Expression of type ConditionalSet

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, Variable, t
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, 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("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Variable("_b", latex_format = r"{_{-}b}"), t)
expr = ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(Add(t, one))), Equals(sub_expr2, sub_expr1)), Conditional(Gate(operation = I).with_implicit_representation(), NotEquals(sub_expr2, sub_expr1)))

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())

\left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) = {_{-}a} \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) \neq {_{-}a}\end{array}\right..

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Conditional	value: 5 condition: 6
4	Conditional	value: 7 condition: 8
5	Operation	operator: 9 operands: 10
6	Operation	operator: 11 operands: 15
7	Operation	operator: 12 operands: 13
8	Operation	operator: 14 operands: 15
9	Literal
10	NamedExprs	element: 16 targets: 17
11	Literal
12	Literal
13	NamedExprs	operation: 18
14	Literal
15	ExprTuple	19, 20
16	Literal
17	Operation	operator: 21 operand: 24
18	Literal
19	Operation	operator: 26 operands: 23
20	Variable
21	Literal
22	ExprTuple	24
23	ExprTuple	25, 28
24	Operation	operator: 26 operands: 27
25	Variable
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Literal