Hamiltonian Simulation benchmark implementation

[raynelfss]

This branch implements the Hamiltonian Simulation of the Heisenberg Model with disordered fields as a benchmark. Worked with @Yelissal on this.

[raynelfss]

Results from running on my Windows machine:

                                                                Benchmark: Hamiltonian Simulation
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┓
┃ Name                                              ┃ Min           ┃ Max           ┃ Mean          ┃ depth      ┃ size        ┃ xi            ┃ fidelity        ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━┩
│ qiskit (Optimization level: 2 on fake_rochester)  │ 0.2465 (1.85) │ 0.2831 (1.38) │ 0.265 (1.63)  │ 68 (1.0)   │ 297 (1.0)   │ 0.436 (3.20)  │ 0.02507 (19.80) │
│ qiskit (Optimization level: 2 on fake_cairo)      │ 0.2277 (1.71) │ 0.2768 (1.35) │ 0.2515 (1.55) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.3641 (287.48) │
│ qiskit (Optimization level: 2 on fake_montreal)   │ 0.2342 (1.76) │ 0.2584 (1.26) │ 0.2467 (1.52) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.3725 (294.12) │
│ qiskit (Optimization level: 3 on fake_guadalupe)  │ 0.5712 (4.30) │ 0.8613 (4.21) │ 0.6695 (4.12) │ 80 (1.18)  │ 420 (1.41)  │ 0.2476 (1.82) │ 0.3204 (253.00) │
│ qiskit (Optimization level: 3 on fake_toronto)    │ 0.6068 (4.56) │ 0.8868 (4.33) │ 0.6995 (4.31) │ 80 (1.18)  │ 420 (1.41)  │ 0.2476 (1.82) │ 0.008377 (6.61) │
│ qiskit (Optimization level: 3 on fake_cairo)      │ 0.5439 (4.09) │ 0.6473 (3.16) │ 0.599 (3.69)  │ 80 (1.18)  │ 420 (1.41)  │ 0.2476 (1.82) │ 0.413 (326.10)  │
│ qiskit (Optimization level: 3 on fake_melbourne)  │ 1.093 (8.22)  │ 1.242 (6.07)  │ 1.187 (7.31)  │ 80 (1.18)  │ 429 (1.44)  │ 0.2993 (2.20) │ 0.05186 (40.95) │
│ qiskit (Optimization level: 3 on fake_montreal)   │ 0.6194 (4.66) │ 0.7304 (3.57) │ 0.6551 (4.04) │ 80 (1.18)  │ 420 (1.41)  │ 0.2476 (1.82) │ 0.4306 (340.00) │
│ qiskit (Optimization level: 0 on fake_melbourne)  │ 0.2402 (1.81) │ 0.2605 (1.27) │ 0.2498 (1.54) │ 250 (3.68) │ 915 (3.08)  │ 0.1985 (1.46) │ 0.04521 (35.70) │
│ qiskit (Optimization level: 2 on fake_brooklyn)   │ 0.2828 (2.13) │ 0.3826 (1.87) │ 0.321 (1.98)  │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.2951 (233.04) │
│ qiskit (Optimization level: 1 on fake_toronto)    │ 0.3863 (2.91) │ 0.4311 (2.11) │ 0.4059 (2.50) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.00647 (5.11)  │
│ qiskit (Optimization level: 0 on fake_toronto)    │ 0.2136 (1.61) │ 0.2735 (1.34) │ 0.2338 (1.44) │ 352 (5.18) │ 1122 (3.78) │ 0.2828 (2.08) │ 0.001266 (1.0)  │
│ qiskit (Optimization level: 2 on fake_toronto)    │ 0.4549 (3.42) │ 0.5043 (2.46) │ 0.4874 (3.00) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.00647 (5.11)  │
│ qiskit (Optimization level: 0 on fake_cairo)      │ 0.213 (1.60)  │ 0.278 (1.36)  │ 0.238 (1.47)  │ 352 (5.18) │ 1122 (3.78) │ 0.2828 (2.08) │ 0.04327 (34.17) │
│ qiskit (Optimization level: 1 on fake_montreal)   │ 0.3417 (2.57) │ 0.5036 (2.46) │ 0.4196 (2.58) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.3725 (294.12) │
