*|0>/2 - sqrt(2)*|1>/2)

and

sage: qapply(Dagger(e0r)*e0r)
1
sage: qapply(Dagger(e0r)*e1r) 
0
sage: qapply(Dagger(e1r)*e0r) 
0
sage: qapply(Dagger(e1r)*e1r) 
1

Linear combinations are also valid, but remember to qapply:

sage: from sympy import Symbol, cos, sin, exp, I
sage: theta = Symbol('theta', real=True); phi = Symbol('varphi', real=True)
sage: Q = cos(theta)*e0 + exp(I*phi)*sin(theta)*e1; Q
exp(I*phi)*sin(theta)*|1> + cos(theta)*|0>
sage: simplify(qapply(Dagger(Q)*Q))
1

Those imports are to avoid the missing conversion (AttributeError) for the Qubit class, for instance if you type qapply(sympify(x*e0)). Alternatively Alternatively, you may sympify the Sage expressions.

The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

Edit: The functionality actually exists, but it requires a systematic application of the qapply method.

First, suppose that we want to just rotate the qubit. We can apply the Hadamard coin as follows:

sage: from sympy.physics.quantum import qapply
sage: from sympy.physics.quantum.gate import H
sage: [e0r, e1r] = [qapply(H(0)*ei) for ei in [e0, e1]]
sage: e0r, e1r
(sqrt(2)*|0>/2 + sqrt(2)*|1>/2, sqrt(2)*|0>/2 - sqrt(2)*|1>/2)

and

sage: qapply(Dagger(e0r)*e0r)
1
sage: qapply(Dagger(e0r)*e1r) 
0
sage: qapply(Dagger(e1r)*e0r) 
0
sage: qapply(Dagger(e1r)*e1r) 
1

Linear combinations are also valid, but remember to qapply:

sage: from sympy import Symbol, cos, sin, exp, I
sage: theta = Symbol('theta', real=True); phi = Symbol('varphi', real=True)
sage: Q = cos(theta)*e0 + exp(I*phi)*sin(theta)*e1; Q
exp(I*phi)*sin(theta)*|1> + cos(theta)*|0>
sage: simplify(qapply(Dagger(Q)*Q))
1

Those imports are to avoid the missing conversion (AttributeError) for the Qubit class, for instance if you type qapply(sympify(x*e0))qapply(x*e0). Alternatively, you may sympify the Sage expressions.

The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

Edit: The functionality actually exists, but it requires a systematic application of the qapply method.

First, suppose that we want to just rotate the qubit. We can apply the Hadamard coin as follows:

sage: from sympy.physics.quantum import qapply
sage: from sympy.physics.quantum.gate import H

sage: # the argument passed to H is the target qubit (starting at 0, as usual)
sage: [e0r, e1r] = [qapply(H(0)*ei) for ei in [e0, e1]]
e1]]    
sage: e0r, e1r
(sqrt(2)*|0>/2 + sqrt(2)*|1>/2, sqrt(2)*|0>/2 - sqrt(2)*|1>/2)

and

sage: qapply(Dagger(e0r)*e0r)
1
sage: qapply(Dagger(e0r)*e1r) 
0
sage: qapply(Dagger(e1r)*e0r) 
0
sage: qapply(Dagger(e1r)*e1r) 
1

Linear combinations are also valid, but remember to qapply:

sage: from sympy import Symbol, cos, sin, exp, I
sage: theta = Symbol('theta', real=True); phi = Symbol('varphi', real=True)
sage: Q = cos(theta)*e0 + exp(I*phi)*sin(theta)*e1; Q
exp(I*phi)*sin(theta)*|1> + cos(theta)*|0>
sage: simplify(qapply(Dagger(Q)*Q))
1

Those imports are to avoid the missing conversion (AttributeError) for the Qubit class, for instance if you type qapply(x*e0). Alternatively, you may sympify the Sage expressions.

The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

Edit: The functionality actually exists, but it requires a systematic application of the qapply method.

First, suppose that we want to just rotate the qubit. We can apply the Hadamard coin as follows:

sage: from sympy.physics.quantum import qapply
sage: from sympy.physics.quantum.gate import H

sage: # the argument passed to H is the target qubit (starting at 0, as usual)
sage: [e0r, e1r] = [qapply(H(0)*ei) for ei in [e0, e1]]    
sage: e0r, e1r
(sqrt(2)*|0>/2 + sqrt(2)*|1>/2, sqrt(2)*|0>/2 - sqrt(2)*|1>/2)

and

sage: qapply(Dagger(e0r)*e0r)
1
sage: qapply(Dagger(e0r)*e1r) 
0
sage: qapply(Dagger(e1r)*e0r) 
0
sage: qapply(Dagger(e1r)*e1r) 
1

Linear combinations are also valid, but remember to qapply:

sage: from sympy import Symbol, cos, sin, exp, I
sage: theta = Symbol('theta', real=True); phi = Symbol('varphi', real=True)
sage: Q = cos(theta)*e0 + exp(I*phi)*sin(theta)*e1; Q
exp(I*phi)*sin(theta)*|1> + cos(theta)*|0>
sage: simplify(qapply(Dagger(Q)*Q))
1

Those imports are to avoid the missing conversion (AttributeError) for the Qubit class, for instance if you type qapply(x*e0). Alternatively, you may sympify the Sage expressions.

Since the Pauli matrices X, Y, Z can also be imported, it is possible to perform an arbitrary operation on a qubit. Multiple qubits can be handled similarly; there are some examples in the package's package documentation.

The Qubit constructor can be used to define an orthonormal basis. The scalar product can be actually computed with the doit() method. For example:

sage: from sympy.physics.quantum.qubit import Qubit
sage: from sympy.physics.quantum import Dagger
sage: e0 = Qubit('0'); e1 = Qubit('1')
sage: c = Dagger(e0)*e1; c
<0|1>
sage: c.doit()
0
sage: (Dagger(e1)*e1).doit()
1
sage: (Dagger(e1)*e0).doit()
0

Edit: The functionality actually exists, but it requires a systematic application use of the qapply method..

First, suppose that we want to just rotate the qubit. We can apply the Hadamard coin as follows:

sage: from sympy.physics.quantum import qapply
sage: from sympy.physics.quantum.gate import H

sage: # the argument passed to H is the target qubit (starting at 0, as usual)
sage: [e0r, e1r] = [qapply(H(0)*ei) for ei in [e0, e1]]    
sage: e0r, e1r
(sqrt(2)*|0>/2 + sqrt(2)*|1>/2, sqrt(2)*|0>/2 - sqrt(2)*|1>/2)

and

sage: qapply(Dagger(e0r)*e0r)
1
sage: qapply(Dagger(e0r)*e1r) 
0
sage: qapply(Dagger(e1r)*e0r) 
0
sage: qapply(Dagger(e1r)*e1r) 
1

Linear combinations are also valid, but valid (but remember to qapply:):

sage: from sympy import Symbol, cos, sin, exp, I
sage: theta = Symbol('theta', real=True); phi = Symbol('varphi', real=True)
sage: Q = cos(theta)*e0 + exp(I*phi)*sin(theta)*e1; Q
exp(I*phi)*sin(theta)*|1> + cos(theta)*|0>
sage: simplify(qapply(Dagger(Q)*Q))
1

Those imports are to avoid the missing conversion (AttributeError) for the Qubit class, for instance if you type qapply(x*e0). Alternatively, you may sympify the Sage expressions.

Since the Pauli matrices X, Y, Z can also be imported, it is possible to perform an arbitrary operation on a qubit. Multiple qubits can be handled similarly; there are some examples in the package documentation.