Expression of type Prob ¶

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, VertExprArray
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
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, Qcircuit
from proveit.statistics import Prob

# 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)
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([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, MultiQubitElem(element = Output(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = sub_expr4), one, sub_expr3)])))

# 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())

\textrm{Pr}\left(QCIRCUIT\left(VertExprArray\left(\begin{array}{c} \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 + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \end{array}\right)\right)\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7, 8
6	ExprTuple	9, 10
7	ExprTuple	11, 12
8	ExprTuple	13
9	ExprRange	lambda_map: 14 start_index: 58 end_index: 65
10	ExprRange	lambda_map: 15 start_index: 58 end_index: 62
11	ExprRange	lambda_map: 16 start_index: 58 end_index: 65
12	ExprRange	lambda_map: 16 start_index: 46 end_index: 50
13	ExprRange	lambda_map: 17 start_index: 58 end_index: 50
14	Lambda	parameter: 49 body: 18
15	Lambda	parameter: 49 body: 19
16	Lambda	parameter: 49 body: 20
17	Lambda	parameter: 49 body: 22
18	Operation	operator: 36 operands: 23
19	Operation	operator: 26 operands: 24
20	Operation	operator: 26 operands: 25
21	ExprTuple	49
22	Operation	operator: 26 operands: 27
23	NamedExprs	state: 28
24	NamedExprs	element: 29 targets: 30
25	NamedExprs	element: 31 targets: 33
26	Literal
27	NamedExprs	element: 32 targets: 33
28	Operation	operator: 34 operand: 45
29	Operation	operator: 36 operands: 37
30	Operation	operator: 43 operands: 38
31	Operation	operator: 39 operands: 40
32	Operation	operator: 41 operands: 42
33	Operation	operator: 43 operands: 44
34	Literal
35	ExprTuple	45
36	Literal
37	NamedExprs	state: 61 part: 49
38	ExprTuple	46, 50
39	Literal
40	NamedExprs	operation: 47 part: 49
41	Literal
42	NamedExprs	state: 48 part: 49
43	Literal
44	ExprTuple	58, 50
45	Literal
46	Operation	operator: 56 operands: 51
47	Operation	operator: 52 operands: 53
48	Operation	operator: 54 operands: 55
49	Variable
50	Operation	operator: 56 operands: 57
51	ExprTuple	65, 58
52	Literal
53	ExprTuple	59, 65
54	Literal
55	ExprTuple	60, 61
56	Literal
57	ExprTuple	65, 62
58	Literal
59	Literal
60	Operation	operator: 63 operand: 65
61	Literal
62	Literal
63	Literal
64	ExprTuple	65
65	Literal

Expression of type Prob¶

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

Expression of type Prob ¶

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