Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

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, Lambda, m, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum import NumBra, Qmult, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda(var_ket_psi, Conditional(Equals(Prob(register_meas), Exp(Abs(Qmult(NumBra(n, m), var_ket_psi)), two)), And(InSet(var_ket_psi, m_ket_domain), normalized_var_ket_psi)))

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())

\lvert \psi \rangle \mapsto \left\{\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right) = \left|{_{m}}\langle n \rvert \thinspace \lvert \psi \rangle\right|^{2} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2^{m}} ,  \left \|\lvert \psi \rangle\right \| = 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: 68 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 16 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 11 operand: 18
8	Operation	operator: 41 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	18
13	ExprTuple	19, 47
14	Literal
15	ExprTuple	68, 20
16	Literal
17	ExprTuple	21, 71
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operand: 33
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operand: 68
22	Literal
23	ExprTuple	30, 31, 32
24	Literal
25	ExprTuple	33
26	Literal
27	ExprTuple	34, 35
28	Literal
29	ExprTuple	68
30	ExprTuple	36
31	ExprTuple	37
32	ExprTuple	38
33	Operation	operator: 39 operands: 40
34	Literal
35	Operation	operator: 41 operands: 42
36	ExprRange	lambda_map: 43 start_index: 71 end_index: 75
37	ExprRange	lambda_map: 44 start_index: 71 end_index: 75
38	ExprRange	lambda_map: 45 start_index: 71 end_index: 75
39	Literal
40	ExprTuple	46, 68
41	Literal
42	ExprTuple	47, 75
43	Lambda	parameter: 70 body: 48
44	Lambda	parameter: 70 body: 49
45	Lambda	parameter: 70 body: 51
46	Operation	operator: 52 operands: 73
47	Literal
48	Operation	operator: 56 operands: 53
49	Operation	operator: 54 operands: 55
50	ExprTuple	70
51	Operation	operator: 56 operands: 57
52	Literal
53	NamedExprs	element: 58 targets: 61
54	Literal
55	NamedExprs	basis: 59
56	Literal
57	NamedExprs	element: 60 targets: 61
58	Operation	operator: 62 operands: 63
59	Literal
60	Operation	operator: 64 operands: 65
61	Operation	operator: 66 operands: 67
62	Literal
63	NamedExprs	state: 68 part: 70
64	Literal
65	NamedExprs	state: 69 part: 70
66	Literal
67	ExprTuple	71, 75
68	Variable
69	Operation	operator: 72 operands: 73
70	Variable
71	Literal
72	Literal
73	ExprTuple	74, 75
74	Variable
75	Variable