Expression of type Len ¶

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.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _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, _s)
sub_expr3 = Interval(one, _t)
expr = Len(operands = [ExprRange(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)), one, sub_expr2), ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr3), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr3), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2)), one, _s)])

# 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_{t} \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_{t} \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_{t} \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{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \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 \Psi \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle~\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)|

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',)

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

Expression of type Len¶

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

Expression of type Len ¶

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