Multi-qubit fusion

[stavros11]

Generalizes the gate fusion algorithm to work with arbitrary number of max_qubits which is now possible since the qibojit backend supports multi-qubit gates. The maximum number of qubits for fusion can be set when calling the circuit.fuse() method. The current default is 2, but we may change it to a different number (for example 5, if we follow qiskit) depending on benchmark results.

Below is some comparison of this implementation to qiskit. In each column we have the ration of qibo simulation time / qiskit simulation time for different choices of fusion max_qubits from 2 to 8. Simulation, not dry run, times are used.

qft

nqubits	max_qubits=2	max_qubits=3	max_qubits=4	max_qubits=5	max_qubits=6	max_qubits=7	max_qubits=8
3	0.20610	0.08418	0.09645	0.09511	0.09376	0.09415	0.09574
4	0.27322	0.20666	0.09970	0.12229	0.12664	0.11661	0.13105
5	0.40971	0.32253	0.24150	0.11827	0.11290	0.11423	0.10994
6	0.51495	0.38617	0.28347	0.24539	0.12872	0.17979	0.18191
7	0.56359	0.36434	0.34203	0.25258	0.41455	0.11300	0.17466
8	0.65333	0.44113	0.36942	0.27612	0.45016	0.55353	0.19977
9	0.67696	0.59501	0.35652	0.38223	0.45030	0.55807	0.90887
10	0.68283	0.60097	0.44080	0.42769	0.53450	0.54176	0.93219
11	0.64424	0.55535	0.41726	0.40138	0.53167	0.41922	0.85935
12	0.56822	0.44630	0.32520	0.30930	0.47301	0.56328	0.61369
13	0.44925	0.38391	0.28012	0.28160	0.46229	0.49167	0.75810
14	0.26829	0.25044	0.21624	0.26319	0.40924	0.43875	0.52741
15	0.20808	0.31032	0.36157	0.44405	0.68985	0.58737	0.37335
16	0.21493	0.34252	0.43177	0.54268	1.09735	0.84952	0.58443
17	0.18826	0.33735	0.52843	0.71947	1.47227	1.25480	0.89972
18	0.20630	0.42695	0.79086	1.24113	2.63374	2.35916	1.93672
19	0.25208	0.57239	1.30136	1.84342	4.54642	4.05777	2.62571
20	0.30024	0.67886	1.92696	2.85587	5.96119	5.44896	4.59788
21	0.34968	0.90667	2.55980	5.94465	10.37865	7.21071	8.71386
22	0.37725	1.00783	2.67319	7.85334	11.91473	14.12240	15.20113
23	0.39422	1.10585	2.95582	5.94947	17.05321	15.46743	15.71536
24	0.51315	1.29089	3.25359	8.20007	16.26323	17.77953	23.17776
25	0.30063	0.60797	2.34548	4.83730	11.16344	12.30776	19.13217
26	0.39397	0.78282	2.06717	4.41566	11.38827	13.81669	20.93561
27	0.40393	0.78935	2.09944	4.64882	11.07182	14.17314	22.99675
28	0.40670	0.75732	2.17397	5.12565	10.67715	14.91259	24.52161
29	0.39942	0.76523	2.29478	5.24375	11.53743	14.19988	24.47468
30	0.39481	0.78706	2.29914	5.18139	11.30671	15.04154	24.41561

