QANTIS: A Hardware-Validated Quantum Platform for POMDP Planning and Multi-Target Data Association

TL;DR

QANTIS is presented, a modular platform that integrates quantum belief update (Grover amplitude amplification and BIQAE), QUBO-based data association via FPC-QAOA, and composable error mitigation, and empirically characterise NISQ feasibility boundaries.

Abstract

Autonomous navigation under uncertainty requires solving partially observable Markov decision processes (POMDPs) for planning and assigning sensor measurements to tracked targets--a task known as multi-target data association (MTDA). Both problems become computationally demanding at scale: belief conditioning costs $\mathcal{O}(P(e)^{-1})$ per node under rare evidence, while MTDA is NP-hard. Quantum amplitude amplification can quadratically reduce the belief-update query cost to $\mathcal{O}(P(e)^{-1/2})$, while QUBO reformulations expose MTDA to quantum and quantum-inspired optimisation heuristics. We present QANTIS, a modular platform that integrates quantum belief update (Grover amplitude amplification and BIQAE), QUBO-based data association via FPC-QAOA, and composable error mitigation, and we report a 45-experiment hardware study on three IBM Heron backends. On hardware, a single Grover iterate applied to a Tiger belief oracle amplifies a rare observation probability from $0.179$ to $0.907$ ($5.1\times$; ISA 18) while preserving the Bayesian posterior (Hellinger $0.0015$), increasing usable-shot yield from 1,463 to 7,429. We interpret this as a hardware validation of the quadratic query-complexity mechanism at $k=1$ with posterior preservation, rather than a wall-clock advantage claim. We further demonstrate, to our knowledge, the first closed-loop hybrid quantum-classical Tiger POMDP on superconducting hardware ($T=8$, max Hellinger below $0.015$), and empirically characterise NISQ feasibility boundaries: ZNE-based error mitigation is beneficial below ISA $\approx 100$ and harmful above ISA $\gtrsim 1{,}000$; FPC-QAOA is meaningful at $\leq 15$ QUBO variables (ISA $\lesssim 450$). These results characterise practical operating regimes on current superconducting hardware rather than wall-clock quantum advantage at today's problem scales.

Figures (3)

• Figure 1: Quantum belief update circuit for a single POMDP step (schematic; register sizes $n_s{=}\lceil\log_2|S|\rceil$, $n_a{=}\lceil\log_2|A|\rceil$, $n_o{=}\lceil\log_2|\Omega|\rceil$, $n_r{=}$ reward precision bits). Unitaries $U_1$, $U_2$, $U_3$ encode the transition, observation, and reward models respectively. Measuring the observation register and conditioning on outcome $o$ (via amplitude amplification) yields the updated belief in the $S_{t+1}$ register. See Appendix \ref{['app:circuit-details']} for the full hardware qubit allocation.
• Figure 2: Modular architecture of the QANTIS platform. The three packages maintain a strict acyclic dependency hierarchy: quantum-pomdp and quantum-mht depend on quantum-common but have no cross-dependency. The backend abstraction layer in quantum-common dispatches to three quantum hardware/simulator backends.
• Figure 3: Log-log scaling of solve and build times with target count $N$ (data from Table \ref{['tab:qubo-scaling']}). The Hungarian algorithm exhibits the expected cubic scaling; the QUBO build time scales quadratically. GNN provides the fastest heuristic but yields suboptimal assignments. All measurements are from classical simulation (single-threaded Python, Intel i7-12700K).