Add benchmarks for transformer primitives and json serialization

[tanujkhattar]

This PR adds representative benchmarks for transformer primitives and circuit serialization, both of which are important use cases as we start dealing with larger circuits.

@kjsatz Can you please take a look at the benchmarks and see if it captures our discussion? Would be also good to get your perspective on what should be the target timings these benchmarks should ideally run in? (cc @maffoo as well)

Tl;Dr is that the performance right now is too slow and we'd have to make sure we address the performance bottlenecks here so that these benchmarks can run significantly faster.

$> asv run -b serialization.SerializeLargeExpandedCircuits -b transformers.transformer_primitives*
· Creating environments
· Discovering benchmarks
· Running 7 total benchmarks (1 commits * 1 environments * 7 benchmarks)
[  0.00%] · For Cirq commit 8ea41a8a <master>:
[  0.00%] ·· Benchmarking virtualenv-py3.8
[  7.14%] ··· Running (serialization.SerializeLargeExpandedCircuits.time_json_serialization--).
[ 14.29%] ··· Running (serialization.SerializeLargeExpandedCircuits.time_json_serialization_gzip--)
[ 28.57%] ··· Running (transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_moments--).
[ 35.71%] ··· Running (transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_operations_apply_tag--).
[ 42.86%] ··· Running (transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_operations_to_optree--).
[ 50.00%] ··· Running (transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_operations_to_optree_and_unroll--).
[ 57.14%] ··· serialization.SerializeLargeExpandedCircuits.time_json_serialization                                                                                                                        ok
[ 57.14%] ··· ============ ============ ============ ============
              --                        num_moments
              ------------ --------------------------------------
               num_qubits      100          1000         4000
              ============ ============ ============ ============
                  100        403±70ms    3.66±0.3s    14.1±0.2s
                  500       1.82±0.06s   18.6±0.3s    1.22±0.01m
                  1000      3.50±0.08s   36.2±0.06s   2.61±0.04m
              ============ ============ ============ ============

[ 64.29%] ··· serialization.SerializeLargeExpandedCircuits.time_json_serialization_gzip                                                                                                                   ok
[ 64.29%] ··· ============ =========== =========== ============
              --                       num_moments
              ------------ ------------------------------------
               num_qubits      100         1000        4000
              ============ =========== =========== ============
                  100        420±30ms   4.12±0.1s    18.8±1s
                  500       2.09±0.3s    22.4±1s    1.54±0.07m
                  1000      4.34±0.6s    45.5±2s    3.49±0.4m
              ============ =========== =========== ============

[ 71.43%] ··· serialization.SerializeLargeExpandedCircuits.track_json_serialization_gzip_size                                                                                                             ok
[ 71.43%] ··· ============ ========= ========= ========
              --                   num_moments
              ------------ ----------------------------
               num_qubits     100       1000     4000
              ============ ========= ========= ========
                  100        "31KB"   "309KB"   "1MB"
                  500       "144KB"    "1MB"    "5MB"
                  1000      "278KB"    "2MB"    "10MB"
              ============ ========= ========= ========

[ 78.57%] ··· transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_moments                                                                                                                ok
[ 78.57%] ··· ============ =========== =========== ===========
              --                       num_moments
              ------------ -----------------------------------
               num_qubits      100         1000        4000
              ============ =========== =========== ===========
                  100        147±40ms   1.15±0.7s    4.49±1s
                  500       797±300ms    8.78±1s     33.6±6s
                  1000      1.46±0.4s    16.2±3s    1.15±0.2m
              ============ =========== =========== ===========

[ 85.71%] ··· transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_operations_apply_tag                                                                                                   ok
[ 85.71%] ··· ============ =========== =========== ===========
              --                       num_moments
              ------------ -----------------------------------
               num_qubits      100         1000        4000
              ============ =========== =========== ===========
                  100        274±40ms   1.77±0.6s   9.47±0.2s
                  500       1.18±0.2s    15.6±2s     45.6±3s
                  1000      1.98±0.4s    24.4±2s    1.65±0.2m
              ============ =========== =========== ===========

[ 92.86%] ··· transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_operations_to_optree                                                                                                   ok
[ 92.86%] ··· ============ =========== =========== ===========
              --                       num_moments
              ------------ -----------------------------------
               num_qubits      100         1000        4000
              ============ =========== =========== ===========
                  100        426±60ms   3.15±0.7s    22.9±4s
                  500       1.66±0.5s    23.1±2s    1.65±0.2m
                  1000      4.32±0.3s    44.2±5s    3.17±0.3m
              ============ =========== =========== ===========

[100.00%] ··· transformers.transformer_primitives.MapLargeExpandedCircuit.time_map_operations_to_optree_and_unroll
                                                                                2/9 failed
[100.00%] ··· ============ =========== ============ ===========
              --                       num_moments
              ------------ ------------------------------------
               num_qubits      100         1000         4000
              ============ =========== ============ ===========
                  100       1.43±0.3s    11.6±1s     1.10±0.2m
                  500       4.37±0.4s    56.4±4s       failed
                  1000      11.9±0.4s   1.80±0.06m     failed
              ============ =========== ============ ===========

[kjsatz]

Thanks @tanujkhattar. From a quick look, the test topics look reasonable. For the scaling, I love the num_qubits in (100, 500, 1000). From the "M3 era QEC" perspective, the relevant num_moments is almost surely 100 (and not 4000) if that helps contextualize, although the scaling on several of those with num_moments is somewhat alarming.

As for how long these should take, I don't really know, but 100 ms is a nice ballpark to work in. I imagine there are some clear limiting bottlenecks you'll discover, and it's a matter of how much low-hanging fruit there might be.

[pavoljuhas]

LGTM with a few small changes.