Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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