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Expression of type ExprRange

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, Variable
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _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 = ExprRange(sub_expr1, MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, Add(_t, _s))), one, _t).with_wrapping_at(2,6)
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())
\begin{array}{l} \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \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 \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 \rangle {\otimes} \lvert u \rangle~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \end{array}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
parameterization'implicit' (default for LaTeX formatting) hides the parameter the ExprRange so the parameterization may be ambiguous (e.g., x_{1+1}, ..., x_{n+1}); 'explicit' (default for string formatting) reveals the parameterization (e.g. x_{1+1}, ..x_{k+1}.., x_{n+1}).NoneNone/False('with_explicit_parameterization', 'with_implicit_parameterization', 'with_default_parameterization_style')
front_expansionThe number of instances to display at the front of the range (e.g., before the ellipsis). Default is 2.22('with_front_expansion', 'get_front_expansion')
back_expansionThe number of instances to display at the back of the range (e.g., after the ellipsis). Default is 1.11('with_back_expansion', 'get_back_expansion')
orderThe default order is 'increasing' (a_1 ... a_3) but to represent a 'decreasing' ExprRange (a_6 ... a_2) the order must be set to 'decreasing'increasingincreasing('with_decreasing_order', 'with_increasing_order')
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()(2 6)('with_wrapping_at',)
case_simplifyIf 'True', simplify formatted instances that are ConditionalSets under proper index assumptionsFalseFalse('with_case_simplification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprRangelambda_map: 1
start_index: 14
end_index: 22
1Lambdaparameter: 13
body: 3
2ExprTuple13
3Operationoperator: 4
operands: 5
4Literal
5NamedExprselement: 6
targets: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9NamedExprsstate: 12
part: 13
10Literal
11ExprTuple14, 15
12Operationoperator: 16
operands: 17
13Variable
14Literal
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple22, 23
20Literal
21Literal
22Literal
23Literal