Cross-library benchmark

QuGrid's built-in solvers are not the only implementations of the algorithms they run. Example 11 solves the same three power system QUBOs — unit commitment of 2 units over 2 periods, controlled islanding of the WSCC 9-bus system, and minimum PMU placement on the PJM 5-bus system — with five solvers from three libraries, through one call:

import qugrid as qg

qg.solve(problem, solver="sa")           # built-in simulated annealing
qg.solve(problem, solver="qaoa", p=2)    # built-in statevector QAOA
qg.solve(problem, solver="dimod-exact")  # dimod.ExactSolver
qg.solve(problem, solver="dwave-sa")     # Ocean SimulatedAnnealingSampler
qg.solve(problem, solver="qiskit-qaoa")  # qiskit-optimization QAOA

Every solver receives the identical QUBO object and returns the identical Result, so objective, feasibility, optimality gap, and wall time are measured the same way for all of them.

Why this page exists

If QuGrid's exact enumeration and dimod.ExactSolver ever disagree, the encoding is wrong — and every quantum result built on it is worthless. This benchmark is the standing check that they agree, and it gives each built-in solver a mature external reference. Example 11 asserts both properties and exits nonzero if either fails.

Measured table

uv run python examples/11_cross_library_benchmark.py, three seeds per cell, run on 2026-08-13 on an Apple silicon laptop:

problem	library	solver	objective	gap %	feasible	P(opt) %	time [s]
island-case9	dimod	dimod-exact	27.0512	0.00	100%	—	0.0003
island-case9	dwave-samplers	dwave-sa	27.0512	0.00	100%	—	0.0015
island-case9	qugrid	qaoa	27.0512	0.00	100%	0.977	0.3585
island-case9	qiskit-optimization	qiskit-qaoa	27.6498	2.21	100%	—	0.3078
island-case9	qugrid	sa	27.0512	0.00	100%	—	0.0593
pmu-case5	dimod	dimod-exact	2.0000	0.00	100%	—	0.0120
pmu-case5	dwave-samplers	dwave-sa	2.0000	0.00	100%	—	0.0122
pmu-case5	qugrid	qaoa	2.0000	0.00	100%	0.134	3.0223
pmu-case5	qugrid	sa	2.0000	0.00	100%	—	0.0957
uc-2gen	dimod	dimod-exact	2908.0000	0.00	100%	—	0.0019
uc-2gen	dwave-samplers	dwave-sa	2908.0000	0.00	100%	—	0.0057
uc-2gen	qugrid	qaoa	10337.3333	255.48	33%	0.057	0.6463
uc-2gen	qugrid	sa	2908.0000	0.00	100%	—	0.0781

Reading the table:

• Both exact solvers land on the same objective to 1e-6 on all three problems (asserted by the script).
• Both simulated annealers reach the exact optimum everywhere. Ocean's C++ inner loop is roughly ten times faster than the built-in NumPy annealer.
• The two QAOA implementations agree on islanding within seed noise: the built-in reaches gap 0 on 3 of 3 seeds here, qiskit-optimization on 2 of 3. Two codebases, one algorithm, one answer.
• Unit commitment QAOA fails the same way in any library, because the constraint penalties stretch the QUBO energy range far beyond the cost separation between schedules. Script 07 measures that failure in detail (see Honest benchmarking).

Honesty box

The external solvers here are mature classical code — exhaustive enumeration and simulated annealing — plus one shot-based QAOA implementation. Nothing on this page is a quantum-hardware claim. Wall times are single-laptop measurements: expect the ordering to transfer to your machine, not the absolute numbers.

Install

pip install "qugrid[dwave]"    # dimod-exact, dwave-sa
pip install "qugrid[qiskit]"   # qiskit-qaoa
pip install "qugrid[all]"      # everything

A missing extra is not an error: example 11 prints SKIP <solver> (pip install qugrid[<extra>]) and validates what remains.