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
from proveit.numbers import Add, Exp, Interval, Mod, Mult, Round, one, two
from proveit.physics.quantum import I, NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE
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(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 = Exp(two, Literal("t", theory = "proveit.physics.quantum.QPE"))
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE(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_expr5), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, sub_expr6, one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(sub_expr4, Literal("phase", latex_format = r"\varphi", theory = "proveit.physics.quantum.QPE"))), sub_expr4), Literal("t", theory = "proveit.physics.quantum.QPE")), 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_expr5), one, Literal("s", theory = "proveit.physics.quantum.QPE"))]))

# 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()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
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	Literal
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	Literal
76	Operation	operator: 79 operands: 80
77	Literal
78	Literal
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	Literal
89	Literal
90	ExprTuple	91, 92
91	Literal
92	Literal

Expression of type Qcircuit¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type Qcircuit ¶

from the theory of proveit.physics.quantum.QPE ¶