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
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

# 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)
expr = VertExprArray([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)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [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)])

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 + \rangle} & \qw 
} \end{array} & \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{
& & \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{
& \qin{\lvert + \rangle} & \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} & \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} \\
\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array} & \vdots & \vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array} & \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{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \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{
& & \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{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{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{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \\
\vdots & \vdots & \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{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \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} \\
\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: 54 end_index: 61
5	ExprRange	lambda_map: 11 start_index: 54 end_index: 58
6	ExprRange	lambda_map: 12 start_index: 54 end_index: 61
7	ExprRange	lambda_map: 12 start_index: 42 end_index: 46
8	ExprRange	lambda_map: 13 start_index: 54 end_index: 61
9	ExprRange	lambda_map: 13 start_index: 42 end_index: 46
10	Lambda	parameter: 45 body: 14
11	Lambda	parameter: 45 body: 15
12	Lambda	parameter: 45 body: 16
13	Lambda	parameter: 45 body: 18
14	Operation	operator: 32 operands: 19
15	Operation	operator: 22 operands: 20
16	Operation	operator: 22 operands: 21
17	ExprTuple	45
18	Operation	operator: 22 operands: 23
19	NamedExprs	state: 24
20	NamedExprs	element: 25 targets: 26
21	NamedExprs	element: 27 targets: 29
22	Literal
23	NamedExprs	element: 28 targets: 29
24	Operation	operator: 30 operand: 41
25	Operation	operator: 32 operands: 33
26	Operation	operator: 39 operands: 34
27	Operation	operator: 35 operands: 36
28	Operation	operator: 37 operands: 38
29	Operation	operator: 39 operands: 40
30	Literal
31	ExprTuple	41
32	Literal
33	NamedExprs	state: 57 part: 45
34	ExprTuple	42, 46
35	Literal
36	NamedExprs	operation: 43 part: 45
37	Literal
38	NamedExprs	state: 44 part: 45
39	Literal
40	ExprTuple	54, 46
41	Literal
42	Operation	operator: 52 operands: 47
43	Operation	operator: 48 operands: 49
44	Operation	operator: 50 operands: 51
45	Variable
46	Operation	operator: 52 operands: 53
47	ExprTuple	61, 54
48	Literal
49	ExprTuple	55, 61
50	Literal
51	ExprTuple	56, 57
52	Literal
53	ExprTuple	61, 58
54	Literal
55	Literal
56	Operation	operator: 59 operand: 61
57	Literal
58	Literal
59	Literal
60	ExprTuple	61
61	Literal