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<p>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 <InlineEquation ID="IEq1"><EquationSource Format="TEX">\({{\mathscr{O}}}(\sqrt{N}\log N)\)</EquationSource><EquationSource Format="MATHML"><math><mi mathvariant="script">O</mi><mrow><mo>(</mo><mrow><msqrt><mrow><mi>N</mi></mrow></msqrt><mi>log</mi><mi>N</mi></mrow><mo>)</mo></mrow></math></EquationSource></InlineEquation>, given Hamiltonian dimension <i>N</i>. 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.</p>

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A 1-bit quantum filter for particle trajectory reconstruction

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年8月4日

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  • Xenofon Chiotopoulos,
  • Davide Nicotra,
  • George Scriven,
  • Kurt Driessens,
  • Marcel Merk,
  • Jochen Schütz,
  • Jacco de Vries,
  • Mark H. M. Winands

摘要

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 \({{\mathscr{O}}}(\sqrt{N}\log N)\)O(NlogN), 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.