Qubit¶
Qubits for quantum computing.
Todo: * Finish implementing measurement logic. This should include POVM. * Update docstrings. * Update tests.
- class sympy.physics.quantum.qubit.IntQubit(*args, **kwargs)[source]¶
A qubit ket that store integers as binary numbers in qubit values.
The differences between this class and
Qubit
are:The form of the constructor.
The qubit values are printed as their corresponding integer, rather than the raw qubit values. The internal storage format of the qubit values in the same as
Qubit
.
- Parameters
values : int, tuple
If a single argument, the integer we want to represent in the qubit values. This integer will be represented using the fewest possible number of qubits. If a pair of integers and the second value is more than one, the first integer gives the integer to represent in binary form and the second integer gives the number of qubits to use. List of zeros and ones is also accepted to generate qubit by bit pattern.
nqubits : int
The integer that represents the number of qubits. This number should be passed with keyword
nqubits=N
. You can use this in order to avoid ambiguity of Qubit-style tuple of bits. Please see the example below for more details.
Examples
Create a qubit for the integer 5:
>>> from sympy.physics.quantum.qubit import IntQubit >>> from sympy.physics.quantum.qubit import Qubit >>> q = IntQubit(5) >>> q |5>
We can also create an
IntQubit
by passing aQubit
instance.>>> q = IntQubit(Qubit('101')) >>> q |5> >>> q.as_int() 5 >>> q.nqubits 3 >>> q.qubit_values (1, 0, 1)
We can go back to the regular qubit form.
>>> Qubit(q) |101>
Please note that
IntQubit
also accepts aQubit
-style list of bits. So, the code below yields qubits 3, not a single bit1
.>>> IntQubit(1, 1) |3>
To avoid ambiguity, use
nqubits
parameter. Use of this keyword is recommended especially when you provide the values by variables.>>> IntQubit(1, nqubits=1) |1> >>> a = 1 >>> IntQubit(a, nqubits=1) |1>
- class sympy.physics.quantum.qubit.IntQubitBra(*args, **kwargs)[source]¶
A qubit bra that store integers as binary numbers in qubit values.
- class sympy.physics.quantum.qubit.Qubit(*args, **kwargs)[source]¶
A multi-qubit ket in the computational (z) basis.
We use the normal convention that the least significant qubit is on the right, so
|00001>
has a 1 in the least significant qubit.- Parameters
values : list, str
The qubit values as a list of ints ([0,0,0,1,1,]) or a string (‘011’).
Examples
Create a qubit in a couple of different ways and look at their attributes:
>>> from sympy.physics.quantum.qubit import Qubit >>> Qubit(0,0,0) |000> >>> q = Qubit('0101') >>> q |0101>
>>> q.nqubits 4 >>> len(q) 4 >>> q.dimension 4 >>> q.qubit_values (0, 1, 0, 1)
We can flip the value of an individual qubit:
>>> q.flip(1) |0111>
We can take the dagger of a Qubit to get a bra:
>>> from sympy.physics.quantum.dagger import Dagger >>> Dagger(q) <0101| >>> type(Dagger(q)) <class 'sympy.physics.quantum.qubit.QubitBra'>
Inner products work as expected:
>>> ip = Dagger(q)*q >>> ip <0101|0101> >>> ip.doit() 1
- class sympy.physics.quantum.qubit.QubitBra(*args, **kwargs)[source]¶
A multi-qubit bra in the computational (z) basis.
We use the normal convention that the least significant qubit is on the right, so
|00001>
has a 1 in the least significant qubit.- Parameters
values : list, str
The qubit values as a list of ints ([0,0,0,1,1,]) or a string (‘011’).
See also
Qubit
Examples using qubits
- sympy.physics.quantum.qubit.matrix_to_density(mat)[source]¶
Works by finding the eigenvectors and eigenvalues of the matrix. We know we can decompose rho by doing: sum(EigenVal*|Eigenvect><Eigenvect|)
- sympy.physics.quantum.qubit.matrix_to_qubit(matrix)[source]¶
Convert from the matrix repr. to a sum of Qubit objects.
