QAOA at 100 Qubits: Real Benchmarks from a Laptop CPU
· 4 min read · ZKSF team
QAOA, the Quantum Approximate Optimization Algorithm, is among the most widely run algorithms in quantum computing research and the standard testbed for claims about quantum optimization. A single figure is worth stating plainly: a 100-qubit, depth-304 QAOA MaxCut circuit simulates in 5.9 seconds on a consumer laptop CPU, fully converged, with an accuracy statement attached.
The left side shows one round of QAOA MaxCut on a ring: an illustrative 8-qubit version of the same pattern used for the real 100-qubit benchmark, a layer of cost-Hamiltonian RZZ gates around alternate ring edges, followed by a mixer round. At n=100, p=3, this pattern reaches depth 304. The right side is the actual reported data: wall times for 50, 80, and 100-qubit runs, each checked for convergence by repeating the run at double the bond dimension, plus a 26-qubit exact-statevector reference row that the approximate engine is required to agree with, and does. The bottom right shows why this matters economically: the same 100-qubit job costs a fraction of a cent to simulate, versus real QPU fees plus gate error, for a noise-free result with a convergence record attached.
No cluster and no GPU were involved; the GPU on the test machine was idle throughout.
Benchmark setup
The benchmark family is QAOA for MaxCut on ring graphs: n qubits, a layer of Hadamard gates, then p rounds of cost-Hamiltonian evolution (RZZ gates along the ring) alternated with mixer rotations (RX on every qubit). This is a canonical structured workload: meaningful entanglement, non-Clifford gates, and realistic circuit depth. At n=100, p=3, the circuit reaches 304 layers of depth as Qiskit counts it.
The engine is a matrix product state simulator, built on the open-source quimb library, run at bond dimension 64 with a convergence check: every run is repeated at bond dimension 128 and the leading outcome probabilities compared.
Circuit Qubits p Wall time Converged (deviation)
QAOA MaxCut ring 50 2 4.1 s yes (0.0)
QAOA MaxCut ring 80 2 4.4 s yes (0.0)
QAOA MaxCut ring 100 3 5.9 s yes (0.0)
Exact reference (ansatz) 26 - 2.7 s exact (ground truth)The exact-reference row is the validation step: at sizes small enough for exact statevector simulation, the approximate MPS engine is required to agree with it, and does.
Interpreting the result
The result changes the economics of QAOA research. A 100-qubit, 1,000-shot QAOA job on a typical superconducting QPU costs roughly $0.30 plus per-shot fees before queue time, and returns results affected by gate error rates near 1 percent. The equivalent simulation costs a fraction of a cent, returns a noise-free value, and carries a convergence record.
This does not make QAOA on real hardware pointless. It relocates the interesting scientific question. Whether QAOA outperforms classical optimizers at problem sizes beyond classical simulation requires either substantially larger hardware or instances with entanglement dense enough that MPS methods no longer converge, a condition this platform's router detects and reports. Those are the experiments worth spending hardware budget on, once the simulable regime has been fully explored.
Every figure above is reproducible: the circuit generators, engine configuration, and benchmark harness ship with the SDK, and the same suite can be run on any machine to check the numbers independently.
Run your own 100-qubit circuit, with an error bar.