Expression of type Bijections

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, Variable, VertExprArray, m
from proveit.logic import Bijections, SetOfAll
from proveit.numbers import Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _m_domain, _t
from proveit.physics.quantum.circuits import Input, Measure, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, _t)
expr = Bijections(_m_domain, SetOfAll(instance_param_or_params = [m], instance_element = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t)])), domain = _m_domain))

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[\{0~\ldotp \ldotp~2^{t} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}}
} \end{array}\right\}_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}}\right]

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	18, 3
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 62 body: 8
7	ExprTuple	62
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16, 17
13	Literal
14	ExprTuple	62, 18
15	ExprTuple	19
16	ExprTuple	20
17	ExprTuple	21
18	Operation	operator: 53 operands: 22
19	ExprRange	lambda_map: 23 start_index: 59 end_index: 63
20	ExprRange	lambda_map: 24 start_index: 59 end_index: 63
21	ExprRange	lambda_map: 25 start_index: 59 end_index: 63
22	ExprTuple	26, 27
23	Lambda	parameter: 58 body: 28
24	Lambda	parameter: 58 body: 29
25	Lambda	parameter: 58 body: 31
26	Literal
27	Operation	operator: 32 operands: 33
28	Operation	operator: 37 operands: 34
29	Operation	operator: 35 operands: 36
30	ExprTuple	58
31	Operation	operator: 37 operands: 38
32	Literal
33	ExprTuple	39, 40
34	NamedExprs	element: 41 targets: 44
35	Literal
36	NamedExprs	basis: 42
37	Literal
38	NamedExprs	element: 43 targets: 44
39	Operation	operator: 45 operands: 46
40	Operation	operator: 47 operand: 59
41	Operation	operator: 49 operands: 50
42	Literal
43	Operation	operator: 51 operands: 52
44	Operation	operator: 53 operands: 54
45	Literal
46	ExprTuple	55, 63
47	Literal
48	ExprTuple	59
49	Literal
50	NamedExprs	state: 56 part: 58
51	Literal
52	NamedExprs	state: 57 part: 58
53	Literal
54	ExprTuple	59, 63
55	Literal
56	Literal
57	Operation	operator: 60 operands: 61
58	Variable
59	Literal
60	Literal
61	ExprTuple	62, 63
62	Variable
63	Literal