Repeatable quantum-hardware execution of a fast local-topology surrogate for hyperthermal sarcomeric oscillations

Cardiac contraction depends on sarcomeres acting locally, but a beating cardiomyocyte is not a perfectly uniform lattice: neighbouring sarcomeres can rapidly rephase while the cell keeps a slower rhythm. Hyperthermal sarcomeric oscillations (HSOs), a warmed-cardiomyocyte phenomenon previously identified at the sarcomere level, provide a compact experimental case of this mesoscale coordination problem. I recast the experimentally defined five-sarcomere HSO topology as a four-qubit quantum-hardware state space: four neighbouring-pair phase relations define 16 basis states, each state is evolved with a short nearest-neighbour two-step Trotter kernel, and IBM EstimatorV2 reads out physiology-linked diagonal observables. These readouts retain the HSO meanings of pattern persistence, one-link reconfiguration, anti-phase-rich occupancy, mismatch placement, and a topology-derived synchrony proxy (Stopo). The locked control_base lane acted as a reproducible hardware anchor. Across three independent 4096-shot candidate panels it produced weighted stay 0.8395 ± 0.0016, single-link fraction 0.9134 ± 0.0049, anti-phase-rich occupancy 0.4517 ± 0.0019, transition edge proxy 0.5437 ± 0.0016, and Stopo 0.2954±0.0002. Candidate panels then used the same lane as a model-family stress test. The overmixed reference marked a high-transition boundary, with transition mass 0.3837 ± 0.0313, single-link fraction 0.8248 ± 0.0198, and anti-phase-rich occupancy 0.4302 ± 0.0036. The edge-like representative edge_candidate_alt3 occupied an intermediate hardware regime, with transition mass 0.2781±0.0038 and anti-phase-rich occupancy 0.4447±0.0020, while preserving statewise ordering for anti-phase-rich occupancy and Stopo. A fixed-prior closed-unitary bound placed the anti-phase-rich ceiling at 0.4642, below the biological HSO reference of 0.509, indicating model headroom rather than hardware readout failure. Thus the device functions as a hardware-aware physiological testbed: HSO-like coordination is constrained local reconfiguration, whereas excessive mixing erodes one-link and anti-phase-rich readouts. Significance statement This study starts from a concrete living-cell phenomenon rather than from an abstract small circuit. Hyperthermal sarcomeric oscillations are warmed-cardiomyocyte sarcomere dynamics in which a beat-scale rhythm persists while neighbouring sarcomeres rapidly redistribute phase. I map a five-sarcomere HSO segment to a four-qubit nearest-neighbour topology and read it out with physiology-linked observables rather than a generic circuit score. The central result is repeatable hardware execution of biologically meaningful local-state observables, and the physiological message is that HSO local grammar is constrained one-link-dominated rephasing, not maximal mixing or simple global synchrony.