Expression of type Equals ¶

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 Conditional, ConditionalSet, ExprRange, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import MatrixExp
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Exp, Interval, Neg, one, two, zero
from proveit.physics.quantum import CONTROL
from proveit.physics.quantum.QPE import _U, _s
from proveit.physics.quantum.circuits import Gate, Igate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(t, one)
sub_expr4 = Add(sub_expr1, t)
expr = Equals(Len(operands = [ExprRange(sub_expr1, [ExprRange(sub_expr2, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr4, sub_expr2)), Conditional(Igate, NotEquals(sub_expr4, sub_expr2))), one, t).with_case_simplification(), ExprRange(sub_expr2, MultiQubitElem(element = Gate(operation = MatrixExp(_U, Exp(two, Neg(sub_expr1))), part = sub_expr2), targets = Interval(sub_expr3, Add(t, _s))), one, _s)], Add(Neg(t), one), zero)]), Variable("_c", latex_format = r"{_{-}c}"))

# 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(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-\left(-t + 1\right)}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-\left(-t + 1\right)}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-\left(-t + 1\right)}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-\left(-t + 2\right)}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-\left(-t + 2\right)}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-\left(-t + 2\right)}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \ldots, \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-0}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-0}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-0}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right)\right)| = {_{-}c}

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

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

Expression of type Equals¶

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

Expression of type Equals ¶

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