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Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

In [1]:
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, ExprTuple, Variable, n
from proveit.core_expr_types import Len
from proveit.numbers import Add, Interval, Mult, four, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE, _U, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output
In [2]:
# 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(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ExprTuple(Len(operands = [ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s), ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3), ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire, ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(n, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]), Add(Mult(four, _t), Mult(four, _s)))
expr:
In [3]:
# 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
In [4]:
# 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 + \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},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\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}\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}\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}\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}\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}\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\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},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \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)|, \left(4 \cdot t\right) + \left(4 \cdot s\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 3
operands: 4
2Operationoperator: 78
operands: 5
3Literal
4ExprTuple6, 7, 8, 9, 10, 11, 12, 13
5ExprTuple14, 15
6ExprRangelambda_map: 16
start_index: 82
end_index: 83
7ExprRangelambda_map: 17
start_index: 82
end_index: 84
8ExprRangelambda_map: 18
start_index: 82
end_index: 83
9ExprRangelambda_map: 18
start_index: 71
end_index: 72
10ExprRangelambda_map: 19
start_index: 82
end_index: 83
11ExprRangelambda_map: 20
start_index: 82
end_index: 84
12ExprRangelambda_map: 21
start_index: 82
end_index: 83
13ExprRangelambda_map: 22
start_index: 82
end_index: 84
14Operationoperator: 24
operands: 23
15Operationoperator: 24
operands: 25
16Lambdaparameter: 70
body: 26
17Lambdaparameter: 70
body: 27
18Lambdaparameter: 70
body: 28
19Lambdaparameter: 70
body: 29
20Lambdaparameter: 70
body: 30
21Lambdaparameter: 70
body: 31
22Lambdaparameter: 70
body: 33
23ExprTuple34, 83
24Literal
25ExprTuple34, 84
26Operationoperator: 56
operands: 35
27Operationoperator: 42
operands: 36
28Operationoperator: 42
operands: 37
29Operationoperator: 38
operands: 39
30Operationoperator: 57
operands: 40
31Operationoperator: 42
operands: 41
32ExprTuple70
33Operationoperator: 42
operands: 43
34Literal
35NamedExprsstate: 44
36NamedExprselement: 45
targets: 53
37NamedExprselement: 46
targets: 47
38Literal
39NamedExprsbasis: 48
40NamedExprsoperation: 49
41NamedExprselement: 50
targets: 51
42Literal
43NamedExprselement: 52
targets: 53
44Operationoperator: 54
operand: 66
45Operationoperator: 56
operands: 63
46Operationoperator: 57
operands: 58
47Operationoperator: 64
operands: 59
48Literal
49Literal
50Operationoperator: 62
operands: 60
51Operationoperator: 64
operands: 61
52Operationoperator: 62
operands: 63
53Operationoperator: 64
operands: 65
54Literal
55ExprTuple66
56Literal
57Literal
58NamedExprsoperation: 67
part: 70
59ExprTuple82, 72
60NamedExprsstate: 68
part: 70
61ExprTuple82, 83
62Literal
63NamedExprsstate: 69
part: 70
64Literal
65ExprTuple71, 72
66Literal
67Operationoperator: 73
operands: 74
68Operationoperator: 75
operands: 76
69Literal
70Variable
71Operationoperator: 78
operands: 77
72Operationoperator: 78
operands: 79
73Literal
74ExprTuple80, 83
75Literal
76ExprTuple81, 83
77ExprTuple83, 82
78Literal
79ExprTuple83, 84
80Literal
81Variable
82Literal
83Literal
84Literal