Expression of type QcircuitEquiv

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, VertExprArray, t
from proveit.linear_algebra import ScalarMult, VecAdd
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 _ket_u, _phase, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output, Qcircuit, QcircuitEquiv

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(Neg(t), one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, _s))), one, _s).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray(Variable("_b", latex_format = r"{_{-}b}"))))

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^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
& \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
& \qout{\vdots} \\
& \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)} \\
& \qout{\lvert u \rangle}
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\{_{-}b} \\ \downarrow\end{array}} & \qw
} \end{array}\right)

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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Variable
10	ExprRange	lambda_map: 12 start_index: 13 end_index: 52
11	ExprRange	lambda_map: 14 start_index: 62 end_index: 46
12	Lambda	parameter: 75 body: 15
13	Operation	operator: 40 operands: 16
14	Lambda	parameter: 75 body: 17
15	Operation	operator: 27 operands: 18
16	ExprTuple	19, 62
17	Operation	operator: 20 operands: 21
18	NamedExprs	state: 22
19	Operation	operator: 73 operand: 45
20	Literal
21	NamedExprs	element: 24 targets: 25
22	Operation	operator: 49 operands: 26
23	ExprTuple	45
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	31, 32
27	Literal
28	NamedExprs	state: 33 part: 75
29	Literal
30	ExprTuple	34, 35
31	Operation	operator: 55 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	Operation	operator: 40 operands: 39
35	Operation	operator: 40 operands: 41
36	ExprTuple	62, 42
37	Literal
38	ExprTuple	43, 44
39	ExprTuple	45, 62
40	Literal
41	ExprTuple	45, 46
42	Operation	operator: 69 operands: 47
43	Operation	operator: 58 operand: 52
44	Operation	operator: 49 operands: 50
45	Variable
46	Literal
47	ExprTuple	71, 51
48	ExprTuple	52
49	Literal
50	ExprTuple	53, 54
51	Operation	operator: 55 operands: 56
52	Literal
53	Operation	operator: 69 operands: 57
54	Operation	operator: 58 operand: 62
55	Literal
56	ExprTuple	62, 71
57	ExprTuple	60, 61
58	Literal
59	ExprTuple	62
60	Literal
61	Operation	operator: 63 operands: 64
62	Literal
63	Literal
64	ExprTuple	71, 65, 66, 67, 68
65	Literal
66	Literal
67	Operation	operator: 69 operands: 70
68	Literal
69	Literal
70	ExprTuple	71, 72
71	Literal
72	Operation	operator: 73 operand: 75
73	Literal
74	ExprTuple	75
75	Variable