from the theory of proveit.physics.quantum.QFT¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import n
from proveit.linear_algebra import Unitary
from proveit.logic import Forall, InSet
from proveit.numbers import Exp, NaturalPos, two
from proveit.physics.quantum.QFT import InverseFourierTransform

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = InSet(InverseFourierTransform(n), Unitary(Exp(two, n))), domain = NaturalPos)

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{n \in \mathbb{N}^+}~\left({\mathrm {FT}}^{\dag}_{n} \in \textrm{U}\left(2^{n}\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 21
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple21, 12
10Operationoperator: 13
operand: 21
11Operationoperator: 15
operand: 17
12Literal
13Literal
14ExprTuple21
15Literal
16ExprTuple17
17Operationoperator: 18
operands: 19
18Literal
19ExprTuple20, 21
20Literal
21Variable