Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left({_{-}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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 59 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	59, 10
8	Operation	operator: 31 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16, 17
12	Literal
13	ExprTuple	18, 55
14	Literal
15	ExprTuple	19, 35
16	Operation	operator: 39 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Operation	operator: 23 operands: 24
20	ExprTuple	46, 25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	28, 46
25	Operation	operator: 53 operands: 29
26	Operation	operator: 42 operand: 35
27	Operation	operator: 31 operands: 32
28	Operation	operator: 57 operand: 38
29	ExprTuple	55, 34
30	ExprTuple	35
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	38
34	Operation	operator: 39 operands: 40
35	Literal
36	Operation	operator: 53 operands: 41
37	Operation	operator: 42 operand: 46
38	Variable
39	Literal
40	ExprTuple	46, 55
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	46
44	Literal
45	Operation	operator: 47 operands: 48
46	Literal
47	Literal
48	ExprTuple	55, 49, 50, 51, 52
49	Literal
50	Literal
51	Operation	operator: 53 operands: 54
52	Literal
53	Literal
54	ExprTuple	55, 56
55	Literal
56	Operation	operator: 57 operand: 59
57	Literal
58	ExprTuple	59
59	Variable