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 = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))
expr = ExprTuple(MultiQubitElem(element = Output(state = sub_expr3, part = one), targets = Interval(sub_expr2, sub_expr2)), Output(state = sub_expr3))

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}~\{{_{-}a} + t~\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)} 
} \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: 3 operands: 4
2	Operation	operator: 8 operands: 5
3	Literal
4	NamedExprs	element: 6 targets: 7
5	NamedExprs	state: 12
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	NamedExprs	state: 12 part: 41
10	Literal
11	ExprTuple	13, 13
12	Operation	operator: 28 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	54, 19
17	Operation	operator: 34 operands: 20
18	Operation	operator: 21 operands: 22
19	Variable
20	ExprTuple	41, 23
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 48 operands: 26
24	Operation	operator: 37 operand: 31
25	Operation	operator: 28 operands: 29
26	ExprTuple	50, 30
27	ExprTuple	31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Operation	operator: 48 operands: 36
33	Operation	operator: 37 operand: 41
34	Literal
35	ExprTuple	41, 50
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41
39	Literal
40	Operation	operator: 42 operands: 43
41	Literal
42	Literal
43	ExprTuple	50, 44, 45, 46, 47
44	Literal
45	Literal
46	Operation	operator: 48 operands: 49
47	Literal
48	Literal
49	ExprTuple	50, 51
50	Literal
51	Operation	operator: 52 operand: 54
52	Literal
53	ExprTuple	54
54	Variable