Expression of type Equals ¶

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 Conditional, ExprRange, IndexedVar, Variable, VertExprArray, m
from proveit.logic import And, Equals, InSet, TRUE
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, _m_domain, _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 = IndexedVar(m, one)
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
sub_expr7 = InSet(sub_expr4, _m_domain)
sub_expr8 = 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_expr5), one, _s)], [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(sub_expr4, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]))
expr = Equals(Conditional(sub_expr8, And(sub_expr7, TRUE)), Conditional(sub_expr8, sub_expr7)).with_wrapping_at(1)

# 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{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m_{1} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m_{1} \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_{1} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m_{1} \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array} \textrm{ if } m_{1} \in \{0~\ldotp \ldotp~2^{t} - 1\} ,  \top\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 m_{1} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m_{1} \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_{1} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m_{1} \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array} \textrm{ if } m_{1} \in \{0~\ldotp \ldotp~2^{t} - 1\}\right.. \end{array} \end{array}

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.	()	(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')

	core type	sub-expressions
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Conditional	value: 6 condition: 5
4	Conditional	value: 6 condition: 11
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15, 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	ExprTuple	25, 26
17	Literal
18	ExprTuple	99, 27
19	ExprRange	lambda_map: 28 start_index: 104 end_index: 100
20	ExprRange	lambda_map: 29 start_index: 104 end_index: 101
21	ExprRange	lambda_map: 30 start_index: 104 end_index: 100
22	ExprRange	lambda_map: 30 start_index: 88 end_index: 89
23	ExprRange	lambda_map: 31 start_index: 104 end_index: 100
24	ExprRange	lambda_map: 32 start_index: 104 end_index: 101
25	ExprRange	lambda_map: 33 start_index: 104 end_index: 100
26	ExprRange	lambda_map: 34 start_index: 104 end_index: 101
27	Operation	operator: 78 operands: 35
28	Lambda	parameter: 87 body: 36
29	Lambda	parameter: 87 body: 37
30	Lambda	parameter: 87 body: 38
31	Lambda	parameter: 87 body: 39
32	Lambda	parameter: 87 body: 40
33	Lambda	parameter: 87 body: 41
34	Lambda	parameter: 87 body: 43
35	ExprTuple	44, 45
36	Operation	operator: 70 operands: 46
37	Operation	operator: 53 operands: 47
38	Operation	operator: 53 operands: 48
39	Operation	operator: 49 operands: 50
40	Operation	operator: 71 operands: 51
41	Operation	operator: 53 operands: 52
42	ExprTuple	87
43	Operation	operator: 53 operands: 54
44	Literal
45	Operation	operator: 96 operands: 55
46	NamedExprs	state: 56
47	NamedExprs	element: 57 targets: 65
48	NamedExprs	element: 58 targets: 59
49	Literal
50	NamedExprs	basis: 60
51	NamedExprs	operation: 61
52	NamedExprs	element: 62 targets: 63
53	Literal
54	NamedExprs	element: 64 targets: 65
55	ExprTuple	66, 67
56	Operation	operator: 68 operand: 83
57	Operation	operator: 70 operands: 77
58	Operation	operator: 71 operands: 72
59	Operation	operator: 78 operands: 73
60	Literal
61	Literal
62	Operation	operator: 76 operands: 74
63	Operation	operator: 78 operands: 75
64	Operation	operator: 76 operands: 77
65	Operation	operator: 78 operands: 79
66	Operation	operator: 80 operands: 81
67	Operation	operator: 82 operand: 104
68	Literal
69	ExprTuple	83
70	Literal
71	Literal
72	NamedExprs	operation: 84 part: 87
73	ExprTuple	104, 89
74	NamedExprs	state: 85 part: 87
75	ExprTuple	104, 100
76	Literal
77	NamedExprs	state: 86 part: 87
78	Literal
79	ExprTuple	88, 89
80	Literal
81	ExprTuple	90, 100
82	Literal
83	Literal
84	Operation	operator: 91 operands: 92
85	Operation	operator: 93 operands: 94
86	Literal
87	Variable
88	Operation	operator: 96 operands: 95
89	Operation	operator: 96 operands: 97
90	Literal
91	Literal
92	ExprTuple	98, 100
93	Literal
94	ExprTuple	99, 100
95	ExprTuple	100, 104
96	Literal
97	ExprTuple	100, 101
98	Literal
99	IndexedVar	variable: 102 index: 104
100	Literal
101	Literal
102	Variable
103	ExprTuple	104
104	Literal

Expression of type Equals¶

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

Expression of type Equals ¶

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