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)]), t)

# 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)| = t

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