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, Neg, one, two, zero
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, _s)
sub_expr3 = TensorProd(_psi_t_ket, _ket_u)
sub_expr4 = Interval(one, sub_expr2)
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(Variable("_b", latex_format = r"{_{-}b}"))), Qcircuit(vert_expr_array = VertExprArray([MultiQubitElem(element = Output(state = sub_expr3, part = one), targets = sub_expr4), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr3, part = Add(sub_expr1, t)), targets = sub_expr4), Add(Neg(t), two), zero), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr3, part = sub_expr1), targets = sub_expr4), Add(t, one), sub_expr2).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{
& \gate{\begin{array}{c} \uparrow \\{_{-}b} \\ \downarrow\end{array}} & \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multiqout{2}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \qout{\vdots} \qwx[1] \\
& \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} \qwx[1] \\
& \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}}
} \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	Variable
9	ExprTuple	10, 11, 12
10	Operation	operator: 29 operands: 13
11	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
12	ExprRange	lambda_map: 17 start_index: 18 end_index: 43
13	NamedExprs	element: 19 targets: 34
14	Lambda	parameter: 49 body: 20
15	Operation	operator: 47 operands: 21
16	Literal
17	Lambda	parameter: 49 body: 23
18	Operation	operator: 47 operands: 24
19	Operation	operator: 36 operands: 25
20	Operation	operator: 29 operands: 26
21	ExprTuple	27, 28
22	ExprTuple	49
23	Operation	operator: 29 operands: 30
24	ExprTuple	55, 42
25	NamedExprs	state: 41 part: 42
26	NamedExprs	element: 31 targets: 34
27	Operation	operator: 32 operand: 55
28	Literal
29	Literal
30	NamedExprs	element: 33 targets: 34
31	Operation	operator: 36 operands: 35
32	Literal
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	NamedExprs	state: 41 part: 40
36	Literal
37	NamedExprs	state: 41 part: 49
38	Literal
39	ExprTuple	42, 43
40	Operation	operator: 47 operands: 44
41	Operation	operator: 45 operands: 46
42	Literal
43	Operation	operator: 47 operands: 48
44	ExprTuple	49, 55
45	Literal
46	ExprTuple	50, 51
47	Literal
48	ExprTuple	55, 52
49	Variable
50	Operation	operator: 53 operand: 55
51	Literal
52	Literal
53	Literal
54	ExprTuple	55
55	Variable