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, m
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 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)
sub_expr3 = Add(_t, one)
sub_expr4 = MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = Len(operands = [[ExprRange(sub_expr1, sub_expr4, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr4, sub_expr3, sub_expr2).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_expr3, 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(\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}\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)|

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
3	ExprTuple	6, 7
4	ExprTuple	8, 9
5	ExprTuple	10, 11
6	ExprRange	lambda_map: 12 start_index: 63 end_index: 64
7	ExprRange	lambda_map: 12 start_index: 51 end_index: 52
8	ExprRange	lambda_map: 13 start_index: 63 end_index: 64
9	ExprRange	lambda_map: 14 start_index: 63 end_index: 65
10	ExprRange	lambda_map: 15 start_index: 63 end_index: 64
11	ExprRange	lambda_map: 16 start_index: 63 end_index: 65
12	Lambda	parameter: 50 body: 17
13	Lambda	parameter: 50 body: 18
14	Lambda	parameter: 50 body: 19
15	Lambda	parameter: 50 body: 20
16	Lambda	parameter: 50 body: 22
17	Operation	operator: 29 operands: 23
18	Operation	operator: 24 operands: 25
19	Operation	operator: 26 operands: 27
20	Operation	operator: 29 operands: 28
21	ExprTuple	50
22	Operation	operator: 29 operands: 30
23	NamedExprs	element: 31 targets: 32
24	Literal
25	NamedExprs	basis: 33
26	Literal
27	NamedExprs	operation: 34
28	NamedExprs	element: 35 targets: 36
29	Literal
30	NamedExprs	element: 37 targets: 38
31	Operation	operator: 39 operands: 40
32	Operation	operator: 46 operands: 41
33	Literal
34	Literal
35	Operation	operator: 44 operands: 42
36	Operation	operator: 46 operands: 43
37	Operation	operator: 44 operands: 45
38	Operation	operator: 46 operands: 47
39	Literal
40	NamedExprs	state: 48 part: 50
41	ExprTuple	63, 52
42	NamedExprs	state: 49 part: 50
43	ExprTuple	63, 64
44	Literal
45	NamedExprs	state: 61 part: 50
46	Literal
47	ExprTuple	51, 52
48	Operation	operator: 53 operands: 54
49	Operation	operator: 55 operands: 56
50	Variable
51	Operation	operator: 58 operands: 57
52	Operation	operator: 58 operands: 59
53	Literal
54	ExprTuple	60, 61
55	Literal
56	ExprTuple	62, 64
57	ExprTuple	64, 63
58	Literal
59	ExprTuple	64, 65
60	Literal
61	Literal
62	Variable
63	Literal
64	Literal
65	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 ¶