cirq.SumOfProducts

Represents control values as AND (product) clauses, each of which applies to all N qubits.

SumOfProducts representation describes the control values as a union of n-bit tuples, where each n-bit tuple represents an allowed assignment of bits for which the control should be activated. This expanded representation allows us to create control values combinations which cannot be factored as a ProductOfSums representation.

For example:

1) (|00><00| + |11><11|) X + (|01><01| + |10><10|) I represents an operator which flips the third qubit if the first two qubits are 00 or 11, and does nothing otherwise. This can be constructed as

```
>>> xor_control_values = cirq.SumOfProducts(((0, 0), (1, 1)))
>>> q0, q1, q2 = cirq.LineQubit.range(3)
>>> xor_cop = cirq.X(q2).controlled_by(q0, q1, control_values=xor_control_values)
```

2) (|00><00| + |01><01| + |10><10|) X + (|11><11|) I represents an operators which flips the third qubit if the nand of first two qubits is 1 (i.e. first two qubits are either 00, 01 or 10), and does nothing otherwise. This can be constructed as:

    nand_control_values = cirq.SumOfProducts(((0, 0), (0, 1), (1, 0)))
    q0, q1, q2 = cirq.LineQubit.range(3)
    nand_cop = cirq.X(q2).controlled_by(q0, q1, control_values=nand_control_values)
        

is_trivial

Methods

expand

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Returns an expanded cirq.SumOfProduct representation of this control values.

validate

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Validates that all control values for ith qubit are in range [0, qid_shaped[i])

__and__

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Returns a cartesian product of all control values predicates in self x other.

The and of two control values cv1 and cv2 represents a control value object acting on the union of qubits represented by cv1 and cv2. For example:

cv1 = cirq.ProductOfSums([(0, 1), 2])
cv2 = cirq.SumOfProducts([[0, 0], [1, 1]])
assert cirq.num_qubits(cv1 & cv2) == cirq.num_qubits(cv1) + cirq.num_qubits(cv2)

Args
other An instance of AbstractControlValues.

Returns
An instance of AbstractControlValues that represents the cartesian product of control values represented by self and other.

__eq__

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__iter__

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Returns the combinations tracked by the object.

__ne__

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__or__

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Returns a union of all control values predicates in self + other.

Both self and other must represent control values for the same set of qubits and hence their or would also be a control value object acting on the same set of qubits. For example:

cv1 = cirq.ProductOfSums([(0, 1), 2])
cv2 = cirq.SumOfProducts([[0, 0], [1, 1]])
assert cirq.num_qubits(cv1 | cv2) == cirq.num_qubits(cv1) == cirq.num_qubits(cv2)

Args
other An instance of AbstractControlValues.

Returns
An instance of AbstractControlValues that represents the union of control values represented by self and other.

Raises
ValueError If cirq.num_qubits(self) != cirq.num_qubits(other).