Expression of type Qcircuit

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 import ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit

# 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 = Interval(one, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = sub_expr1), targets = sub_expr4)
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, 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())

\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{4}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle}
} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
spacing	change the spacing of a circuit using the format '@C=1em @R=.7em' where C is the column spacing and R is the row spacing	@C=1em @R=.7em	@C=1em @R=.7em

# 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, 5
3	ExprTuple	6, 7
4	ExprTuple	8, 9
5	ExprTuple	10, 11
6	ExprRange	lambda_map: 12 start_index: 56 end_index: 63
7	ExprRange	lambda_map: 13 start_index: 56 end_index: 60
8	ExprRange	lambda_map: 14 start_index: 56 end_index: 63
9	ExprRange	lambda_map: 14 start_index: 44 end_index: 48
10	ExprRange	lambda_map: 15 start_index: 56 end_index: 63
11	ExprRange	lambda_map: 15 start_index: 44 end_index: 48
12	Lambda	parameter: 47 body: 16
13	Lambda	parameter: 47 body: 17
14	Lambda	parameter: 47 body: 18
15	Lambda	parameter: 47 body: 20
16	Operation	operator: 34 operands: 21
17	Operation	operator: 24 operands: 22
18	Operation	operator: 24 operands: 23
19	ExprTuple	47
20	Operation	operator: 24 operands: 25
21	NamedExprs	state: 26
22	NamedExprs	element: 27 targets: 28
23	NamedExprs	element: 29 targets: 31
24	Literal
25	NamedExprs	element: 30 targets: 31
26	Operation	operator: 32 operand: 43
27	Operation	operator: 34 operands: 35
28	Operation	operator: 41 operands: 36
29	Operation	operator: 37 operands: 38
30	Operation	operator: 39 operands: 40
31	Operation	operator: 41 operands: 42
32	Literal
33	ExprTuple	43
34	Literal
35	NamedExprs	state: 59 part: 47
36	ExprTuple	44, 48
37	Literal
38	NamedExprs	operation: 45 part: 47
39	Literal
40	NamedExprs	state: 46 part: 47
41	Literal
42	ExprTuple	56, 48
43	Literal
44	Operation	operator: 54 operands: 49
45	Operation	operator: 50 operands: 51
46	Operation	operator: 52 operands: 53
47	Variable
48	Operation	operator: 54 operands: 55
49	ExprTuple	63, 56
50	Literal
51	ExprTuple	57, 63
52	Literal
53	ExprTuple	58, 59
54	Literal
55	ExprTuple	63, 60
56	Literal
57	Literal
58	Operation	operator: 61 operand: 63
59	Literal
60	Literal
61	Literal
62	ExprTuple	63
63	Variable