Expression of type QcircuitEquiv

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, t
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum.QPE import _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output, Qcircuit, QcircuitEquiv

# 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 = MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi_t_ket, part = sub_expr1), targets = Interval(one, t)), one, t).with_wrapping_at(2,6), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr4, one, t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr4, 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())

\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qout{\lvert \psi_{t} \rangle} \\
& \qout{\lvert u \rangle}
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multiqout{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle}
} \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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# 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	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	ExprTuple	12, 13
10	ExprRange	lambda_map: 14 start_index: 48 end_index: 54
11	ExprRange	lambda_map: 15 start_index: 48 end_index: 51
12	ExprRange	lambda_map: 16 start_index: 48 end_index: 54
13	ExprRange	lambda_map: 16 start_index: 39 end_index: 42
14	Lambda	parameter: 41 body: 17
15	Lambda	parameter: 41 body: 18
16	Lambda	parameter: 41 body: 20
17	Operation	operator: 23 operands: 21
18	Operation	operator: 23 operands: 22
19	ExprTuple	41
20	Operation	operator: 23 operands: 24
21	NamedExprs	element: 25 targets: 26
22	NamedExprs	element: 27 targets: 28
23	Literal
24	NamedExprs	element: 29 targets: 30
25	Operation	operator: 35 operands: 31
26	Operation	operator: 37 operands: 32
27	Operation	operator: 35 operands: 33
28	Operation	operator: 37 operands: 34
29	Operation	operator: 35 operands: 36
30	Operation	operator: 37 operands: 38
31	NamedExprs	state: 49 part: 41
32	ExprTuple	48, 54
33	NamedExprs	state: 50 part: 41
34	ExprTuple	39, 42
35	Literal
36	NamedExprs	state: 40 part: 41
37	Literal
38	ExprTuple	48, 42
39	Operation	operator: 46 operands: 43
40	Operation	operator: 44 operands: 45
41	Variable
42	Operation	operator: 46 operands: 47
43	ExprTuple	54, 48
44	Literal
45	ExprTuple	49, 50
46	Literal
47	ExprTuple	54, 51
48	Literal
49	Operation	operator: 52 operand: 54
50	Literal
51	Literal
52	Literal
53	ExprTuple	54
54	Variable