variational

nqubits	max_qubits=2	max_qubits=3	max_qubits=4	max_qubits=5	max_qubits=6	max_qubits=7	max_qubits=8
3	0.12918	0.09290	0.08594	0.09214	0.08508	0.09395	0.08972
4	0.18967	0.15728	0.12452	0.12445	0.12743	0.11498	0.12063
5	0.18312	0.12131	0.11739	0.10515	0.11403	0.11452	0.11861
6	0.21155	0.19054	0.13579	0.13514	0.14059	0.13832	0.13581
7	0.15907	0.19177	0.13408	0.07640	0.12939	0.13033	0.13017
8	0.25479	0.23260	0.15107	0.09917	0.15304	0.15601	0.16794
9	0.22643	0.22130	0.11500	0.14922	0.14968	0.14661	0.14751
10	0.25891	0.23123	0.16976	0.16812	0.15939	0.13411	0.16588
11	0.22037	0.21210	0.13780	0.13355	0.13947	0.14536	0.14594
12	0.21001	0.21413	0.12321	0.14195	0.14099	0.12954	0.14125
13	0.17822	0.16634	0.12994	0.13138	0.12488	0.12003	0.12780
14	0.14624	0.13456	0.10552	0.10943	0.10540	0.10389	0.10276
15	0.16319	0.19073	0.21613	0.15735	0.19986	0.16632	0.20181
16	0.23841	0.24610	0.27855	0.16029	0.27180	0.26562	0.23745
17	0.30894	0.31406	0.31256	0.36604	0.30217	0.34898	0.35583
18	0.38848	0.42418	0.46097	0.33544	0.50544	0.58581	0.39120
19	0.52558	0.63272	0.81654	0.82585	0.90594	0.89172	0.90314
20	0.69194	0.73752	1.60976	1.70846	1.55462	1.62007	1.65468
21	0.91445	1.01003	1.81093	1.78431	1.85583	2.00530	1.46395
22	0.85691	0.98048	3.18528	2.97109	2.72203	2.47227	2.90535
23	0.89021	1.04287	3.12754	3.69202	3.18779	3.14014	3.11378
24	1.01610	1.44653	3.03373	3.77333	3.70526	4.04854	3.82562
25	0.88843	1.11728	2.68815	2.57932	2.58797	2.63095	2.74291
26	0.93132	1.13162	2.16047	2.22403	1.96750	1.96645	2.21386
27	0.95482	1.08215	2.42035	2.42800	2.39451	2.27586	2.43179
28	0.95274	1.08452	2.08856	1.82675	1.92931	2.12992	1.90313
29	0.89881	1.06306	2.20685	2.10730	2.11960	2.16078	2.20331
30	0.89803	1.09436	1.79687	2.04702	2.01804	2.00824	1.91996

bv

nqubits	max_qubits=2	max_qubits=3	max_qubits=4	max_qubits=5	max_qubits=6	max_qubits=7	max_qubits=8
3	0.14046	0.09433	0.09977	0.09303	0.09360	0.09551	0.09758
4	0.15804	0.12529	0.08938	0.08877	0.08911	0.07797	0.08929
5	0.18130	0.07570	0.12299	0.06886	0.09190	0.08925	0.08764
6	0.19775	0.14274	0.09069	0.11481	0.13008	1.40166	0.35120
7	0.21799	0.13275	0.11079	0.10585	0.37708	0.15507	0.14809
8	0.25241	0.10077	0.08963	0.10498	0.16405	0.19358	0.26652
9	0.24323	0.15083	0.12333	0.09043	0.12245	0.14011	0.26402
10	0.25635	0.12911	0.11816	0.11939	0.13918	0.18002	2.24682
11	0.24559	0.15046	0.13610	0.11116	0.81163	0.19060	0.25346
12	0.22763	0.15529	0.11538	0.09731	0.16024	0.17813	0.27084
13	0.20325	0.12372	0.10788	0.10755	0.16054	0.20719	0.23125
14	0.15441	0.09457	0.09682	0.09443	0.13800	0.21770	0.19311
15	0.20877	0.16530	0.12949	0.12885	0.70206	0.36953	0.48522
16	0.25112	0.17574	0.16176	0.14049	0.40476	0.42186	0.59605
17	0.26999	0.25599	0.26621	0.31260	0.67065	0.72790	1.07239
18	0.44030	0.42344	0.44516	0.53626	0.99000	1.38535	1.81131
19	0.56456	0.57529	0.67419	0.68721	1.25608	2.03198	2.61977
20	0.73946	0.81816	0.68421	1.21963	2.50002	3.38620	4.82185
21	1.01244	1.14231	0.99468	1.75723	3.53384	3.88030	5.53282
22	1.04583	1.22304	1.36087	1.93512	3.90660	4.42056	7.75701
23	1.16903	0.85674	1.49083	2.34718	4.46741	3.81819	7.72695
24	1.22028	1.37409	1.68582	2.55020	4.37161	5.22531	7.66486
25	0.90181	1.17182	0.84762	2.06576	3.52038	3.88060	4.89322
26	0.92277	1.16616	1.25146	1.52189	3.82825	3.99823	4.90486
27	0.93529	1.15219	1.24572	1.65897	3.67626	3.69007	5.24249
28	0.89754	0.87682	1.13180	1.57908	3.31576	3.36319	4.48362
29	0.89685	1.01265	0.85730	1.24307	3.37984	3.15174	4.97647
30	0.93569	0.90918	0.98798	1.44764	3.24347	3.23044	4.65742

