# 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.
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import one
from proveit.physics.quantum import Z
from proveit.physics.quantum.QPE import _t
from proveit.physics.quantum.circuits import Measure

In [2]:
# build up the expression from sub-expressions
expr = Equals(Len(operands = [ExprRange(Variable("_a", latex_format = r"{_{-}a}"), Measure(basis = Z), one, _t)]), _t)

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{
& & \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}\right)| = t

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 9
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6
6ExprRangelambda_map: 7
start_index: 8
end_index: 9
7Lambdaparameter: 12
body: 11
8Literal
9Literal
10ExprTuple12
11Operationoperator: 13
operands: 14
12Variable
13Literal
14NamedExprsbasis: 15
15Literal