HaPPY gravity: a route to quantum advantage

Public research series · August 2026

Can a gravity-inspired quantum model become a task that a quantum processor solves faster than strong classical methods? This series follows the full audit trail—from a two-mass phase gate to a 61-qubit dynamic HaPPY benchmark.

The result today: the chosen depth-2 task of 42 local observables is classically tractable. A PEA/ZNE hardware run may still deliver a task-specific QPU-time advantage at about 1% precision, but that comparison has not yet been measured or quality matched.
N = 145HaPPY boundary size

The layered construction produces 61 dynamic bulk qubits and 80 bulk edges.

42Frozen observables

Thirteen X, thirteen Z and sixteen ZZ probes, requiring only two measurement bases.

31–45 sEstimated QPU time

A transfer estimate for PEA/ZNE at roughly 1% precision—not a measured HaPPY runtime.

The research path

gravitational phase→bosonic modes→HaPPY graph→classical audit→hardware test

The starting point is the Bose–Marletto–Vedral idea: branch-dependent gravitational phases can entangle two masses. Reduced to two position qubits, the entangling content is a controlled-phase gate. That makes the physics transparent, but it is far too small for computational advantage.

The next step uses a bosonic, gravity-inspired interaction and checks that the answer is stable as the local bosonic cutoff grows. Only after that physical and numerical audit does the project introduce a scalable circuit family: non-Clifford Floquet dynamics on the bulk graph of a layered HaPPY construction.

What the largest calculation says

Task Classical result Status
42 local observables, depth 1 All exact through backward causal cones Quantum advantage ruled out
42 local observables, depth 2 41 exact; the 32-qubit central cone is MPS-converged Classically tractable
Full 61-qubit state or global sampling Tested global MPS is not converged at χ = 128 Open, not proven hard
Depth-2 observables with PEA/ZNE Estimated 31–45 charged QPU seconds at about 1% Candidate; not yet executed

Why the negative result matters

A large Hilbert space, high entanglement or failure of one tensor-network ordering does not establish quantum advantage. The decisive question is whether the requested output can be computed efficiently. Here, local causal cones collapse most of the apparently global 61-qubit problem into exact calculations of at most 24 qubits, plus one converged 32-qubit local MPS.

Claim boundary. This is a candidate for a practical, task-specific runtime comparison. It is not evidence for an asymptotic computational advantage, and it is not an experimental test of quantum gravity.

Sources and reproducibility

Project status: 14 August 2026. Numerical values come from the frozen public research artifacts; claim boundaries are deliberately preserved.