Add explicit adjoint for qubitization walk operator

[tanujkhattar]

Fixes #936

Note that symbolic case reported in #935 (comment) but that is now because of a niche sympy error. The core issue is that big_O() notation does not play well with "add up summations of individual terms" logic implemented in the T-complexity protocol.

See the details below for the error raised when testing t-complexity for symbolic hamiltonian simulation via gqsp bloq

>       _ = symbolic_hamsim_by_gqsp.gqsp.t_complexity()

qualtran/bloqs/hamiltonian_simulation/hamiltonian_simulation_by_gqsp_test.py:103:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
qualtran/_infra/bloq.py:427: in t_complexity
    return t_complexity(self)
qualtran/cirq_interop/t_complexity_protocol.py:246: in t_complexity
    ret = _t_complexity_for_gate_or_op(stc)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/cachetools/__init__.py:675: in wrapper
    v = func(*args, **kwargs)
qualtran/cirq_interop/t_complexity_protocol.py:230: in _t_complexity_for_gate_or_op
    return _t_complexity_from_strategies(gate_or_op, strategies)
qualtran/cirq_interop/t_complexity_protocol.py:209: in _t_complexity_from_strategies
    ret = strategy(stc)
qualtran/cirq_interop/t_complexity_protocol.py:171: in _from_bloq_build_call_graph
    ret += n * r
qualtran/cirq_interop/t_complexity_protocol.py:57: in __add__
    self.t + other.t, self.clifford + other.clifford, self.rotations + other.rotations
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/decorators.py:236: in _func
    return func(self, other)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/decorators.py:106: in binary_op_wrapper
    return func(self, other)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/expr.py:198: in __add__
    return Add(self, other)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/operations.py:98: in __new__
    c_part, nc_part, order_symbols = cls.flatten(args)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/add.py:367: in flatten
    if o.contains(t):
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/series/order.py:452: in contains
    obj = self.func(expr, *self.args[1:])
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/series/order.py:203: in __new__
    expr = expr.subs(s)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/basic.py:1040: in subs
    rv = rv._subs(old, new, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/basic.py:1154: in _subs
    rv = fallback(self, old, new)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/basic.py:1126: in fallback
    arg = arg._subs(old, new, **hints)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/basic.py:1154: in _subs
    rv = fallback(self, old, new)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/basic.py:1126: in fallback
    arg = arg._subs(old, new, **hints)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/basic.py:1152: in _subs
    rv = self._eval_subs(old, new)
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/series/order.py:499: in _eval_subs
    return Order(newexpr, *zip(newvars, newpt))
../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/core/cache.py:72: in wrapper
    retval = cfunc(*args, **kwargs)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

cls = <class 'sympy.series.order.Order'>, expr = t + log(_Dummy_434)/log(-log(_Dummy_434)), args = [(_Dummy_434, 0), (t, oo)], kwargs = {}, variables = [_Dummy_434, t], a = (t, oo), v = t, p = oo

    @cacheit
    def __new__(cls, expr, *args, **kwargs):
        expr = sympify(expr)

        if not args:
            if expr.is_Order:
                variables = expr.variables
                point = expr.point
            else:
                variables = list(expr.free_symbols)
                point = [S.Zero]*len(variables)
        else:
            args = list(args if is_sequence(args) else [args])
            variables, point = [], []
            if is_sequence(args[0]):
                for a in args:
                    v, p = list(map(sympify, a))
                    variables.append(v)
                    point.append(p)
            else:
                variables = list(map(sympify, args))
                point = [S.Zero]*len(variables)

        if not all(v.is_symbol for v in variables):
            raise TypeError('Variables are not symbols, got %s' % variables)

        if len(list(uniq(variables))) != len(variables):
            raise ValueError('Variables are supposed to be unique symbols, got %s' % variables)

        if expr.is_Order:
            expr_vp = dict(expr.args[1:])
            new_vp = dict(expr_vp)
            vp = dict(zip(variables, point))
            for v, p in vp.items():
                if v in new_vp.keys():
                    if p != new_vp[v]:
                        raise NotImplementedError(
                            "Mixing Order at different points is not supported.")
                else:
                    new_vp[v] = p
            if set(expr_vp.keys()) == set(new_vp.keys()):
                return expr
            else:
                variables = list(new_vp.keys())
                point = [new_vp[v] for v in variables]

        if expr is S.NaN:
            return S.NaN

        if any(x in p.free_symbols for x in variables for p in point):
            raise ValueError('Got %s as a point.' % point)

        if variables:
            if any(p != point[0] for p in point):
>               raise NotImplementedError(
                    "Multivariable orders at different points are not supported.")
E               NotImplementedError: Multivariable orders at different points are not supported.

../../opt/anaconda3/envs/qualtran2/lib/python3.11/site-packages/sympy/series/order.py:184: NotImplementedError

This case can be fixed in a followup PR. cc @anurudhp