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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, s, t
from proveit.numbers import Add, Interval, Mod, Mult, Round, one
from proveit.physics.quantum import NumKet, var_ket_u
from proveit.physics.quantum.QPE import phase, two_pow_t
from proveit.physics.quantum.circuits import MultiQubitElem, Output
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(two_pow_t, phase)), two_pow_t), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, s))), one, 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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \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)
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
1ExprRangelambda_map: 3
start_index: 32
end_index: 47
2ExprRangelambda_map: 4
start_index: 32
end_index: 33
3Lambdaparameter: 23
body: 5
4Lambdaparameter: 23
body: 7
5Operationoperator: 9
operands: 8
6ExprTuple23
7Operationoperator: 9
operands: 10
8NamedExprselement: 11
targets: 12
9Literal
10NamedExprselement: 13
targets: 14
11Operationoperator: 17
operands: 15
12Operationoperator: 19
operands: 16
13Operationoperator: 17
operands: 18
14Operationoperator: 19
operands: 20
15NamedExprsstate: 21
part: 23
16ExprTuple32, 47
17Literal
18NamedExprsstate: 22
part: 23
19Literal
20ExprTuple24, 25
21Operationoperator: 26
operands: 27
22Variable
23Variable
24Operationoperator: 29
operands: 28
25Operationoperator: 29
operands: 30
26Literal
27ExprTuple31, 47
28ExprTuple47, 32
29Literal
30ExprTuple47, 33
31Operationoperator: 34
operands: 35
32Literal
33Variable
34Literal
35ExprTuple36, 42
36Operationoperator: 37
operand: 39
37Literal
38ExprTuple39
39Operationoperator: 40
operands: 41
40Literal
41ExprTuple42, 43
42Operationoperator: 44
operands: 45
43Variable
44Literal
45ExprTuple46, 47
46Literal
47Variable