│ qiskit (Optimization level: 1 on fake_melbourne)  │ 0.3479 (2.62) │ 0.446 (2.18)  │ 0.3914 (2.41) │ 80 (1.18)  │ 351 (1.18)  │ 0.3673 (2.70) │ 0.04541 (35.86) │
│ qiskit (Optimization level: 1 on fake_washington) │ 0.3281 (2.47) │ 0.4031 (1.97) │ 0.3754 (2.31) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.07028 (55.49) │
│ qiskit (Optimization level: 3 on fake_brooklyn)   │ 0.9115 (6.86) │ 1.206 (5.89)  │ 1.015 (6.25)  │ 80 (1.18)  │ 420 (1.41)  │ 0.2476 (1.82) │ 0.356 (281.06)  │
│ qiskit (Optimization level: 2 on fake_washington) │ 0.6062 (4.56) │ 0.7094 (3.46) │ 0.6733 (4.15) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.3945 (311.51) │
│ qiskit (Optimization level: 2 on fake_melbourne)  │ 0.6996 (5.26) │ 0.7032 (3.43) │ 0.7014 (4.32) │ 80 (1.18)  │ 351 (1.18)  │ 0.3673 (2.70) │ 0.04541 (35.86) │
│ qiskit (Optimization level: 3 on fake_rochester)  │ 0.8876 (6.68) │ 1.226 (5.99)  │ 1.002 (6.17)  │ 68 (1.0)   │ 297 (1.0)   │ 0.436 (3.20)  │ 0.02507 (19.80) │
│ qiskit (Optimization level: 1 on fake_rochester)  │ 0.4119 (3.10) │ 0.4645 (2.27) │ 0.441 (2.72)  │ 68 (1.0)   │ 297 (1.0)   │ 0.436 (3.20)  │ 0.02507 (19.80) │
│ qiskit (Optimization level: 1 on fake_guadalupe)  │ 0.2272 (1.71) │ 0.2934 (1.43) │ 0.2633 (1.62) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.2496 (197.08) │
│ qiskit (Optimization level: 1 on fake_brooklyn)   │ 0.2348 (1.77) │ 0.3689 (1.80) │ 0.318 (1.96)  │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.137 (108.19)  │
│ qiskit (Optimization level: 0 on fake_montreal)   │ 0.942 (7.09)  │ 1.5 (7.32)    │ 1.127 (6.95)  │ 352 (5.18) │ 1122 (3.78) │ 0.2828 (2.08) │ 0.06958 (54.94) │
│ qiskit (Optimization level: 3 on fake_washington) │ 0.6952 (5.23) │ 1.615 (7.89)  │ 1.141 (7.03)  │ 80 (1.18)  │ 420 (1.41)  │ 0.2476 (1.82) │ 0.4693 (370.59) │
│ qiskit (Optimization level: 1 on fake_cairo)      │ 0.2385 (1.79) │ 0.3038 (1.48) │ 0.2747 (1.69) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.3641 (287.48) │
│ qiskit (Optimization level: 0 on fake_guadalupe)  │ 0.8656 (6.51) │ 1.089 (5.32)  │ 0.9764 (6.01) │ 338 (4.97) │ 1098 (3.70) │ 0.267 (1.96)  │ 0.04883 (38.55) │
│ qiskit (Optimization level: 0 on fake_brooklyn)   │ 0.1608 (1.21) │ 0.221 (1.08)  │ 0.1953 (1.20) │ 158 (2.32) │ 933 (3.14)  │ 0.1362 (1.0)  │ 0.1334 (105.30) │
│ qiskit (Optimization level: 0 on fake_washington) │ 0.1329 (1.0)  │ 0.2048 (1.0)  │ 0.1623 (1.0)  │ 158 (2.32) │ 933 (3.14)  │ 0.1362 (1.0)  │ 0.06825 (53.89) │
│ qiskit (Optimization level: 2 on fake_guadalupe)  │ 0.6662 (5.01) │ 1.001 (4.89)  │ 0.8338 (5.14) │ 89 (1.31)  │ 465 (1.57)  │ 0.2757 (2.02) │ 0.2496 (197.08) │
│ qiskit (Optimization level: 0 on fake_rochester)  │ 0.4723 (3.55) │ 0.6176 (3.02) │ 0.545 (3.36)  │ 164 (2.41) │ 699 (2.35)  │ 0.4689 (3.44) │ 0.007324 (5.78) │
└───────────────────────────────────────────────────┴───────────────┴───────────────┴───────────────┴────────────┴─────────────┴───────────────┴─────────────────┘


