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.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

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
sub_expr3 = Add(_t, one)
sub_expr4 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = VertExprArray([ExprRange(sub_expr1, sub_expr4, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr4, sub_expr3, sub_expr2).with_wrapping_at(2,6)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr2)), 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 {\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{
& & \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 {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \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 {\otimes} \lvert u \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \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 \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{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 \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 2~\mbox{on}~\{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 \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{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: 61 end_index: 62
5	ExprRange	lambda_map: 10 start_index: 49 end_index: 50
6	ExprRange	lambda_map: 11 start_index: 61 end_index: 62
7	ExprRange	lambda_map: 12 start_index: 61 end_index: 63
8	ExprRange	lambda_map: 13 start_index: 61 end_index: 62
9	ExprRange	lambda_map: 14 start_index: 61 end_index: 63
10	Lambda	parameter: 48 body: 15
11	Lambda	parameter: 48 body: 16
12	Lambda	parameter: 48 body: 17
13	Lambda	parameter: 48 body: 18
14	Lambda	parameter: 48 body: 20
15	Operation	operator: 27 operands: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 24 operands: 25
18	Operation	operator: 27 operands: 26
19	ExprTuple	48
20	Operation	operator: 27 operands: 28
21	NamedExprs	element: 29 targets: 30
22	Literal
23	NamedExprs	basis: 31
24	Literal
25	NamedExprs	operation: 32
26	NamedExprs	element: 33 targets: 34
27	Literal
28	NamedExprs	element: 35 targets: 36
29	Operation	operator: 37 operands: 38
30	Operation	operator: 44 operands: 39
31	Literal
32	Literal
33	Operation	operator: 42 operands: 40
34	Operation	operator: 44 operands: 41
35	Operation	operator: 42 operands: 43
36	Operation	operator: 44 operands: 45
37	Literal
38	NamedExprs	state: 46 part: 48
39	ExprTuple	61, 50
40	NamedExprs	state: 47 part: 48
41	ExprTuple	61, 62
42	Literal
43	NamedExprs	state: 59 part: 48
44	Literal
45	ExprTuple	49, 50
46	Operation	operator: 51 operands: 52
47	Operation	operator: 53 operands: 54
48	Variable
49	Operation	operator: 56 operands: 55
50	Operation	operator: 56 operands: 57
51	Literal
52	ExprTuple	58, 59
53	Literal
54	ExprTuple	60, 62
55	ExprTuple	62, 61
56	Literal
57	ExprTuple	62, 63
58	Literal
59	Literal
60	Variable
61	Literal
62	Literal
63	Literal