Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

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 Conditional, Lambda, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import QubitSpace, ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, Conditional(InSet(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), QubitSpace), InSet(sub_expr1, Interval(Add(Neg(t), one), zero))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

{_{-}a} \mapsto \left\{\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2} \textrm{ if } {_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 58 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	58, 9
7	Operation	operator: 30 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	17, 54
13	Literal
14	ExprTuple	18, 34
15	Operation	operator: 38 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Operation	operator: 22 operands: 23
19	ExprTuple	45, 24
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	27, 45
24	Operation	operator: 52 operands: 28
25	Operation	operator: 41 operand: 34
26	Operation	operator: 30 operands: 31
27	Operation	operator: 56 operand: 37
28	ExprTuple	54, 33
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	37
33	Operation	operator: 38 operands: 39
34	Literal
35	Operation	operator: 52 operands: 40
36	Operation	operator: 41 operand: 45
37	Variable
38	Literal
39	ExprTuple	45, 54
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Literal
44	Operation	operator: 46 operands: 47
45	Literal
46	Literal
47	ExprTuple	54, 48, 49, 50, 51
48	Literal
49	Literal
50	Operation	operator: 52 operands: 53
51	Literal
52	Literal
53	ExprTuple	54, 55
54	Literal
55	Operation	operator: 56 operand: 58
56	Literal
57	ExprTuple	58
58	Variable