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.
Abstract (translated)
在不确定性下的自主导航需要解决部分可观测马尔可夫决策过程（POMDPs）以进行规划，并将传感器测量值分配给跟踪目标，这被称为多目标数据关联（MTDA）。当问题规模增大时，这两个问题的计算需求都会变得非常大：在稀有证据下每个节点的状态条件化成本为$\mathcal{O}(P(e)^{-1})$，而MTDA则是NP难解的问题。量子振幅放大可以将信念更新查询成本二次减少至$\mathcal{O}(P(e)^{-1/2})$，而QUBO（二次约束优化）重新表述则使得MTDA能够利用量子和启发式的量子优化方法。 我们在此介绍一个模块化平台QANTIS，它集成了量子信念更新（Grover振幅放大与BIQAE）、基于FPC-QAOA的QUBO数据关联以及可组合错误缓解。我们在IBM Heron后端上进行了一项包含45个实验的硬件研究。 在硬件层面，当应用到虎信念预言机时，单次Grover迭代将稀有观察的概率从$0.179$放大至$0.907$（倍增了约$5.1$倍；ISA 18），同时保持贝叶斯后验概率不变（赫林距离为$0.0015$），使有效量子拍数从1,463增加到7,429。我们将此解读为对在$k=1$时保留后验的二次查询复杂性机制的有效硬件验证，而非所谓的即时性能优势。 此外，我们展示了（据我们所知）首个闭合回路混合量子-经典虎POMDP实验，并在超导设备上实现了时间步长$T=8$且最大赫林距离低于$0.015$的结果。通过实证分析了NISQ（近似不可信量子计算）可行性边界：基于ZNE（零噪声极限）的错误缓解在ISA$\approx 100$以下有益，在ISA$\gtrsim 1{,}000$以上则有害；FPC-QAOA对于最多不超过15个变量（ISA $\lesssim 450$）是有效的。 这些结果描述了当前超导硬件上的实际运行范围，而非在今天的问题规模下的即时量子优势。
URL
https://arxiv.org/abs/2603.00785
