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 ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(sub_expr1, t)
sub_expr3 = Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), part = one)
expr = ExprTuple(MultiQubitElem(element = sub_expr3, targets = Interval(Add(Add(sub_expr1, Neg(one), t), one), sub_expr2)), MultiQubitElem(element = sub_expr3, targets = Interval(sub_expr2, sub_expr2)))

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\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)~\mbox{part}~1~\mbox{on}~\{\left({_{-}a} - 1 + t\right) + 1~\ldotp \ldotp~{_{-}a} + t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\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)~\mbox{part}~1~\mbox{on}~\{{_{-}a} + t~\ldotp \ldotp~{_{-}a} + t\}} 
} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	NamedExprs	element: 7 targets: 6
4	Literal
5	NamedExprs	element: 7 targets: 8
6	Operation	operator: 12 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 16
10	Literal
11	NamedExprs	state: 15 part: 48
12	Literal
13	ExprTuple	16, 16
14	Operation	operator: 23 operands: 17
15	Operation	operator: 35 operands: 18
16	Operation	operator: 23 operands: 19
17	ExprTuple	20, 48
18	ExprTuple	21, 22
19	ExprTuple	61, 29
20	Operation	operator: 23 operands: 24
21	Operation	operator: 41 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	ExprTuple	61, 28, 29
25	ExprTuple	48, 30
26	Literal
27	ExprTuple	31, 32
28	Operation	operator: 59 operand: 48
29	Variable
30	Operation	operator: 55 operands: 33
31	Operation	operator: 44 operand: 38
32	Operation	operator: 35 operands: 36
33	ExprTuple	57, 37
34	ExprTuple	38
35	Literal
36	ExprTuple	39, 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Operation	operator: 55 operands: 43
40	Operation	operator: 44 operand: 48
41	Literal
42	ExprTuple	48, 57
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48
46	Literal
47	Operation	operator: 49 operands: 50
48	Literal
49	Literal
50	ExprTuple	57, 51, 52, 53, 54
51	Literal
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	57, 58
57	Literal
58	Operation	operator: 59 operand: 61
59	Literal
60	ExprTuple	61
61	Variable