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 t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, 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 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 = Equals(MultiQubitElem(element = Output(state = sub_expr1, part = one), targets = Interval(Add(zero, 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())

\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}~\{0 + 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}

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