                                                                TLDR
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━┓
┃ Name                                              ┃ Mean         ┃               ┃               ┃              ┃                ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━┩
│ qiskit (Optimization level: 0 on fake_brooklyn)   │ 1 (1.20)     │ 1 (2.32)      │ 1 (3.14)      │ 1 (1.0)      │ 1 (105.30)     │
│ qiskit (Optimization level: 0 on fake_cairo)      │ 1.219 (1.47) │ 2.228 (5.18)  │ 1.203 (3.78)  │ 2.076 (2.08) │ 0.3245 (34.17) │
│ qiskit (Optimization level: 0 on fake_guadalupe)  │ 5 (6.01)     │ 2.139 (4.97)  │ 1.177 (3.70)  │ 1.96 (1.96)  │ 0.3661 (38.55) │
│ qiskit (Optimization level: 0 on fake_melbourne)  │ 1.279 (1.54) │ 1.582 (3.68)  │ 0.9807 (3.08) │ 1.457 (1.46) │ 0.339 (35.70)  │
│ qiskit (Optimization level: 0 on fake_montreal)   │ 5.774 (6.95) │ 2.228 (5.18)  │ 1.203 (3.78)  │ 2.076 (2.08) │ 0.5217 (54.94) │
│ qiskit (Optimization level: 0 on fake_rochester)  │ 2.791 (3.36) │ 1.038 (2.41)  │ 0.7492 (2.35) │ 3.442 (3.44) │ 0.05492 (5.78) │
│ qiskit (Optimization level: 0 on fake_toronto)    │ 1.197 (1.44) │ 2.228 (5.18)  │ 1.203 (3.78)  │ 2.076 (2.08) │ 0.009497 (1.0) │
│ qiskit (Optimization level: 0 on fake_washington) │ 0.8313 (1.0) │ 1 (2.32)      │ 1 (3.14)      │ 1 (1.0)      │ 0.5118 (53.89) │
│ qiskit (Optimization level: 1 on fake_brooklyn)   │ 1.628 (1.96) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 1.027 (108.19) │
│ qiskit (Optimization level: 1 on fake_cairo)      │ 1.407 (1.69) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 2.73 (287.48)  │
│ qiskit (Optimization level: 1 on fake_guadalupe)  │ 1.348 (1.62) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 1.872 (197.08) │
│ qiskit (Optimization level: 1 on fake_melbourne)  │ 2.004 (2.41) │ 0.5063 (1.18) │ 0.3762 (1.18) │ 2.697 (2.70) │ 0.3405 (35.86) │
│ qiskit (Optimization level: 1 on fake_montreal)   │ 2.149 (2.58) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 2.793 (294.12) │
│ qiskit (Optimization level: 1 on fake_rochester)  │ 2.258 (2.72) │ 0.4304 (1.0)  │ 0.3183 (1.0)  │ 3.201 (3.20) │ 0.188 (19.80)  │
│ qiskit (Optimization level: 1 on fake_toronto)    │ 2.079 (2.50) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 0.04851 (5.11) │
│ qiskit (Optimization level: 1 on fake_washington) │ 1.923 (2.31) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 0.527 (55.49)  │
│ qiskit (Optimization level: 2 on fake_brooklyn)   │ 1.644 (1.98) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 2.213 (233.04) │
