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, m
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, 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, _s)
expr = Prob(Qcircuit(vert_expr_array = VertExprArray([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)])))

# 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 \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) \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
7	ExprTuple	10, 11
8	ExprTuple	12, 13
9	ExprRange	lambda_map: 14 start_index: 65 end_index: 54
10	ExprRange	lambda_map: 15 start_index: 65 end_index: 66
11	ExprRange	lambda_map: 16 start_index: 65 end_index: 67
12	ExprRange	lambda_map: 17 start_index: 65 end_index: 66
13	ExprRange	lambda_map: 18 start_index: 65 end_index: 67
14	Lambda	parameter: 52 body: 19
15	Lambda	parameter: 52 body: 20
16	Lambda	parameter: 52 body: 21
17	Lambda	parameter: 52 body: 22
18	Lambda	parameter: 52 body: 24
19	Operation	operator: 31 operands: 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operands: 29
22	Operation	operator: 31 operands: 30
23	ExprTuple	52
24	Operation	operator: 31 operands: 32
25	NamedExprs	element: 33 targets: 34
26	Literal
27	NamedExprs	basis: 35
28	Literal
29	NamedExprs	operation: 36
30	NamedExprs	element: 37 targets: 38
31	Literal
32	NamedExprs	element: 39 targets: 40
33	Operation	operator: 41 operands: 42
34	Operation	operator: 48 operands: 43
35	Literal
36	Literal
37	Operation	operator: 46 operands: 44
38	Operation	operator: 48 operands: 45
39	Operation	operator: 46 operands: 47
40	Operation	operator: 48 operands: 49
41	Literal
42	NamedExprs	state: 50 part: 52
43	ExprTuple	65, 54
44	NamedExprs	state: 51 part: 52
45	ExprTuple	65, 66
46	Literal
47	NamedExprs	state: 63 part: 52
48	Literal
49	ExprTuple	53, 54
50	Operation	operator: 55 operands: 56
51	Operation	operator: 57 operands: 58
52	Variable
53	Operation	operator: 60 operands: 59
54	Operation	operator: 60 operands: 61
55	Literal
56	ExprTuple	62, 63
57	Literal
58	ExprTuple	64, 66
59	ExprTuple	66, 65
60	Literal
61	ExprTuple	66, 67
62	Literal
63	Literal
64	Variable
65	Literal
66	Literal
67	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 ¶