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, U, m
from proveit.linear_algebra import Unitary
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, one, two
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import unitary_gate_op
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Conditional(Equals(Prob(unitary_gate_op), one), And(InSet(U, Unitary(Exp(two, m))), InSet(var_ket_psi, m_ket_domain)))

# 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{
\qin{\lvert \psi \rangle} & \gate{U} & \qout{U \thinspace \lvert \psi \rangle}
} \end{array}\right) = 1 \textrm{ if } U \in \textrm{U}\left(2^{m}\right) ,  \lvert \psi \rangle \in \mathbb{C}^{2^{m}}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 60
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 15
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	ExprTuple	15
12	ExprTuple	64, 16
13	Literal
14	ExprTuple	65, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operand: 28
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 25, 26
20	Literal
21	ExprTuple	28
22	Literal
23	ExprTuple	27, 28
24	ExprTuple	29
25	ExprTuple	30
26	ExprTuple	31
27	Literal
28	Operation	operator: 32 operands: 33
29	ExprRange	lambda_map: 34 start_index: 60 end_index: 61
30	ExprRange	lambda_map: 35 start_index: 60 end_index: 61
31	ExprRange	lambda_map: 36 start_index: 60 end_index: 61
32	Literal
33	ExprTuple	37, 61
34	Lambda	parameter: 59 body: 38
35	Lambda	parameter: 59 body: 39
36	Lambda	parameter: 59 body: 41
37	Literal
38	Operation	operator: 44 operands: 42
39	Operation	operator: 44 operands: 43
40	ExprTuple	59
41	Operation	operator: 44 operands: 45
42	NamedExprs	element: 46 targets: 49
43	NamedExprs	element: 47 targets: 49
44	Literal
45	NamedExprs	element: 48 targets: 49
46	Operation	operator: 50 operands: 51
47	Operation	operator: 52 operands: 53
48	Operation	operator: 54 operands: 55
49	Operation	operator: 56 operands: 57
50	Literal
51	NamedExprs	state: 65 part: 59
52	Literal
53	NamedExprs	operation: 64 part: 59
54	Literal
55	NamedExprs	state: 58 part: 59
56	Literal
57	ExprTuple	60, 61
58	Operation	operator: 62 operands: 63
59	Variable
60	Literal
61	Variable
62	Literal
63	ExprTuple	64, 65
64	Variable
65	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 ¶