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 ExprRange, Variable, VertExprArray, m
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _phase_est_circuit, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, MultiQubitElem, Output, Qcircuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, _t)
sub_expr3 = Interval(Add(_t, one), Add(_t, _s))
expr = Equals(Prob(_phase_est_circuit), Prob(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_expr3), one, _s)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [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_expr3), one, _s)])))).with_wrapping_at(2)

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