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

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^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~1\}} 
} \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^{-\left(-t + 1\right)} \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: 52
10	Literal
11	ExprTuple	52, 52
12	Operation	operator: 24 operands: 13
13	ExprTuple	14, 15
14	Operation	operator: 30 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	52, 19
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 43 operands: 22
20	Operation	operator: 33 operand: 27
21	Operation	operator: 24 operands: 25
22	ExprTuple	45, 26
23	ExprTuple	27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operands: 31
27	Literal
28	Operation	operator: 43 operands: 32
29	Operation	operator: 33 operand: 52
30	Literal
31	ExprTuple	52, 45
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	52
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	45, 39, 40, 41, 42
39	Literal
40	Literal
41	Operation	operator: 43 operands: 44
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Operation	operator: 53 operand: 48
47	ExprTuple	48
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Operation	operator: 53 operand: 55
52	Literal
53	Literal
54	ExprTuple	55
55	Variable