Expression of type VertExprArray

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.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

# 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 = 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)])

expr:

# 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}{ccc} 
 \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array} & \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{
& \qin{\lvert \Psi \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \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} \\
\vdots & \begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array} & \vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array} & \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{
& \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{
& & \qw & \qw 
} \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{
& \qin{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \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} \\
\vdots & \begin{array}{c}:\\ \left(s - 3\right) \times \\:\end{array} & \vdots \\
\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} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} & \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} \\
\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	with_justification

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3
1	ExprTuple	4, 5
2	ExprTuple	6, 7
3	ExprTuple	8, 9
4	ExprRange	lambda_map: 10 start_index: 60 end_index: 61
5	ExprRange	lambda_map: 11 start_index: 60 end_index: 62
6	ExprRange	lambda_map: 12 start_index: 60 end_index: 61
7	ExprRange	lambda_map: 13 start_index: 60 end_index: 62
8	ExprRange	lambda_map: 14 start_index: 60 end_index: 61
9	ExprRange	lambda_map: 15 start_index: 60 end_index: 62
10	Lambda	parameter: 51 body: 16
11	Lambda	parameter: 51 body: 17
12	Lambda	parameter: 51 body: 18
13	Lambda	parameter: 51 body: 19
14	Lambda	parameter: 51 body: 20
15	Lambda	parameter: 51 body: 22
16	Operation	operator: 30 operands: 23
17	Operation	operator: 30 operands: 24
18	Operation	operator: 25 operands: 26
19	Operation	operator: 27 operands: 28
20	Operation	operator: 30 operands: 29
21	ExprTuple	51
22	Operation	operator: 30 operands: 31
23	NamedExprs	element: 32 targets: 37
24	NamedExprs	element: 33 targets: 39
25	Literal
26	NamedExprs	basis: 34
27	Literal
28	NamedExprs	operation: 35
29	NamedExprs	element: 36 targets: 37
30	Literal
31	NamedExprs	element: 38 targets: 39
32	Operation	operator: 41 operands: 40
33	Operation	operator: 41 operands: 45
34	Literal
35	Literal
36	Operation	operator: 44 operands: 42
37	Operation	operator: 46 operands: 43
38	Operation	operator: 44 operands: 45
39	Operation	operator: 46 operands: 47
40	NamedExprs	state: 48 part: 51
41	Literal
42	NamedExprs	state: 49 part: 51
43	ExprTuple	60, 61
44	Literal
45	NamedExprs	state: 50 part: 51
46	Literal
47	ExprTuple	52, 53
48	Literal
49	Operation	operator: 54 operands: 55
50	Literal
51	Variable
52	Operation	operator: 57 operands: 56
53	Operation	operator: 57 operands: 58
54	Literal
55	ExprTuple	59, 61
56	ExprTuple	61, 60
57	Literal
58	ExprTuple	61, 62
59	Variable
60	Literal
61	Literal
62	Literal