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 Conditional, ConditionalSet, ExprRange, Variable, VertExprArray, t
from proveit.linear_algebra import MatrixExp
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Exp, Interval, Neg, one, two, zero
from proveit.physics.quantum import CONTROL
from proveit.physics.quantum.QPE import QPE1, _U, _s
from proveit.physics.quantum.circuits import Gate, Igate, MultiQubitElem, Qcircuit, QcircuitEquiv
# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(t, one)
sub_expr4 = Add(sub_expr1, t)
sub_expr5 = Add(t, _s)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr2), targets = Interval(one, sub_expr5))
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(ExprRange(sub_expr1, [ExprRange(sub_expr2, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr4, sub_expr2)), Conditional(Igate, NotEquals(sub_expr4, sub_expr2))), one, t).with_case_simplification(), ExprRange(sub_expr2, MultiQubitElem(element = Gate(operation = MatrixExp(_U, Exp(two, Neg(sub_expr1))), part = sub_expr2), targets = Interval(sub_expr3, sub_expr5)), one, _s)], Add(Neg(t), one), zero).with_decreasing_order().with_case_simplification())), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr2, sub_expr6, one, t), ExprRange(sub_expr2, sub_expr6, sub_expr3, sub_expr5)])))
# 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")
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
stored_expr.style_options()
# display the expression information
stored_expr.expr_info()