Expression of type ExprTuple ¶

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, ExprTuple, Variable, VertExprArray
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi__t_ket, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, 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 = Add(_t, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = Interval(one, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = sub_expr5)
sub_expr7 = MultiQubitElem(element = Output(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = sub_expr5)
sub_expr8 = [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)]
sub_expr9 = [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)]
expr = ExprTuple(Prob(Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr9, [ExprRange(sub_expr1, sub_expr7, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr7, sub_expr2, sub_expr3).with_wrapping_at(2,6)]))), Prob(Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr9, [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi__t_ket, 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(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{4}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle}
} \end{array}\right), \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right)\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

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

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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