Theorem unitary_gate_operation of type Forall ¶

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

In [1]:

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.circuits import unitary_gate_operation

In [2]:

# check that the built expression is the same as the stored expression
assert unitary_gate_operation.expr == stored_expr
assert unitary_gate_operation.expr._style_id == stored_expr._style_id
print("Passed sanity check: unitary_gate_operation matches stored_expr")

Passed sanity check: unitary_gate_operation matches stored_expr

In [3]:

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{m \in \mathbb{N}^+}~\left[\forall_{U \in \textrm{U}\left(2^{m}\right), \lvert \psi \rangle \in \mathbb{C}^{2^{m}}}~\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\right)\right]

In [4]:

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

In [5]:

# display the expression information
stored_expr.expr_info()

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