Expression of type ExprRange ¶

from the theory of proveit.physics.quantum.circuits ¶

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, IndexedVar, U, Variable, m, t
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Interval, one
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)
expr = ExprRange(sub_expr1, [ExprRange(sub_expr2, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr1, sub_expr2)), Conditional(Gate(operation = I).with_implicit_representation(), NotEquals(sub_expr1, sub_expr2))), one, t).with_case_simplification(), ExprRange(sub_expr2, MultiQubitElem(element = Gate(operation = IndexedVar(U, sub_expr1), part = sub_expr2), targets = Interval(sub_expr3, Add(t, m))), one, m)], one, t).with_case_simplification()

# 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(\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}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{1}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{1}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{1}~\mbox{part}~m~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}\right), \left(\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}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{2}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{2}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{2}~\mbox{part}~m~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}\right), \ldots, \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \ldots, \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_{t}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{t}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{t}~\mbox{part}~m~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
parameterization	'implicit' (default for LaTeX formatting) hides the parameter the ExprRange so the parameterization may be ambiguous (e.g., x_{1+1}, ..., x_{n+1}); 'explicit' (default for string formatting) reveals the parameterization (e.g. x_{1+1}, ..x_{k+1}.., x_{n+1}).	None	None/False	('with_explicit_parameterization', 'with_implicit_parameterization', 'with_default_parameterization_style')
front_expansion	The number of instances to display at the front of the range (e.g., before the ellipsis). Default is 2.	2	2	('with_front_expansion', 'get_front_expansion')
back_expansion	The number of instances to display at the back of the range (e.g., after the ellipsis). Default is 1.	1	1	('with_back_expansion', 'get_back_expansion')
order	The default order is 'increasing' (a_1 ... a_3) but to represent a 'decreasing' ExprRange (a_6 ... a_2) the order must be set to 'decreasing'	increasing	increasing	('with_decreasing_order', 'with_increasing_order')
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
case_simplify	If 'True', simplify formatted instances that are ConditionalSets under proper index assumptions	False	True	('with_case_simplification',)

	core type	sub-expressions
0	ExprRange	lambda_map: 1 start_index: 48 end_index: 47
1	Lambda	parameter: 42 body: 2
2	ExprTuple	3, 4
3	ExprRange	lambda_map: 5 start_index: 48 end_index: 47
4	ExprRange	lambda_map: 6 start_index: 48 end_index: 43
5	Lambda	parameter: 36 body: 7
6	Lambda	parameter: 36 body: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	36
9	Operation	operator: 24 operands: 12
10	Literal
11	ExprTuple	13, 14
12	NamedExprs	element: 15 targets: 16
13	Conditional	value: 17 condition: 18
14	Conditional	value: 19 condition: 20
15	Operation	operator: 27 operands: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 24 operands: 25
18	Operation	operator: 26 operands: 30
19	Operation	operator: 27 operands: 28
20	Operation	operator: 29 operands: 30
21	NamedExprs	operation: 31 part: 36
22	Literal
23	ExprTuple	44, 32
24	Literal
25	NamedExprs	element: 33 targets: 34
26	Literal
27	Literal
28	NamedExprs	operation: 35
29	Literal
30	ExprTuple	42, 36
31	IndexedVar	variable: 37 index: 42
32	Operation	operator: 45 operands: 39
33	Literal
34	Operation	operator: 40 operand: 44
35	Literal
36	Variable
37	Variable
38	ExprTuple	42
39	ExprTuple	47, 43
40	Literal
41	ExprTuple	44
42	Variable
43	Variable
44	Operation	operator: 45 operands: 46
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Literal

Expression of type ExprRange¶

from the theory of proveit.physics.quantum.circuits¶

Expression of type ExprRange ¶

from the theory of proveit.physics.quantum.circuits ¶