qv

nqubits	max_qubits=2	max_qubits=3	max_qubits=4	max_qubits=5	max_qubits=6	max_qubits=7	max_qubits=8
3	0.07972	0.08622	0.08548	0.09056	0.08614	0.07924	0.08409
4	0.09611	0.09486	0.09618	0.09040	0.09326	0.09768	0.07663
5	0.07130	0.09411	0.07661	0.09970	0.09812	0.10103	0.09753
6	0.10242	0.10223	0.07555	0.09979	0.08906	0.09955	0.08913
7	0.10127	0.09349	0.10022	0.09771	0.10146	0.10033	0.10205
8	0.08205	0.10600	0.10717	0.10601	0.10192	0.10154	0.08370
9	0.10548	0.10217	0.10361	0.09952	0.10319	0.11312	0.10619
10	0.10175	0.10480	0.10218	0.10309	0.06639	0.10195	0.10490
11	0.09763	0.09813	0.10887	0.09700	0.09699	0.09347	0.08686
12	0.08248	0.08634	0.08728	0.08543	0.08669	0.08458	0.08298
13	0.07463	0.06815	0.07507	0.07472	0.07574	0.06587	0.08072
14	0.05429	0.05585	0.05454	0.05713	0.05731	0.05610	0.05676
15	0.06211	0.07913	0.10723	0.08873	0.08217	0.07110	0.10935
16	0.13401	0.10590	0.09858	0.12210	0.12991	0.11383	0.11997
17	0.14661	0.15896	0.11433	0.13356	0.14244	0.16005	0.15299
18	0.26181	0.15049	0.20880	0.27519	0.29655	0.27144	0.26564
19	0.37015	0.34550	0.35441	0.35916	0.24331	0.32887	0.35295
20	0.47275	0.38712	0.44274	0.43299	0.37914	0.38492	0.43410
21	0.66819	0.45920	0.73919	0.69654	0.73265	0.71700	0.70866
22	0.90577	0.89172	0.81400	0.75514	0.81090	0.85714	0.67504
23	0.99608	0.97397	1.03261	1.04973	1.01202	0.83660	1.02322
24	1.25176	1.16575	1.34000	1.38282	1.29723	1.31792	1.41917
25	0.84464	0.83522	1.25010	1.27026	1.23742	1.24251	1.23506
26	0.85442	0.92253	1.29354	1.33722	1.33915	1.34331	1.37436
27	0.91009	0.91450	1.26692	1.38259	1.26216	1.38267	1.37792
28	0.85104	0.84939	1.49258	1.41522	1.47279	1.37034	1.35312
29	0.87187	0.94674	1.38148	1.43085	1.37936	1.45328	1.37813
30	0.86447	0.86306	1.38349	1.41236	1.39658	1.37901	1.37201

Clearly the fusion algorithm is not optimal for max_qubits > 3.

TODO:

• Improve the algorithm to get competitive performance. Potential ways to fix this is to compare the fused circuits for various examples with the ones from qiskit or others, or even check the fusion code of other libraries.
• Add tests for fusion with max_qubits > 2.

[codecov]

Codecov Report

Merging #505 (0ac873f) into master (fe91300) will not change coverage.
The diff coverage is 100.00%.

@@            Coverage Diff            @@
##            master      #505   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           83        83           
  Lines        11917     11935   +18     
=========================================
+ Hits         11917     11935   +18     

Flag	Coverage Δ
unittests	100.00% <100.00%> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/qibo/abstractions/abstract_gates.py	100.00% <100.00%> (ø)
src/qibo/abstractions/circuit.py	100.00% <100.00%> (ø)
src/qibo/abstractions/gates.py	100.00% <100.00%> (ø)
src/qibo/core/circuit.py	100.00% <100.00%> (ø)
src/qibo/core/gates.py	100.00% <100.00%> (ø)
src/qibo/tests/test_abstract_gates.py	100.00% <100.00%> (ø)
src/qibo/tests/test_core_fusion.py	100.00% <100.00%> (ø)
src/qibo/tests/test_core_gates.py	100.00% <100.00%> (ø)

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[stavros11]

Closing in favor of a different implementation in #577.