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 = Add(_t, _s)
expr = Equals(Len(operands = [[ExprRange(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)), one, sub_expr2)], [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), sub_expr2)), one, _s)]]), 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 \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 + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \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, 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
9	ExprTuple	13, 14
10	ExprTuple	15, 16
11	ExprRange	lambda_map: 17 start_index: 70 end_index: 18
12	ExprRange	lambda_map: 19 start_index: 70 end_index: 59
13	ExprRange	lambda_map: 20 start_index: 70 end_index: 71
14	ExprRange	lambda_map: 21 start_index: 70 end_index: 72
15	ExprRange	lambda_map: 22 start_index: 70 end_index: 71
16	ExprRange	lambda_map: 23 start_index: 70 end_index: 72
17	Lambda	parameter: 57 body: 57
18	Literal
19	Lambda	parameter: 57 body: 24
20	Lambda	parameter: 57 body: 25
21	Lambda	parameter: 57 body: 26
22	Lambda	parameter: 57 body: 27
23	Lambda	parameter: 57 body: 29
24	Operation	operator: 36 operands: 30
25	Operation	operator: 31 operands: 32
26	Operation	operator: 33 operands: 34
27	Operation	operator: 36 operands: 35
28	ExprTuple	57
29	Operation	operator: 36 operands: 37
30	NamedExprs	element: 38 targets: 39
31	Literal
32	NamedExprs	basis: 40
33	Literal
34	NamedExprs	operation: 41
35	NamedExprs	element: 42 targets: 43
36	Literal
37	NamedExprs	element: 44 targets: 45
38	Operation	operator: 46 operands: 47
39	Operation	operator: 53 operands: 48
40	Literal
41	Literal
42	Operation	operator: 51 operands: 49
43	Operation	operator: 53 operands: 50
44	Operation	operator: 51 operands: 52
45	Operation	operator: 53 operands: 54
46	Literal
47	NamedExprs	state: 55 part: 57
48	ExprTuple	70, 59
49	NamedExprs	state: 56 part: 57
50	ExprTuple	70, 71
51	Literal
52	NamedExprs	state: 68 part: 57
53	Literal
54	ExprTuple	58, 59
55	Operation	operator: 60 operands: 61
56	Operation	operator: 62 operands: 63
57	Variable
58	Operation	operator: 65 operands: 64
59	Operation	operator: 65 operands: 66
60	Literal
61	ExprTuple	67, 68
62	Literal
63	ExprTuple	69, 71
64	ExprTuple	71, 70
65	Literal
66	ExprTuple	71, 72
67	Literal
68	Literal
69	Variable
70	Literal
71	Literal
72	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 ¶