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 Conditional, ConditionalSet, ExprRange, U, Variable, VertExprArray, s, t
from proveit.linear_algebra import MatrixExp
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Exp, Interval, Neg, one, two, zero
from proveit.physics.quantum import CONTROL, I
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(t, one)
sub_expr4 = Add(sub_expr1, t)
expr = VertExprArray(ExprRange(sub_expr1, [ExprRange(sub_expr2, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr4, sub_expr2)), Conditional(Gate(operation = I).with_implicit_representation(), NotEquals(sub_expr4, sub_expr2))), one, t).with_case_simplification(), ExprRange(sub_expr2, MultiQubitElem(element = Gate(operation = MatrixExp(U, Exp(two, Neg(sub_expr1))), part = sub_expr2), targets = Interval(sub_expr3, Add(t, s))), one, s)], Add(Neg(t), one), zero).with_decreasing_order().with_case_simplification())

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}{cccc} 
 \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \\
\vdots & \vdots & \ddots & \vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 1}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 2}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{0}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 1}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 2}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{0}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} \\
\vdots & \vdots & \ddots & \vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 1}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 2}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{0}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \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
1	ExprRange	lambda_map: 2 start_index: 3 end_index: 4
2	Lambda	parameter: 64 body: 5
3	Operation	operator: 56 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	9, 61
7	ExprRange	lambda_map: 10 start_index: 61 end_index: 60
8	ExprRange	lambda_map: 11 start_index: 61 end_index: 52
9	Operation	operator: 62 operand: 60
10	Lambda	parameter: 43 body: 13
11	Lambda	parameter: 43 body: 15
12	ExprTuple	60
13	Operation	operator: 16 operands: 17
14	ExprTuple	43
15	Operation	operator: 30 operands: 18
16	Literal
17	ExprTuple	19, 20
18	NamedExprs	element: 21 targets: 22
19	Conditional	value: 23 condition: 24
20	Conditional	value: 25 condition: 26
21	Operation	operator: 33 operands: 27
22	Operation	operator: 28 operands: 29
23	Operation	operator: 30 operands: 31
24	Operation	operator: 32 operands: 36
25	Operation	operator: 33 operands: 34
26	Operation	operator: 35 operands: 36
27	NamedExprs	operation: 37 part: 43
28	Literal
29	ExprTuple	53, 38
30	Literal
31	NamedExprs	element: 39 targets: 40
32	Literal
33	Literal
34	NamedExprs	operation: 41
35	Literal
36	ExprTuple	42, 43
37	Operation	operator: 44 operands: 45
38	Operation	operator: 56 operands: 46
39	Literal
40	Operation	operator: 47 operand: 53
41	Literal
42	Operation	operator: 56 operands: 49
43	Variable
44	Literal
45	ExprTuple	50, 51
46	ExprTuple	60, 52
47	Literal
48	ExprTuple	53
49	ExprTuple	64, 60
50	Variable
51	Operation	operator: 54 operands: 55
52	Variable
53	Operation	operator: 56 operands: 57
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60, 61
58	Literal
59	Operation	operator: 62 operand: 64
60	Variable
61	Literal
62	Literal
63	ExprTuple	64
64	Variable