│ qiskit (Optimization level: 2 on fake_cairo)      │ 1.288 (1.55) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 2.73 (287.48)  │
│ qiskit (Optimization level: 2 on fake_guadalupe)  │ 4.27 (5.14)  │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 1.872 (197.08) │
│ qiskit (Optimization level: 2 on fake_melbourne)  │ 3.592 (4.32) │ 0.5063 (1.18) │ 0.3762 (1.18) │ 2.697 (2.70) │ 0.3405 (35.86) │
│ qiskit (Optimization level: 2 on fake_montreal)   │ 1.263 (1.52) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 2.793 (294.12) │
│ qiskit (Optimization level: 2 on fake_rochester)  │ 1.357 (1.63) │ 0.4304 (1.0)  │ 0.3183 (1.0)  │ 3.201 (3.20) │ 0.188 (19.80)  │
│ qiskit (Optimization level: 2 on fake_toronto)    │ 2.496 (3.00) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 0.04851 (5.11) │
│ qiskit (Optimization level: 2 on fake_washington) │ 3.448 (4.15) │ 0.5633 (1.31) │ 0.4984 (1.57) │ 2.024 (2.02) │ 2.958 (311.51) │
│ qiskit (Optimization level: 3 on fake_brooklyn)   │ 5.199 (6.25) │ 0.5063 (1.18) │ 0.4502 (1.41) │ 1.817 (1.82) │ 2.669 (281.06) │
│ qiskit (Optimization level: 3 on fake_cairo)      │ 3.068 (3.69) │ 0.5063 (1.18) │ 0.4502 (1.41) │ 1.817 (1.82) │ 3.097 (326.10) │
│ qiskit (Optimization level: 3 on fake_guadalupe)  │ 3.429 (4.12) │ 0.5063 (1.18) │ 0.4502 (1.41) │ 1.817 (1.82) │ 2.403 (253.00) │
│ qiskit (Optimization level: 3 on fake_melbourne)  │ 6.076 (7.31) │ 0.5063 (1.18) │ 0.4598 (1.44) │ 2.197 (2.20) │ 0.3889 (40.95) │
│ qiskit (Optimization level: 3 on fake_montreal)   │ 3.355 (4.04) │ 0.5063 (1.18) │ 0.4502 (1.41) │ 1.817 (1.82) │ 3.229 (340.00) │
│ qiskit (Optimization level: 3 on fake_rochester)  │ 5.13 (6.17)  │ 0.4304 (1.0)  │ 0.3183 (1.0)  │ 3.201 (3.20) │ 0.188 (19.80)  │
│ qiskit (Optimization level: 3 on fake_toronto)    │ 3.582 (4.31) │ 0.5063 (1.18) │ 0.4502 (1.41) │ 1.817 (1.82) │ 0.06281 (6.61) │
│ qiskit (Optimization level: 3 on fake_washington) │ 5.842 (7.03) │ 0.5063 (1.18) │ 0.4502 (1.41) │ 1.817 (1.82) │ 3.519 (370.59) │
└───────────────────────────────────────────────────┴──────────────┴───────────────┴───────────────┴──────────────┴────────────────┘

[danielleodigie]

LGTM! YASSSSS

[mtreinish]

Overall this LGTM, just a few minor inline comments I'm also curious if we need custom gate generators when I think there are equivalent (although maybe not exactly the same) gates in the circuit library.

[Lementknight]

I just ran your benchmark on my machine and it worked. Great job, Ray!

[danielleodigie]

looks good to me, benchmark runs :)

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❌ Raynel Sanchez

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