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, m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _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 = Add(_t, _s)
sub_expr3 = Interval(one, _t)
sub_expr4 = Interval(Add(_t, one), sub_expr2)
sub_expr5 = [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire]
sub_expr6 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr3), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]
expr = ExprTuple(Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)), one, sub_expr2)], sub_expr5, sub_expr6))), Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr3), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)], sub_expr5, sub_expr6))))

# 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(QCIRCUIT\left(VertExprArray\left(\begin{array}{c} \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right),  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(s - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}\right),  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \end{array}\right)\right)\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)\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, 13, 14
9	Literal
10	ExprTuple	12, 13, 14
11	ExprTuple	15
12	ExprTuple	16, 17
13	ExprTuple	18, 19
14	ExprTuple	20, 21
15	ExprRange	lambda_map: 22 start_index: 82 end_index: 71
16	ExprRange	lambda_map: 23 start_index: 82 end_index: 83
17	ExprRange	lambda_map: 24 start_index: 82 end_index: 84
18	ExprRange	lambda_map: 25 start_index: 82 end_index: 83
19	ExprRange	lambda_map: 26 start_index: 82 end_index: 84
20	ExprRange	lambda_map: 27 start_index: 82 end_index: 83
21	ExprRange	lambda_map: 28 start_index: 82 end_index: 84
22	Lambda	parameter: 69 body: 29
23	Lambda	parameter: 69 body: 30
24	Lambda	parameter: 69 body: 31
25	Lambda	parameter: 69 body: 32
26	Lambda	parameter: 69 body: 33
27	Lambda	parameter: 69 body: 34
28	Lambda	parameter: 69 body: 36
29	Operation	operator: 45 operands: 37
30	Operation	operator: 45 operands: 38
31	Operation	operator: 45 operands: 39
32	Operation	operator: 40 operands: 41
33	Operation	operator: 42 operands: 43
34	Operation	operator: 45 operands: 44
35	ExprTuple	69
36	Operation	operator: 45 operands: 46
37	NamedExprs	element: 47 targets: 48
38	NamedExprs	element: 49 targets: 54
39	NamedExprs	element: 50 targets: 56
40	Literal
41	NamedExprs	basis: 51
42	Literal
43	NamedExprs	operation: 52
44	NamedExprs	element: 53 targets: 54
45	Literal
46	NamedExprs	element: 55 targets: 56
47	Operation	operator: 60 operands: 57
48	Operation	operator: 65 operands: 58
49	Operation	operator: 60 operands: 59
50	Operation	operator: 60 operands: 64
51	Literal
52	Literal
53	Operation	operator: 63 operands: 61
54	Operation	operator: 65 operands: 62
55	Operation	operator: 63 operands: 64
56	Operation	operator: 65 operands: 66
57	NamedExprs	state: 67 part: 69
58	ExprTuple	82, 71
59	NamedExprs	state: 79 part: 69
60	Literal
61	NamedExprs	state: 68 part: 69
62	ExprTuple	82, 83
63	Literal
64	NamedExprs	state: 80 part: 69
65	Literal
66	ExprTuple	70, 71
67	Operation	operator: 72 operands: 73
68	Operation	operator: 74 operands: 75
69	Variable
70	Operation	operator: 77 operands: 76
71	Operation	operator: 77 operands: 78
72	Literal
73	ExprTuple	79, 80
74	Literal
75	ExprTuple	81, 83
76	ExprTuple	83, 82
77	Literal
78	ExprTuple	83, 84
79	Literal
80	Literal
81	Variable
82	Literal
83	Literal
84	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 ¶