We use "is" equality in a bunch of places when comparing dimensions. This is problematic given the current approach for the json saving and loading functionality, since sympify will generate distinct Symbol objects. We could replace the is equality uses with ==, but that is anywhere from a few times to 50 times slower:

In [13]: from unyt.dimensions import length, energy

In [14]: %timeit length is length
34.8 ns ± 0.326 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

In [15]: %timeit length == length
128 ns ± 6.87 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

In [16]: %timeit length is not energy
39.8 ns ± 5.37 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

In [17]: %timeit length == energy
2.38 µs ± 155 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

In [18]: 128/34.8
Out[18]: 3.6781609195402303

In [19]: 2380/39.8
Out[19]: 59.798994974874375

The solution for the particular instance of this issue we're running into here is to use the locals keyword argument for sympify, which gives it access to a namespace of objects to substitute in expressions, which allows us to use the dimensions in unyt.dimensions to populate the dimensions of the restored unit registries.