Expression of type NotEquals ¶

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 NotEquals
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 = NotEquals(_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)])))

# 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{
\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) \neq \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)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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')

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

Expression of type NotEquals¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type NotEquals ¶

from the theory of proveit.physics.quantum.QPE ¶