# from the theory of proveit.physics.quantum.QPE¶

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.
# import Expression classes needed to build the expression
from proveit import Lambda, Variable, l
from proveit.numbers import Interval, one
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import ModAdd, _b_floor, _t
from proveit.physics.quantum.circuits import MultiQubitElem, Output

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, MultiQubitElem(element = Output(state = NumKet(ModAdd(_b_floor, l), _t), part = sub_expr1), targets = Interval(one, _t)))

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())

{_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert b_{\textit{f}} \oplus l \rangle_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}}
} \end{array}

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameter: 12
body: 2
1ExprTuple12
2Operationoperator: 3
operands: 4
3Literal
4NamedExprselement: 5
targets: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
part: 12
9Literal
10ExprTuple13, 17
11Operationoperator: 14
operands: 15
12Variable
13Literal
14Literal
15ExprTuple16, 17
16Operationoperator: 18
operands: 19
17Literal
18Literal
19ExprTuple20, 21
20Literal
21Variable