QuERLoc: Towards Next-Generation Localization with Quantum-Enhanced Ranging

TL;DR

QuERLoc tackles range-based localization by introducing quantum-enhanced ranging (QuER) that uses entangled probes to encode a linear combination of squared distances, converting a non-convex localization problem into a convex weighted least-squares formulation. The method defines phase-distance relations $\chi_k = \frac{4 \gamma}{c^2} \sum_{i \in I_k} w_{i,k} d_i^2$ and constructs a linear system $\bm{L}\bm{x}=\bm{h}$ whose solution yields the sensor position with low computational cost. Extensive simulations show QuERLoc significantly outperforms classical baselines in both RMSE and latency, while saturating the CRLB, demonstrating its potential for next-generation localization. The work provides a theoretical and practical foundation for quantum-enabled localization and opens new research directions in sensor networks and quantum sensing.

Abstract

Remarkable advances have been achieved in localization techniques in past decades, rendering it one of the most important technologies indispensable to our daily lives. In this paper, we investigate a novel localization approach for future computing by presenting QuERLoc, the first study on localization using quantum-enhanced ranging. By fine-tuning the evolution of an entangled quantum probe, quantum ranging can output the information integrated in the probe as a specific mapping of distance-related parameters. QuERLoc is inspired by this unique property to measure a special combination of distances between a target sensor and multiple anchors within one single physical measurement. Leveraging this capability, QuERLoc settles two drawbacks of classical localization approaches: (i) the target-anchor distances must be measured individually and sequentially, and (ii) the resulting optimization problems are non-convex and are sensitive to noise. We first present the theoretical formulation of preparing the probing quantum state and controlling its dynamic to induce a convexified localization problem, and then solve it efficiently via optimization. We conduct extensive numerical analysis of QuERLoc under various settings. The results show that QuERLoc consistently outperforms classical approaches in accuracy and closely follows the theoretical lowerbound, while maintaining low time complexity. It achieves a minimum reduction of 73% in RMSE and 97.6% in time consumption compared to baselines. By introducing range-based quantum localization to the mobile computing community and showing its superior performance, QuERLoc sheds light on next-generation localization technologies and opens up new directions for future research.

Figures (7)

• Figure 1: Workflow of QuERLoc
• Figure 2: Dynamics of qubit with coupled energy levels
• Figure 3: Comparison of real relative phase $\Delta \theta_{\text{real}}(t)$ and $\gamma t^2$. Minor outliers ($50$ out of $5 \times 10^6$ data points) are filtered out. Here we set $\gamma =10^3 ~\text{rad}/\text{sec}^2$, $\omega_0 = 10^{-2}~\text{rad}/\text{sec}$, and $\nu / \hbar = 10^{10}$. $\frac{1-\tau}{\tau^2 + \tau} = 2.5 \times 10^{-11}$. Absolute discrepancy is bounded by $5 \times 10^{-10}$ while relative phase is on the order of $10^{-4}$. Parameters can be adjusted subject to prior estimation on the order of probe ToF.
• Figure 4: Quantum circuit of ${\mathscr{E}( \{1, -1, 1, -1\} )}$ applied to $\ket{0}^{\otimes 4}$. The section outlined by dash line prepares a $4$-qubit GHZ state QCQI, while the following $\sigma_x$ gates conduct bit-flipping.
• Figure 5: Performance of QuERLoc and baselines over different noise levels. The CDF of localization error to all localization approaches when $m=3, 4$ and $5$ are plotted under noise levels $1\%$ and $5\%$.