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, m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, MultiQubitElem, Output, Qcircuit, QcircuitEquiv

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, _t)
sub_expr3 = Add(_t, one)
sub_expr4 = Add(_t, _s)
sub_expr5 = Interval(sub_expr3, sub_expr4)
sub_expr6 = [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire]
sub_expr7 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)], sub_expr6, sub_expr8)), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr7, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr7, sub_expr3, sub_expr4).with_wrapping_at(2,6)], sub_expr6, sub_expr8))).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{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) \\  \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{4}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) \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, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 10, 11
6	Literal
7	ExprTuple	9, 10, 11
8	ExprTuple	12, 13
9	ExprTuple	14, 15
10	ExprTuple	16, 17
11	ExprTuple	18, 19
12	ExprRange	lambda_map: 20 start_index: 80 end_index: 81
13	ExprRange	lambda_map: 21 start_index: 80 end_index: 82
14	ExprRange	lambda_map: 22 start_index: 80 end_index: 81
15	ExprRange	lambda_map: 22 start_index: 68 end_index: 69
16	ExprRange	lambda_map: 23 start_index: 80 end_index: 81
17	ExprRange	lambda_map: 24 start_index: 80 end_index: 82
18	ExprRange	lambda_map: 25 start_index: 80 end_index: 81
19	ExprRange	lambda_map: 26 start_index: 80 end_index: 82
20	Lambda	parameter: 67 body: 27
21	Lambda	parameter: 67 body: 28
22	Lambda	parameter: 67 body: 29
23	Lambda	parameter: 67 body: 30
24	Lambda	parameter: 67 body: 31
25	Lambda	parameter: 67 body: 32
26	Lambda	parameter: 67 body: 34
27	Operation	operator: 43 operands: 35
28	Operation	operator: 43 operands: 36
29	Operation	operator: 43 operands: 37
30	Operation	operator: 38 operands: 39
31	Operation	operator: 40 operands: 41
32	Operation	operator: 43 operands: 42
33	ExprTuple	67
34	Operation	operator: 43 operands: 44
35	NamedExprs	element: 45 targets: 52
36	NamedExprs	element: 46 targets: 54
37	NamedExprs	element: 47 targets: 48
38	Literal
39	NamedExprs	basis: 49
40	Literal
41	NamedExprs	operation: 50
42	NamedExprs	element: 51 targets: 52
43	Literal
44	NamedExprs	element: 53 targets: 54
45	Operation	operator: 56 operands: 55
46	Operation	operator: 56 operands: 62
47	Operation	operator: 56 operands: 57
48	Operation	operator: 63 operands: 58
49	Literal
50	Literal
51	Operation	operator: 61 operands: 59
52	Operation	operator: 63 operands: 60
53	Operation	operator: 61 operands: 62
54	Operation	operator: 63 operands: 64
55	NamedExprs	state: 77 part: 67
56	Literal
57	NamedExprs	state: 65 part: 67
58	ExprTuple	80, 69
59	NamedExprs	state: 66 part: 67
60	ExprTuple	80, 81
61	Literal
62	NamedExprs	state: 78 part: 67
63	Literal
64	ExprTuple	68, 69
65	Operation	operator: 70 operands: 71
66	Operation	operator: 72 operands: 73
67	Variable
68	Operation	operator: 75 operands: 74
69	Operation	operator: 75 operands: 76
70	Literal
71	ExprTuple	77, 78
72	Literal
73	ExprTuple	79, 81
74	ExprTuple	81, 80
75	Literal
76	ExprTuple	81, 82
77	Literal
78	Literal
79	Variable
80	Literal
81	Literal
82	Literal