Expression of type Not

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, n
from proveit.logic import Equals, Not
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE, _U, _ket_u, _phase_est_circuit, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Not(Equals(_phase_est_circuit, Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(n, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]))))

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())

\lnot \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) = \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert n \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert n \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert n \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	12, 13, 14, 11
9	Literal
10	ExprTuple	12, 13, 14, 15
11	ExprTuple	16, 24
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	ExprRange	lambda_map: 25 start_index: 95 end_index: 96
17	ExprRange	lambda_map: 26 start_index: 95 end_index: 96
18	ExprRange	lambda_map: 27 start_index: 95 end_index: 97
19	ExprRange	lambda_map: 28 start_index: 95 end_index: 96
20	ExprRange	lambda_map: 28 start_index: 82 end_index: 83
21	ExprRange	lambda_map: 29 start_index: 95 end_index: 96
22	ExprRange	lambda_map: 30 start_index: 95 end_index: 97
23	ExprRange	lambda_map: 31 start_index: 95 end_index: 96
24	ExprRange	lambda_map: 32 start_index: 95 end_index: 97
25	Lambda	parameter: 81 body: 33
26	Lambda	parameter: 81 body: 34
27	Lambda	parameter: 81 body: 35
28	Lambda	parameter: 81 body: 36
29	Lambda	parameter: 81 body: 37
30	Lambda	parameter: 81 body: 38
31	Lambda	parameter: 81 body: 39
32	Lambda	parameter: 81 body: 41
33	Operation	operator: 50 operands: 42
34	Operation	operator: 66 operands: 43
35	Operation	operator: 50 operands: 44
36	Operation	operator: 50 operands: 45
37	Operation	operator: 46 operands: 47
38	Operation	operator: 67 operands: 48
39	Operation	operator: 50 operands: 49
40	ExprTuple	81
41	Operation	operator: 50 operands: 51
42	NamedExprs	element: 52 targets: 60
43	NamedExprs	state: 53
44	NamedExprs	element: 54 targets: 62
45	NamedExprs	element: 55 targets: 56
46	Literal
47	NamedExprs	basis: 57
48	NamedExprs	operation: 58
49	NamedExprs	element: 59 targets: 60
50	Literal
51	NamedExprs	element: 61 targets: 62
52	Operation	operator: 72 operands: 63
53	Operation	operator: 64 operand: 77
54	Operation	operator: 66 operands: 73
55	Operation	operator: 67 operands: 68
56	Operation	operator: 74 operands: 69
57	Literal
58	Literal
59	Operation	operator: 72 operands: 70
60	Operation	operator: 74 operands: 71
61	Operation	operator: 72 operands: 73
62	Operation	operator: 74 operands: 75
63	NamedExprs	state: 76 part: 81
64	Literal
65	ExprTuple	77
66	Literal
67	Literal
68	NamedExprs	operation: 78 part: 81
69	ExprTuple	95, 83
70	NamedExprs	state: 79 part: 81
71	ExprTuple	95, 96
72	Literal
73	NamedExprs	state: 80 part: 81
74	Literal
75	ExprTuple	82, 83
76	Operation	operator: 87 operands: 84
77	Literal
78	Operation	operator: 85 operands: 86
79	Operation	operator: 87 operands: 88
80	Literal
81	Variable
82	Operation	operator: 90 operands: 89
83	Operation	operator: 90 operands: 91
84	ExprTuple	92, 96
85	Literal
86	ExprTuple	93, 96
87	Literal
88	ExprTuple	94, 96
89	ExprTuple	96, 95
90	Literal
91	ExprTuple	96, 97
92	Variable
93	Literal
94	Variable
95	Literal
96	Literal
97	Literal