Expression of type Equals

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 ExprRange, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(t)
sub_expr3 = frac(one, sqrt(two))
expr = Equals(Len(operands = [Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1)))), ExprRange(sub_expr1, Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(sub_expr2, two), zero)]), t).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} |\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)} 
} \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 + 2\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \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 + 3\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \ldots, \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^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}\right)| \\  = t \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(1)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 73
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 15 operands: 8
7	ExprRange	lambda_map: 9 start_index: 10 end_index: 39
8	NamedExprs	state: 11
9	Lambda	parameter: 70 body: 12
10	Operation	operator: 65 operands: 13
11	Operation	operator: 35 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	68, 63
14	ExprTuple	22, 17
15	Literal
16	NamedExprs	state: 18
17	Operation	operator: 26 operands: 19
18	Operation	operator: 35 operands: 20
19	ExprTuple	30, 21
20	ExprTuple	22, 23
21	Operation	operator: 35 operands: 24
22	Operation	operator: 43 operands: 25
23	Operation	operator: 26 operands: 27
24	ExprTuple	28, 41
25	ExprTuple	69, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 60 operands: 32
29	Operation	operator: 60 operands: 33
30	Operation	operator: 46 operand: 39
31	Operation	operator: 35 operands: 36
32	ExprTuple	49, 37
33	ExprTuple	63, 38
34	ExprTuple	39
35	Literal
36	ExprTuple	40, 41
37	Operation	operator: 52 operands: 42
38	Operation	operator: 43 operands: 44
39	Literal
40	Operation	operator: 60 operands: 45
41	Operation	operator: 46 operand: 69
42	ExprTuple	63, 55, 56, 48, 58
43	Literal
44	ExprTuple	69, 63
45	ExprTuple	49, 50
46	Literal
47	ExprTuple	69
48	Operation	operator: 60 operands: 51
49	Literal
50	Operation	operator: 52 operands: 53
51	ExprTuple	63, 54
52	Literal
53	ExprTuple	63, 55, 56, 57, 58
54	Operation	operator: 71 operand: 62
55	Literal
56	Literal
57	Operation	operator: 60 operands: 61
58	Literal
59	ExprTuple	62
60	Literal
61	ExprTuple	63, 64
62	Operation	operator: 65 operands: 66
63	Literal
64	Operation	operator: 71 operand: 70
65	Literal
66	ExprTuple	68, 69
67	ExprTuple	70
68	Operation	operator: 71 operand: 73
69	Literal
70	Variable
71	Literal
72	ExprTuple	73
73	Variable