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(one, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Output(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = sub_expr4)
sub_expr7 = [ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s)]
sub_expr8 = [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)]
expr = ExprTuple(Prob(Qcircuit(vert_expr_array = VertExprArray(sub_expr7, sub_expr8, [ExprRange(sub_expr1, sub_expr6, one, sub_expr3)]))), Prob(Qcircuit(vert_expr_array = VertExprArray(sub_expr7, sub_expr8, [ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3).with_wrapping_at(2,6)]))))

# 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 + \rangle} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right),  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right),  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \end{array}\right)\right)\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{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)\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
12	ExprTuple	16, 17
13	ExprTuple	18, 19
14	ExprTuple	20, 21
15	ExprRange	lambda_map: 25 start_index: 66 end_index: 58
16	ExprRange	lambda_map: 22 start_index: 66 end_index: 73
17	ExprRange	lambda_map: 23 start_index: 66 end_index: 70
18	ExprRange	lambda_map: 24 start_index: 66 end_index: 73
19	ExprRange	lambda_map: 24 start_index: 54 end_index: 58
20	ExprRange	lambda_map: 25 start_index: 66 end_index: 73
21	ExprRange	lambda_map: 25 start_index: 54 end_index: 58
22	Lambda	parameter: 57 body: 26
23	Lambda	parameter: 57 body: 27
24	Lambda	parameter: 57 body: 28
25	Lambda	parameter: 57 body: 30
26	Operation	operator: 44 operands: 31
27	Operation	operator: 34 operands: 32
28	Operation	operator: 34 operands: 33
29	ExprTuple	57
30	Operation	operator: 34 operands: 35
31	NamedExprs	state: 36
32	NamedExprs	element: 37 targets: 38
33	NamedExprs	element: 39 targets: 41
34	Literal
35	NamedExprs	element: 40 targets: 41
36	Operation	operator: 42 operand: 53
37	Operation	operator: 44 operands: 45
38	Operation	operator: 51 operands: 46
39	Operation	operator: 47 operands: 48
40	Operation	operator: 49 operands: 50
41	Operation	operator: 51 operands: 52
42	Literal
43	ExprTuple	53
44	Literal
45	NamedExprs	state: 69 part: 57
46	ExprTuple	54, 58
47	Literal
48	NamedExprs	operation: 55 part: 57
49	Literal
50	NamedExprs	state: 56 part: 57
51	Literal
52	ExprTuple	66, 58
53	Literal
54	Operation	operator: 64 operands: 59
55	Operation	operator: 60 operands: 61
56	Operation	operator: 62 operands: 63
57	Variable
58	Operation	operator: 64 operands: 65
59	ExprTuple	73, 66
60	Literal
61	ExprTuple	67, 73
62	Literal
63	ExprTuple	68, 69
64	Literal
65	ExprTuple	73, 70
66	Literal
67	Literal
68	Operation	operator: 71 operand: 73
69	Literal
70	Literal
71	Literal
72	ExprTuple	73
73	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 ¶