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, Literal, Variable, VertExprArray, t
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE1, SubIndexed
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(Literal("t", theory = "proveit.physics.quantum.QPE"), one)
sub_expr3 = Add(Literal("t", theory = "proveit.physics.quantum.QPE"), Literal("s", theory = "proveit.physics.quantum.QPE"))
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(Literal("U", theory = "proveit.physics.quantum.QPE"), Literal("t", theory = "proveit.physics.quantum.QPE")), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = Literal("|u>", latex_format = r"\lvert u \rangle", theory = "proveit.physics.quantum.QPE"), part = sub_expr1), targets = sub_expr4), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, sub_expr5, one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = SubIndexed(Literal("psi", latex_format = r"\psi", theory = "proveit.physics.quantum.QPE"), [t]), part = sub_expr1), targets = Interval(one, Literal("t", theory = "proveit.physics.quantum.QPE"))), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = Literal("|u>", latex_format = r"\lvert u \rangle", theory = "proveit.physics.quantum.QPE"), part = sub_expr1), targets = sub_expr4), one, Literal("s", theory = "proveit.physics.quantum.QPE"))]))

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{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \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} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\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: 65 end_index: 66
7	ExprRange	lambda_map: 13 start_index: 65 end_index: 67
8	ExprRange	lambda_map: 14 start_index: 65 end_index: 66
9	ExprRange	lambda_map: 14 start_index: 54 end_index: 55
10	ExprRange	lambda_map: 15 start_index: 65 end_index: 66
11	ExprRange	lambda_map: 16 start_index: 65 end_index: 67
12	Lambda	parameter: 53 body: 17
13	Lambda	parameter: 53 body: 18
14	Lambda	parameter: 53 body: 19
15	Lambda	parameter: 53 body: 20
16	Lambda	parameter: 53 body: 22
17	Operation	operator: 39 operands: 23
18	Operation	operator: 27 operands: 24
19	Operation	operator: 27 operands: 25
20	Operation	operator: 27 operands: 26
21	ExprTuple	53
22	Operation	operator: 27 operands: 28
23	NamedExprs	state: 29
24	NamedExprs	element: 30 targets: 36
25	NamedExprs	element: 31 targets: 32
26	NamedExprs	element: 33 targets: 34
27	Literal
28	NamedExprs	element: 35 targets: 36
29	Operation	operator: 37 operand: 49
30	Operation	operator: 39 operands: 46
31	Operation	operator: 40 operands: 41
32	Operation	operator: 47 operands: 42
33	Operation	operator: 45 operands: 43
34	Operation	operator: 47 operands: 44
35	Operation	operator: 45 operands: 46
36	Operation	operator: 47 operands: 48
37	Literal
38	ExprTuple	49
39	Literal
40	Literal
41	NamedExprs	operation: 50 part: 53
42	ExprTuple	65, 55
43	NamedExprs	state: 51 part: 53
44	ExprTuple	65, 66
45	Literal
46	NamedExprs	state: 52 part: 53
47	Literal
48	ExprTuple	54, 55
49	Literal
50	Operation	operator: 56 operands: 57
51	Operation	operator: 58 operand: 64
52	Literal
53	Variable
54	Operation	operator: 61 operands: 60
55	Operation	operator: 61 operands: 62
56	Literal
57	ExprTuple	63, 66
58	Literal
59	ExprTuple	64
60	ExprTuple	66, 65
61	Literal
62	ExprTuple	66, 67
63	Literal
64	Variable
65	Literal
66	Literal
67	Literal