Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda(m, 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))))))

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())

\left(m \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 95 body: 3
2	ExprTuple	95
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11, 12, 13
8	Literal
9	ExprTuple	95, 14
10	ExprTuple	15, 16
11	ExprTuple	17, 18
12	ExprTuple	19, 20
13	ExprTuple	21, 22
14	Operation	operator: 77 operands: 23
15	ExprRange	lambda_map: 24 start_index: 96 end_index: 97
16	ExprRange	lambda_map: 25 start_index: 96 end_index: 98
17	ExprRange	lambda_map: 26 start_index: 96 end_index: 97
18	ExprRange	lambda_map: 26 start_index: 85 end_index: 86
19	ExprRange	lambda_map: 27 start_index: 96 end_index: 97
20	ExprRange	lambda_map: 28 start_index: 96 end_index: 98
21	ExprRange	lambda_map: 29 start_index: 96 end_index: 97
22	ExprRange	lambda_map: 30 start_index: 96 end_index: 98
23	ExprTuple	31, 32
24	Lambda	parameter: 84 body: 33
25	Lambda	parameter: 84 body: 34
26	Lambda	parameter: 84 body: 35
27	Lambda	parameter: 84 body: 36
28	Lambda	parameter: 84 body: 37
29	Lambda	parameter: 84 body: 38
30	Lambda	parameter: 84 body: 40
31	Literal
32	Operation	operator: 92 operands: 41
33	Operation	operator: 69 operands: 42
34	Operation	operator: 49 operands: 43
35	Operation	operator: 49 operands: 44
36	Operation	operator: 45 operands: 46
37	Operation	operator: 70 operands: 47
38	Operation	operator: 49 operands: 48
39	ExprTuple	84
40	Operation	operator: 49 operands: 50
41	ExprTuple	51, 52
42	NamedExprs	state: 53
43	NamedExprs	element: 54 targets: 62
44	NamedExprs	element: 55 targets: 56
45	Literal
46	NamedExprs	basis: 57
47	NamedExprs	operation: 58
48	NamedExprs	element: 59 targets: 60
49	Literal
50	NamedExprs	element: 61 targets: 62
51	Operation	operator: 63 operands: 64
52	Operation	operator: 65 operand: 96
53	Operation	operator: 67 operand: 80
54	Operation	operator: 69 operands: 76
55	Operation	operator: 70 operands: 71
56	Operation	operator: 77 operands: 72
57	Literal
58	Literal
59	Operation	operator: 75 operands: 73
60	Operation	operator: 77 operands: 74
61	Operation	operator: 75 operands: 76
62	Operation	operator: 77 operands: 78
63	Literal
64	ExprTuple	79, 97
65	Literal
66	ExprTuple	96
67	Literal
68	ExprTuple	80
69	Literal
70	Literal
71	NamedExprs	operation: 81 part: 84
72	ExprTuple	96, 86
73	NamedExprs	state: 82 part: 84
74	ExprTuple	96, 97
75	Literal
76	NamedExprs	state: 83 part: 84
77	Literal
78	ExprTuple	85, 86
79	Literal
80	Literal
81	Operation	operator: 87 operands: 88
82	Operation	operator: 89 operands: 90
83	Literal
84	Variable
85	Operation	operator: 92 operands: 91
86	Operation	operator: 92 operands: 93
87	Literal
88	ExprTuple	94, 97
89	Literal
90	ExprTuple	95, 97
91	ExprTuple	97, 96
92	Literal
93	ExprTuple	97, 98
94	Literal
95	Variable
96	Literal
97	Literal
98	Literal