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.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one, three
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr3 = Add(_t, _s)
sub_expr4 = Add(_t, one)
sub_expr5 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Equals(Len(operands = [ExprRange(sub_expr1, sub_expr5, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr5, sub_expr4, sub_expr3).with_wrapping_at(2,6), 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(sub_expr4, sub_expr3)), one, _s)]), Len(operands = [ExprRange(sub_expr2, ExprRange(sub_expr1, [sub_expr2, sub_expr1], one, sub_expr3), one, three)]))

# 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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\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},\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)| = |\left(\left(1, 1\right), \left(1, 2\right), \ldots, \left(1, t + s\right), \left(2, 1\right), \left(2, 2\right), \ldots, \left(2, t + s\right), \ldots\ldots, \left(3, 1\right), \left(3, 2\right), \ldots, \left(3, t + s\right)\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, 10, 11, 12, 13
6	Literal
7	ExprTuple	14
8	ExprRange	lambda_map: 15 start_index: 73 end_index: 74
9	ExprRange	lambda_map: 15 start_index: 61 end_index: 62
10	ExprRange	lambda_map: 16 start_index: 73 end_index: 74
11	ExprRange	lambda_map: 17 start_index: 73 end_index: 75
12	ExprRange	lambda_map: 18 start_index: 73 end_index: 74
13	ExprRange	lambda_map: 19 start_index: 73 end_index: 75
14	ExprRange	lambda_map: 20 start_index: 73 end_index: 21
15	Lambda	parameter: 60 body: 22
16	Lambda	parameter: 60 body: 23
17	Lambda	parameter: 60 body: 24
18	Lambda	parameter: 60 body: 25
19	Lambda	parameter: 60 body: 26
20	Lambda	parameter: 57 body: 28
21	Literal
22	Operation	operator: 35 operands: 29
23	Operation	operator: 30 operands: 31
24	Operation	operator: 32 operands: 33
25	Operation	operator: 35 operands: 34
26	Operation	operator: 35 operands: 36
27	ExprTuple	57
28	ExprRange	lambda_map: 37 start_index: 73 end_index: 62
29	NamedExprs	element: 38 targets: 39
30	Literal
31	NamedExprs	basis: 40
32	Literal
33	NamedExprs	operation: 41
34	NamedExprs	element: 42 targets: 43
35	Literal
36	NamedExprs	element: 44 targets: 45
37	Lambda	parameter: 60 body: 47
38	Operation	operator: 48 operands: 49
39	Operation	operator: 55 operands: 50
40	Literal
41	Literal
42	Operation	operator: 53 operands: 51
43	Operation	operator: 55 operands: 52
44	Operation	operator: 53 operands: 54
45	Operation	operator: 55 operands: 56
46	ExprTuple	60
47	ExprTuple	57, 60
48	Literal
49	NamedExprs	state: 58 part: 60
50	ExprTuple	73, 62
51	NamedExprs	state: 59 part: 60
52	ExprTuple	73, 74
53	Literal
54	NamedExprs	state: 71 part: 60
55	Literal
56	ExprTuple	61, 62
57	Variable
58	Operation	operator: 63 operands: 64
59	Operation	operator: 65 operands: 66
60	Variable
61	Operation	operator: 68 operands: 67
62	Operation	operator: 68 operands: 69
63	Literal
64	ExprTuple	70, 71
65	Literal
66	ExprTuple	72, 74
67	ExprTuple	74, 73
68	Literal
69	ExprTuple	74, 75
70	Literal
71	Literal
72	Variable
73	Literal
74	Literal
75	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 ¶