Expression of type Conditional ¶

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 Conditional, ExprRange, Literal, Variable, VertExprArray, m
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, one, subtract, two, zero
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 = Interval(sub_expr2, sub_expr3)
sub_expr5 = 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 = Conditional(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, 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(m, 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_expr4), one, Literal("s", theory = "proveit.physics.quantum.QPE"))])), InSet(m, Interval(zero, subtract(Exp(two, Literal("t", theory = "proveit.physics.quantum.QPE")), one))))

# 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{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \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 m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array} \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8, 9, 10
5	Literal
6	ExprTuple	92, 11
7	ExprTuple	12, 13
8	ExprTuple	14, 15
9	ExprTuple	16, 17
10	ExprTuple	18, 19
11	Operation	operator: 74 operands: 20
12	ExprRange	lambda_map: 21 start_index: 93 end_index: 94
13	ExprRange	lambda_map: 22 start_index: 93 end_index: 95
14	ExprRange	lambda_map: 23 start_index: 93 end_index: 94
15	ExprRange	lambda_map: 23 start_index: 82 end_index: 83
16	ExprRange	lambda_map: 24 start_index: 93 end_index: 94
17	ExprRange	lambda_map: 25 start_index: 93 end_index: 95
18	ExprRange	lambda_map: 26 start_index: 93 end_index: 94
19	ExprRange	lambda_map: 27 start_index: 93 end_index: 95
20	ExprTuple	28, 29
21	Lambda	parameter: 81 body: 30
22	Lambda	parameter: 81 body: 31
23	Lambda	parameter: 81 body: 32
24	Lambda	parameter: 81 body: 33
25	Lambda	parameter: 81 body: 34
26	Lambda	parameter: 81 body: 35
27	Lambda	parameter: 81 body: 37
28	Literal
29	Operation	operator: 89 operands: 38
30	Operation	operator: 66 operands: 39
31	Operation	operator: 46 operands: 40
32	Operation	operator: 46 operands: 41
33	Operation	operator: 42 operands: 43
34	Operation	operator: 67 operands: 44
35	Operation	operator: 46 operands: 45
36	ExprTuple	81
37	Operation	operator: 46 operands: 47
38	ExprTuple	48, 49
39	NamedExprs	state: 50
40	NamedExprs	element: 51 targets: 59
41	NamedExprs	element: 52 targets: 53
42	Literal
43	NamedExprs	basis: 54
44	NamedExprs	operation: 55
45	NamedExprs	element: 56 targets: 57
46	Literal
47	NamedExprs	element: 58 targets: 59
48	Operation	operator: 60 operands: 61
49	Operation	operator: 62 operand: 93
50	Operation	operator: 64 operand: 77
51	Operation	operator: 66 operands: 73
52	Operation	operator: 67 operands: 68
53	Operation	operator: 74 operands: 69
54	Literal
55	Literal
56	Operation	operator: 72 operands: 70
57	Operation	operator: 74 operands: 71
58	Operation	operator: 72 operands: 73
59	Operation	operator: 74 operands: 75
60	Literal
61	ExprTuple	76, 94
62	Literal
63	ExprTuple	93
64	Literal
65	ExprTuple	77
66	Literal
67	Literal
68	NamedExprs	operation: 78 part: 81
69	ExprTuple	93, 83
70	NamedExprs	state: 79 part: 81
71	ExprTuple	93, 94
72	Literal
73	NamedExprs	state: 80 part: 81
74	Literal
75	ExprTuple	82, 83
76	Literal
77	Literal
78	Operation	operator: 84 operands: 85
79	Operation	operator: 86 operands: 87
80	Literal
81	Variable
82	Operation	operator: 89 operands: 88
83	Operation	operator: 89 operands: 90
84	Literal
85	ExprTuple	91, 94
86	Literal
87	ExprTuple	92, 94
88	ExprTuple	94, 93
89	Literal
90	ExprTuple	94, 95
91	Literal
92	Variable
93	Literal
94	Literal
95	Literal

Expression of type Conditional¶

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

Expression of type Conditional ¶

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