fix: pxe notes crashing spuriously

[alexghr]

This PR refactors how the PXE stores notes. They're now stored by their index in the note hash tree which should provide both uniqueness and a sorted order for notes.

This gets rid of the "nullifiedNotes" set so reading and removing notes should be cleaner and more efficient.

[AztecBot]

Benchmark results

No metrics with a significant change found.

Detailed results

All benchmarks are run on txs on the Benchmarking contract on the repository. Each tx consists of a batch call to create_note and increment_balance, which guarantees that each tx has a private call, a nested private call, a public call, and a nested public call, as well as an emitted private note, an unencrypted log, and public storage read and write.

This benchmark source data is available in JSON format on S3 here.

Values are compared against data from master at commit e28a6bf1 and shown if the difference exceeds 1%.

L2 block published to L1

Each column represents the number of txs on an L2 block published to L1.

Metric	8 txs	32 txs	128 txs
l1_rollup_calldata_size_in_bytes	45,444	179,588	716,132
l1_rollup_calldata_gas	220,932	865,892	3,444,776
l1_rollup_execution_gas	934,076	3,968,366	24,788,312
l2_block_processing_time_in_ms	1,390 (-8%)	5,109	21,112 (-1%)
l2_block_building_time_in_ms	15,158 (+2%)	59,396	237,379
l2_block_rollup_simulation_time_in_ms	10,778 (+3%)	42,000	168,305
l2_block_public_tx_process_time_in_ms	4,349	17,305 (+1%)	68,802

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 16 txs.

Metric	5 blocks	10 blocks
node_history_sync_time_in_ms	14,916 (-1%)	28,531
node_database_size_in_bytes	3,624,087	3,728,775

Circuits stats

Stats on running time and I/O sizes collected for every circuit run across all benchmarks.

Circuit	circuit_simulation_time_in_ms	circuit_input_size_in_bytes	circuit_output_size_in_bytes
private-kernel-init	212 (-1%)	44,681	25,561
private-kernel-ordering	166 (+1%)	43,753	14,809
base-rollup	1,067	128,338	881
root-rollup	78.8 (-2%)	4,088	677
private-kernel-inner	292 (+1%)	71,208	25,561
public-kernel-private-input	205	31,863	25,561
public-kernel-non-first-iteration	203	31,905	25,561
merge-rollup	7.59 (-9%)	2,608	881

Tree insertion stats

The duration to insert a fixed batch of leaves into each tree type.

Metric	1 leaves	2 leaves	8 leaves	16 leaves	32 leaves	128 leaves	64 leaves	512 leaves	1024 leaves	2048 leaves	8192 leaves
batch_insert_into_append_only_tree_16_depth_ms	11.1	16.3	13.8	17.9	23.8	65.0	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	N/A	N/A	N/A	78.2	49.9	241	473	914	3,562
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	110	59.5	363	731	1,403	5,555
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	64.2	N/A	N/A	N/A	N/A	N/A	N/A	N/A

Miscellaneous

Transaction sizes based on how many contracts are deployed in the tx.

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	15,455	32,224

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	377	1,083

Metric	1 public data writes
tx_sequencer_processing_time_ms	534