Expression of type SetOfAll ¶

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, Literal, Variable, VertExprArray, m
from proveit.logic import SetOfAll
from proveit.numbers import Add, Exp, Interval, one, subtract, two, zero
from proveit.physics.quantum import I, NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE
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(Literal("t", theory = "proveit.physics.quantum.QPE"), one)
sub_expr3 = Add(Literal("t", theory = "proveit.physics.quantum.QPE"), Literal("s", theory = "proveit.physics.quantum.QPE"))
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(Literal("U", theory = "proveit.physics.quantum.QPE"), Literal("t", theory = "proveit.physics.quantum.QPE")), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = SetOfAll(instance_param_or_params = [m], instance_element = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = Literal("|u>", latex_format = r"\lvert u \rangle", theory = "proveit.physics.quantum.QPE"), part = sub_expr1), targets = sub_expr4), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, sub_expr5, one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, Literal("t", theory = "proveit.physics.quantum.QPE")), part = sub_expr1), targets = Interval(one, Literal("t", theory = "proveit.physics.quantum.QPE"))), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = Literal("|u>", latex_format = r"\lvert u \rangle", theory = "proveit.physics.quantum.QPE"), part = sub_expr1), targets = sub_expr4), one, Literal("s", theory = "proveit.physics.quantum.QPE"))])), domain = Interval(zero, subtract(Exp(two, Literal("t", theory = "proveit.physics.quantum.QPE")), one)))

# 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\}_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}}

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

	core type	sub-expressions
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 97 body: 5
4	ExprTuple	97
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13, 14, 15
10	Literal
11	ExprTuple	97, 16
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	Operation	operator: 79 operands: 25
17	ExprRange	lambda_map: 26 start_index: 98 end_index: 99
18	ExprRange	lambda_map: 27 start_index: 98 end_index: 100
19	ExprRange	lambda_map: 28 start_index: 98 end_index: 99
20	ExprRange	lambda_map: 28 start_index: 87 end_index: 88
21	ExprRange	lambda_map: 29 start_index: 98 end_index: 99
22	ExprRange	lambda_map: 30 start_index: 98 end_index: 100
23	ExprRange	lambda_map: 31 start_index: 98 end_index: 99
24	ExprRange	lambda_map: 32 start_index: 98 end_index: 100
25	ExprTuple	33, 34
26	Lambda	parameter: 86 body: 35
27	Lambda	parameter: 86 body: 36
28	Lambda	parameter: 86 body: 37
29	Lambda	parameter: 86 body: 38
30	Lambda	parameter: 86 body: 39
31	Lambda	parameter: 86 body: 40
32	Lambda	parameter: 86 body: 42
33	Literal
34	Operation	operator: 94 operands: 43
35	Operation	operator: 71 operands: 44
36	Operation	operator: 51 operands: 45
37	Operation	operator: 51 operands: 46
38	Operation	operator: 47 operands: 48
39	Operation	operator: 72 operands: 49
40	Operation	operator: 51 operands: 50
41	ExprTuple	86
42	Operation	operator: 51 operands: 52
43	ExprTuple	53, 54
44	NamedExprs	state: 55
45	NamedExprs	element: 56 targets: 64
46	NamedExprs	element: 57 targets: 58
47	Literal
48	NamedExprs	basis: 59
49	NamedExprs	operation: 60
50	NamedExprs	element: 61 targets: 62
51	Literal
52	NamedExprs	element: 63 targets: 64
53	Operation	operator: 65 operands: 66
54	Operation	operator: 67 operand: 98
55	Operation	operator: 69 operand: 82
56	Operation	operator: 71 operands: 78
57	Operation	operator: 72 operands: 73
58	Operation	operator: 79 operands: 74
59	Literal
60	Literal
61	Operation	operator: 77 operands: 75
62	Operation	operator: 79 operands: 76
63	Operation	operator: 77 operands: 78
64	Operation	operator: 79 operands: 80
65	Literal
66	ExprTuple	81, 99
67	Literal
68	ExprTuple	98
69	Literal
70	ExprTuple	82
71	Literal
72	Literal
73	NamedExprs	operation: 83 part: 86
74	ExprTuple	98, 88
75	NamedExprs	state: 84 part: 86
76	ExprTuple	98, 99
77	Literal
78	NamedExprs	state: 85 part: 86
79	Literal
80	ExprTuple	87, 88
81	Literal
82	Literal
83	Operation	operator: 89 operands: 90
84	Operation	operator: 91 operands: 92
85	Literal
86	Variable
87	Operation	operator: 94 operands: 93
88	Operation	operator: 94 operands: 95
89	Literal
90	ExprTuple	96, 99
91	Literal
92	ExprTuple	97, 99
93	ExprTuple	99, 98
94	Literal
95	ExprTuple	99, 100
96	Literal
97	Variable
98	Literal
99	Literal
100	Literal

Expression of type SetOfAll¶

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

Expression of type SetOfAll ¶

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