# cirq.flatten¶

cirq.flatten(val: Any) → Tuple[Any, cirq.study.flatten_expressions.ExpressionMap][source]
Creates a copy of val with any symbols or expressions replaced with
new symbols. val can be a Circuit, Gate, Operation, or other
type.

flatten goes through every parameter in val and does the following:

• If the parameter is a number, don’t change it.

• If the parameter is a symbol, don’t change it.

• If the parameter is an expression, replace it with a symbol. The new symbol will be sympy.Symbol('<x + 1>') if the expression was sympy.Symbol('x') + 1. In the unlikely case that an expression with a different meaning also has the string 'x + 1', a number is appended to the name to avoid collision: sympy.Symbol('<x + 1>_1').

This function also creates a dictionary mapping from expressions and symbols
in val to the new symbols in the flattened copy of val. E.g
cirq.ExpressionMap({sympy.Symbol('x')+1: sympy.Symbol('<x + 1>')}). This
ExpressionMap can be used to transform a sweep over the symbols in val
to a sweep over the flattened symbols e.g. a sweep over sympy.Symbol('x')
to a sweep over sympy.Symbol('<x + 1>').
Parameters
• val – The value to copy and substitute parameter expressions with

• symbols. (flattened) –

Returns

The tuple (new value, expression map) where new value and expression map are described above.

Examples

>>> qubit = cirq.LineQubit(0)
>>> a = sympy.Symbol('a')
>>> circuit = cirq.Circuit(
...     cirq.X(qubit) ** (a/4),
...     cirq.Y(qubit) ** (1-a/2),
... )
>>> print(circuit)
0: ───X^(a/4)───Y^(1 - a/2)───

>>> sweep = cirq.Linspace(a, start=0, stop=3, length=4)
>>> print(cirq.ListSweep(sweep))
Sweep:
{'a': 0.0}
{'a': 1.0}
{'a': 2.0}
{'a': 3.0}

>>> c_flat, expr_map = cirq.flatten(circuit)
>>> print(c_flat)
0: ───X^(<a/4>)───Y^(<1 - a/2>)───
>>> expr_map
cirq.ExpressionMap({a/4: <a/4>, 1 - a/2: <1 - a/2>})

>>> new_sweep = expr_map.transform_sweep(sweep)
>>> print(new_sweep)
Sweep:
{'<a/4>': 0.0, '<1 - a/2>': 1.0}
{'<a/4>': 0.25, '<1 - a/2>': 0.5}
{'<a/4>': 0.5, '<1 - a/2>': 0.0}
{'<a/4>': 0.75, '<1 - a/2>': -0.5}

>>> for params in sweep:  # Original
...     print(circuit,
...           '=>',
...           cirq.resolve_parameters(circuit, params))
0: ───X^(a/4)───Y^(1 - a/2)─── => 0: ───X^0───Y───
0: ───X^(a/4)───Y^(1 - a/2)─── => 0: ───X^0.25───Y^0.5───
0: ───X^(a/4)───Y^(1 - a/2)─── => 0: ───X^0.5───Y^0───
0: ───X^(a/4)───Y^(1 - a/2)─── => 0: ───X^0.75───Y^-0.5───

>>> for params in new_sweep:  # Flattened
...     print(c_flat, '=>', end=' ')
...     print(cirq.resolve_parameters(c_flat, params))
0: ───X^(<a/4>)───Y^(<1 - a/2>)─── => 0: ───X^0───Y───
0: ───X^(<a/4>)───Y^(<1 - a/2>)─── => 0: ───X^0.25───Y^0.5───
0: ───X^(<a/4>)───Y^(<1 - a/2>)─── => 0: ───X^0.5───Y^0───
0: ───X^(<a/4>)───Y^(<1 - a/2>)─── => 0: ───X^0.75───Y^-0.5───