Expression of type Conditional ¶

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, 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 = 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))

# 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\{\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()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

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

Expression of type Conditional ¶

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