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 ExprRange, Variable, m
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one, two
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Measure, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [[ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), Add(_t, _s))), one, _s)]]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

# 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{
& & \meter 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(s - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)\right)| = |\left(1, \ldots, 2\right)|

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

Expression of type Equals¶

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

Expression of type Equals ¶

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