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
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 ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi__t_ket, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Interval(one, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Output(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = sub_expr4)
expr = Equals(Len(operands = [[ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3).with_wrapping_at(2,6)]]), Len(operands = [ExprRange(sub_expr1, sub_expr1, 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(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}_1\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)\right)| = |\left(1, 2, \ldots, 3\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
6	Literal
7	ExprTuple	11
8	ExprTuple	12, 13
9	ExprTuple	14, 15
10	ExprTuple	16, 17
11	ExprRange	lambda_map: 18 start_index: 64 end_index: 19
12	ExprRange	lambda_map: 20 start_index: 64 end_index: 71
13	ExprRange	lambda_map: 21 start_index: 64 end_index: 68
14	ExprRange	lambda_map: 22 start_index: 64 end_index: 71
15	ExprRange	lambda_map: 22 start_index: 52 end_index: 56
16	ExprRange	lambda_map: 23 start_index: 64 end_index: 71
17	ExprRange	lambda_map: 23 start_index: 52 end_index: 56
18	Lambda	parameter: 55 body: 55
19	Literal
20	Lambda	parameter: 55 body: 24
21	Lambda	parameter: 55 body: 25
22	Lambda	parameter: 55 body: 26
23	Lambda	parameter: 55 body: 28
24	Operation	operator: 42 operands: 29
25	Operation	operator: 32 operands: 30
26	Operation	operator: 32 operands: 31
27	ExprTuple	55
28	Operation	operator: 32 operands: 33
29	NamedExprs	state: 34
30	NamedExprs	element: 35 targets: 36
31	NamedExprs	element: 37 targets: 39
32	Literal
33	NamedExprs	element: 38 targets: 39
34	Operation	operator: 40 operand: 51
35	Operation	operator: 42 operands: 43
36	Operation	operator: 49 operands: 44
37	Operation	operator: 45 operands: 46
38	Operation	operator: 47 operands: 48
39	Operation	operator: 49 operands: 50
40	Literal
41	ExprTuple	51
42	Literal
43	NamedExprs	state: 67 part: 55
44	ExprTuple	52, 56
45	Literal
46	NamedExprs	operation: 53 part: 55
47	Literal
48	NamedExprs	state: 54 part: 55
49	Literal
50	ExprTuple	64, 56
51	Literal
52	Operation	operator: 62 operands: 57
53	Operation	operator: 58 operands: 59
54	Operation	operator: 60 operands: 61
55	Variable
56	Operation	operator: 62 operands: 63
57	ExprTuple	71, 64
58	Literal
59	ExprTuple	65, 71
60	Literal
61	ExprTuple	66, 67
62	Literal
63	ExprTuple	71, 68
64	Literal
65	Literal
66	Operation	operator: 69 operand: 71
67	Literal
68	Literal
69	Literal
70	ExprTuple	71
71	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 ¶