Quantum Benchmark Zoo

← All benchmarks

Deceptive cluster loops

Platform-specific historical

Frustrated cluster loops with a tunable coupling scale λ that conceals the planted structure, built to test whether annealer speedups survive against structure-exploiting classical solvers.

Measures
Whole-annealer time-to-solution (99% success) on Chimera FCL instances whose inter-cell couplers are scaled by a structure-concealing factor λ, versus state-of-the-art classical heuristics
Introduced by
Mandrà (NASA Ames) & Katzgraber (Texas A&M) (2017)
Also known as
DCL, deceptive cluster loop problems

Deceptive cluster loops (DCL) are the adversarial refinement of frustrated cluster loops, introduced by Mandrà and Katzgraber in “A deceptive step towards quantum speedup detection” (2017; Quantum Sci. Technol. 2018). After classical solvers aware of FCL’s planted cluster structure erased D-Wave’s reported advantage, DCL posed the sharper question: does an annealer still win when that structure is hidden?

How it works

DCL instances are FCL problems on the Chimera graph with one extra dial: intra-cell couplers keep magnitude 1, while every inter-cell coupler is scaled by a factor λ. Small λ collapses each K4,4 cell into a single virtual spin, so cluster-style algorithms win; large λ makes chains across cells dominate, favoring chain-aware mappings; intermediate λ defeats both shortcuts while leaving the planted problem intact. Performance is scored as time-to-solution at 99% success probability against state-of-the-art classical heuristics: the Hamze–de Freitas–Selby algorithm and parallel tempering with isoenergetic cluster moves.

Strengths and limitations

DCL directly probes whether an annealer’s edge survives once structure exploitation is off the table, and near λ ≈ 7 the D-Wave 2000Q outperformed all classical heuristics then known. That headline is easy to overread: the advantage was a constant factor only, with the authors stating that a scaling improvement “remains elusive”, yet DCL is often miscited as a demonstrated quantum speedup. Like its parent class, it names a planted-instance problem family scored via time-to-solution comparisons, not a fixed protocol producing a single-number score.

Notable results

DCL is of historical interest today: it is defined for the Chimera topology of the retired D-Wave 2000Q/2X (current machines use Pegasus and Zephyr), the Chook suite that ships its generator has been dormant since v0.2.0 (March 2021), and no 2024–2026 study appears to run DCL instances. It survives as a cited milestone in the quantum-speedup-detection debate and in classical-solver benchmarking such as the thermal cycling algorithm study.

Key papers

Reference implementations

  • Frustrated cluster loops : Planted-solution Ising benchmark of the D-Wave 2000Q era: frustrated loops laid over ferromagnetic qubit clusters with tunable ruggedness, scored by time-to-solution against classical solvers.
  • Chook : Open-source Python suite that generates Ising, QUBO, and higher-order optimization problems with planted, a-priori-known ground states and tunable hardness across five planting schemes.
  • Time-to-solution : The standard quantum-annealing benchmark: wall-clock time to find the ground state at least once with 99% probability, compared against optimized classical solvers to test for quantum speedup.