- Parameters
matrix : Matrix, numpy.matrix, scipy.sparse
The matrix to build the Qubit representation of. This works with sympy matrices, numpy matrices and scipy.sparse sparse matrices.
Examples
Represent a state and then go back to its qubit form:
>>> from sympy.physics.quantum.qubit import matrix_to_qubit, Qubit >>> from sympy.physics.quantum.represent import represent >>> q = Qubit('01') >>> matrix_to_qubit(represent(q)) |01>
- sympy.physics.quantum.qubit.measure_all(qubit, format='sympy', normalize=True)[source]¶
Perform an ensemble measurement of all qubits.
- Parameters
qubit : Qubit, Add
The qubit to measure. This can be any Qubit or a linear combination of them.
format : str
The format of the intermediate matrices to use. Possible values are (‘sympy’,’numpy’,’scipy.sparse’). Currently only ‘sympy’ is implemented.
- Returns
result : list
A list that consists of primitive states and their probabilities.
Examples
>>> from sympy.physics.quantum.qubit import Qubit, measure_all >>> from sympy.physics.quantum.gate import H >>> from sympy.physics.quantum.qapply import qapply
>>> c = H(0)*H(1)*Qubit('00') >>> c H(0)*H(1)*|00> >>> q = qapply(c) >>> measure_all(q) [(|00>, 1/4), (|01>, 1/4), (|10>, 1/4), (|11>, 1/4)]
- sympy.physics.quantum.qubit.measure_all_oneshot(qubit, format='sympy')[source]¶
Perform a oneshot ensemble measurement on all qubits.
A oneshot measurement is equivalent to performing a measurement on a quantum system. This type of measurement does not return the probabilities like an ensemble measurement does, but rather returns one of the possible resulting states. The exact state that is returned is determined by picking a state randomly according to the ensemble probabilities.
- Parameters
qubits : Qubit
The qubit to measure. This can be any Qubit or a linear combination of them.
format : str
The format of the intermediate matrices to use. Possible values are (‘sympy’,’numpy’,’scipy.sparse’). Currently only ‘sympy’ is implemented.
- Returns
result : Qubit
The qubit that the system collapsed to upon measurement.
- sympy.physics.quantum.qubit.measure_partial(qubit, bits, format='sympy', normalize=True)[source]¶
Perform a partial ensemble measure on the specified qubits.
- Parameters
qubits : Qubit
The qubit to measure. This can be any Qubit or a linear combination of them.
bits : tuple
The qubits to measure.
format : str
The format of the intermediate matrices to use. Possible values are (‘sympy’,’numpy’,’scipy.sparse’). Currently only ‘sympy’ is implemented.
- Returns
result : list
A list that consists of primitive states and their probabilities.
Examples
>>> from sympy.physics.quantum.qubit import Qubit, measure_partial >>> from sympy.physics.quantum.gate import H >>> from sympy.physics.quantum.qapply import qapply
>>> c = H(0)*H(1)*Qubit('00') >>> c H(0)*H(1)*|00> >>> q = qapply(c) >>> measure_partial(q, (0,)) [(sqrt(2)*|00>/2 + sqrt(2)*|10>/2, 1/2), (sqrt(2)*|01>/2 + sqrt(2)*|11>/2, 1/2)]
- sympy.physics.quantum.qubit.measure_partial_oneshot(qubit, bits, format='sympy')[source]¶
Perform a partial oneshot measurement on the specified qubits.
A oneshot measurement is equivalent to performing a measurement on a quantum system. This type of measurement does not return the probabilities like an ensemble measurement does, but rather returns one of the possible resulting states. The exact state that is returned is determined by picking a state randomly according to the ensemble probabilities.
- Parameters
qubits : Qubit
The qubit to measure. This can be any Qubit or a linear combination of them.
bits : tuple
The qubits to measure.
format : str
The format of the intermediate matrices to use. Possible values are (‘sympy’,’numpy’,’scipy.sparse’). Currently only ‘sympy’ is implemented.
- Returns
result : Qubit
The qubit that the system collapsed to upon measurement.