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A 1-bit quantum filter for particle trajectory reconstruction
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DOI：10.1038/s42005-026-02780-8.png)
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Abstract
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The transition to the High-Luminosity Large Hadron Collider (HL-LHC) presents a computational challenge where particle reconstruction complexity may outpace classical computing resources. While quantum computing offers potential speedups, standard algorithms like Harrow-Hassidim-Lloyd (HHL) require prohibitive circuit depths for near-term hardware. Here, we introduce a 1-Bit Quantum Filter, a domain-specific adaptation of HHL that reformulates tracking from matrix inversion to binary ground-state filtering. By replacing high-precision phase estimation with a single-ancilla spectral threshold and exploiting the Hamiltonian’s sparsity, we achieve an asymptotic gate complexity of $${{\mathscr{O}}}(\sqrt{N}\log N)$$, given Hamiltonian dimension N. We validate this approach on LHCb Monte Carlo events, demonstrating segment finding efficiency highly competitive with the classical state-of-the-art methods. Furthermore, we benchmark performance using the Quantinuum System Model H2 trapped-ion processor and IBM Heron R3 superconducting processor. This work establishes a quantum track reconstruction method capable of solving realistic event topologies on noise-free simulators and smaller tracking scenarios within the current constraints of the Noisy Intermediate Scale Quantum (NISQ) era. Remaining challenges toward a full end-to-end tracking solution include an efficient readout and Hamiltonian construction. Trajectory reconstruction of elementary particles in future high-energy collider experiments is a highly complex combinatorial problem. A 1-Bit quantum filter, presented here, is a candidate to be applied in a Quantum-Classical workflow. Here we show the algorithm’s performance on quantum hardware and noise-free simulators.
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