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, U, Variable, VertExprArray, s, t
from proveit.numbers import Add, Interval, Mod, Mult, Round, one
from proveit.physics.quantum import I, NumKet, Z, ket_plus, var_ket_u
from proveit.physics.quantum.QPE import QPE, phase, two_pow_t
from proveit.physics.quantum.circuits import Gate, Input, Measure, 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(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr4), one, s)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(two_pow_t, phase)), two_pow_t), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = sub_expr4), one, s)]))

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}\left(U, t\right)} & \meter & \multiqout{3}{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \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, 6
3	ExprTuple	7, 8
4	ExprTuple	9, 10
5	ExprTuple	11, 12
6	ExprTuple	13, 14
7	ExprRange	lambda_map: 15 start_index: 77 end_index: 92
8	ExprRange	lambda_map: 16 start_index: 77 end_index: 78
9	ExprRange	lambda_map: 17 start_index: 77 end_index: 92
10	ExprRange	lambda_map: 17 start_index: 66 end_index: 67
11	ExprRange	lambda_map: 18 start_index: 77 end_index: 92
12	ExprRange	lambda_map: 19 start_index: 77 end_index: 78
13	ExprRange	lambda_map: 20 start_index: 77 end_index: 92
14	ExprRange	lambda_map: 21 start_index: 77 end_index: 78
15	Lambda	parameter: 65 body: 22
16	Lambda	parameter: 65 body: 23
17	Lambda	parameter: 65 body: 24
18	Lambda	parameter: 65 body: 25
19	Lambda	parameter: 65 body: 26
20	Lambda	parameter: 65 body: 27
21	Lambda	parameter: 65 body: 29
22	Operation	operator: 51 operands: 30
23	Operation	operator: 37 operands: 31
24	Operation	operator: 37 operands: 32
25	Operation	operator: 33 operands: 34
26	Operation	operator: 52 operands: 35
27	Operation	operator: 37 operands: 36
28	ExprTuple	65
29	Operation	operator: 37 operands: 38
30	NamedExprs	state: 39
31	NamedExprs	element: 40 targets: 48
32	NamedExprs	element: 41 targets: 42
33	Literal
34	NamedExprs	basis: 43
35	NamedExprs	operation: 44
36	NamedExprs	element: 45 targets: 46
37	Literal
38	NamedExprs	element: 47 targets: 48
39	Operation	operator: 49 operand: 61
40	Operation	operator: 51 operands: 58
41	Operation	operator: 52 operands: 53
42	Operation	operator: 59 operands: 54
43	Literal
44	Literal
45	Operation	operator: 57 operands: 55
46	Operation	operator: 59 operands: 56
47	Operation	operator: 57 operands: 58
48	Operation	operator: 59 operands: 60
49	Literal
50	ExprTuple	61
51	Literal
52	Literal
53	NamedExprs	operation: 62 part: 65
54	ExprTuple	77, 67
55	NamedExprs	state: 63 part: 65
56	ExprTuple	77, 92
57	Literal
58	NamedExprs	state: 64 part: 65
59	Literal
60	ExprTuple	66, 67
61	Literal
62	Operation	operator: 68 operands: 69
63	Operation	operator: 70 operands: 71
64	Variable
65	Variable
66	Operation	operator: 73 operands: 72
67	Operation	operator: 73 operands: 74
68	Literal
69	ExprTuple	75, 92
70	Literal
71	ExprTuple	76, 92
72	ExprTuple	92, 77
73	Literal
74	ExprTuple	92, 78
75	Variable
76	Operation	operator: 79 operands: 80
77	Literal
78	Variable
79	Literal
80	ExprTuple	81, 87
81	Operation	operator: 82 operand: 84
82	Literal
83	ExprTuple	84
84	Operation	operator: 85 operands: 86
85	Literal
86	ExprTuple	87, 88
87	Operation	operator: 89 operands: 90
88	Variable
89	Literal
90	ExprTuple	91, 92
91	Literal
92	Variable