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.numbers import Add, Interval, one
from proveit.physics.quantum import I, ket_plus
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import QPE1, _Psi_ket, _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(one, _t)
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
sub_expr7 = ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)]
sub_expr9 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]
expr = ExprTuple(Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, _t), sub_expr7], [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], sub_expr8, sub_expr9))), Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr4), one, _t), sub_expr7], sub_expr8, sub_expr9))))

# 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)} & \multigate{3}{{\mathrm {FT}}^{\dag}_{t}} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right), \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \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	11, 12, 14, 15
9	Literal
10	ExprTuple	13, 14, 15
11	ExprTuple	16, 20
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	ExprRange	lambda_map: 25 start_index: 94 end_index: 95
17	ExprRange	lambda_map: 26 start_index: 94 end_index: 95
18	ExprRange	lambda_map: 26 start_index: 83 end_index: 84
19	ExprRange	lambda_map: 27 start_index: 94 end_index: 95
20	ExprRange	lambda_map: 28 start_index: 94 end_index: 96
21	ExprRange	lambda_map: 29 start_index: 94 end_index: 95
22	ExprRange	lambda_map: 30 start_index: 94 end_index: 96
23	ExprRange	lambda_map: 31 start_index: 94 end_index: 95
24	ExprRange	lambda_map: 32 start_index: 94 end_index: 96
25	Lambda	parameter: 82 body: 33
26	Lambda	parameter: 82 body: 34
27	Lambda	parameter: 82 body: 35
28	Lambda	parameter: 82 body: 36
29	Lambda	parameter: 82 body: 37
30	Lambda	parameter: 82 body: 38
31	Lambda	parameter: 82 body: 39
32	Lambda	parameter: 82 body: 41
33	Operation	operator: 67 operands: 42
34	Operation	operator: 49 operands: 43
35	Operation	operator: 49 operands: 44
36	Operation	operator: 49 operands: 45
37	Operation	operator: 49 operands: 46
38	Operation	operator: 68 operands: 47
39	Operation	operator: 49 operands: 48
40	ExprTuple	82
41	Operation	operator: 49 operands: 50
42	NamedExprs	state: 51
43	NamedExprs	element: 52 targets: 53
44	NamedExprs	element: 54 targets: 59
45	NamedExprs	element: 55 targets: 61
46	NamedExprs	element: 56 targets: 59
47	NamedExprs	operation: 57
48	NamedExprs	element: 58 targets: 59
49	Literal
50	NamedExprs	element: 60 targets: 61
51	Operation	operator: 62 operand: 76
52	Operation	operator: 68 operands: 64
53	Operation	operator: 74 operands: 65
54	Operation	operator: 67 operands: 66
55	Operation	operator: 67 operands: 73
56	Operation	operator: 68 operands: 69
57	Literal
58	Operation	operator: 72 operands: 70
59	Operation	operator: 74 operands: 71
60	Operation	operator: 72 operands: 73
61	Operation	operator: 74 operands: 75
62	Literal
63	ExprTuple	76
64	NamedExprs	operation: 77 part: 82
65	ExprTuple	94, 84
66	NamedExprs	state: 78 part: 82
67	Literal
68	Literal
69	NamedExprs	operation: 79 part: 82
70	NamedExprs	state: 80 part: 82
71	ExprTuple	94, 95
72	Literal
73	NamedExprs	state: 81 part: 82
74	Literal
75	ExprTuple	83, 84
76	Literal
77	Operation	operator: 85 operands: 86
78	Operation	operator: 87 operand: 95
79	Operation	operator: 88 operand: 95
80	Literal
81	Literal
82	Variable
83	Operation	operator: 91 operands: 90
84	Operation	operator: 91 operands: 92
85	Literal
86	ExprTuple	93, 95
87	Literal
88	Literal
89	ExprTuple	95
90	ExprTuple	95, 94
91	Literal
92	ExprTuple	95, 96
93	Literal
94	Literal
95	Literal
96	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 ¶