Trackhhl Advances Particle Tracking Using 1-Bit Quantum Filtering with Scalable Gate Complexity

Reconstructing particle trajectories at the forthcoming High-Luminosity Large Hadron Collider will demand computational methods capable of handling unprecedented data complexity. Xenofon Chiotopoulos, Davide Nicotra, and George Scriven, from Maastricht University and Nikhef, alongside Kurt Driessens, Marcel Merk and Jochen Schütz et al., have addressed this challenge with a novel quantum algorithm called TrackHHL. Their research introduces the 1-Bit Filter, a streamlined adaptation of the Harrow-Hassidim-Lloyd algorithm which reformulates particle tracking as a binary ground-state filtering problem. This innovative approach significantly reduces the computational burden, achieving a lower asymptotic gate complexity and demonstrating the potential for real-time track reconstruction using near-term quantum hardware. The team validates their method through simulations of LHCb data and benchmarking against current quantum processor noise models, paving the way for resource-efficient data analysis in the era of high-energy physics.

Their research introduces the 1-Bit Filter, a streamlined adaptation of the Harrow-Hassidim-Lloyd algorithm which reformulates particle tracking as a binary ground-state filtering problem. This innovative approach significantly reduces the computational burden, achieving a lower asymptotic gate complexity and demonstrating the potential for real-time track reconstruction using near-term quantum hardware. This research pioneers the 1-Bit Quantum Filter, a domain-specific adaptation of the Harrow-Hassidim-Lloyd algorithm, reformulating particle tracking from a computationally expensive matrix inversion into a binary ground-state filtering problem. By replacing high-precision phase estimation with a single-ancilla spectral threshold, the team drastically reduced the required quantum resources. Exploiting the inherent sparsity within the Hamiltonian, the study achieves an asymptotic gate complexity of O(√N logN), where N represents the Hamiltonian dimension.

To validate this innovative method, researchers constructed a detailed toy model simulating events from the LHCb Vertex Locator. This simulation allowed for rigorous testing of the algorithm’s performance under realistic conditions, mirroring the detector’s configuration of 52 silicon pixel modules positioned 5mm from the interaction point. The study meticulously benchmarked performance using the noise models of both Quantinuum’s H2 trapped-ion processor and IBM’s Heron superconducting processor, providing a comparative analysis of hardware suitability. This comparative analysis revealed that the all-to-all connectivity and lower error rates of the trapped-ion architecture offered improved solution fidelity for smaller systems, though both platforms currently face limitations with gate error accumulation.

The core methodological innovation lies in formulating track reconstruction as the search for the ground state of an Ising-like Hamiltonian, inspired by the Denby-Peterson model. Scientists harnessed the Hamiltonian’s sparsity by implementing a custom Hamiltonian evolution via Direct Structural Synthesis, which constructs exact unitary operators and significantly reduces circuit depth. Furthermore, the research establishes a polynomial speedup over classical inversion methods, with a sampling complexity of O(N logN) for accurate track reconstruction using state tomography. Experiments demonstrate successful track reconstruction on noise-free simulators and smaller tracking scenarios, establishing a resource-efficient method capable of tackling realistic event topologies within the constraints of current Noisy Intermediate-Scale Quantum technology. Researchers have introduced the 1-Bit Filter, a quantum algorithm designed to address the increasing complexity of tracking tasks. This work reformulates particle tracking from a computationally intensive matrix inversion problem into a binary ground-state filtering process, offering a potentially significant resource reduction. Experiments demonstrate an asymptotic gate complexity of O(√N logN), where N represents the Hamiltonian dimension, marking a polynomial speedup compared to classical inversion methods.

The team validated this approach through simulations of events generated by the LHCb Vertex Locator, employing a toy model to mimic detector behaviour. Benchmarking was performed using noise models derived from Quantinuum’s H2 trapped-ion processor and IBM’s Heron superconducting processor. Results show successful track reconstruction in both ideal simulations and emulations on small-scale quantum hardware, establishing a viable pathway for quantum particle track reconstruction. The study analytically derived a sampling complexity of O(N logN) for accurate track reconstruction using state tomography, further quantifying the algorithm’s efficiency.

Scientists measured the performance of the 1-Bit Quantum Filter using a custom simulation of the LHCb VELO detector, which comprises 52 silicon pixel detector modules. Each beam crossing at the HL-LHC generates approximately 20 simultaneous collisions, resulting in around 1000 produced particles travelling along straight trajectories. The research team formulated the track reconstruction task within a Hamiltonian framework, adapting previous approaches to the specific geometry of the VELO. This framework represents potential track segments as binary variables, where a value of 1 indicates an active segment and 0 signifies inactivity.

The algorithm’s performance was assessed by evaluating segment efficiency, the percentage of correctly identified track segments, as a function of the total number of tracks. Data shows segment efficiency consistently exceeding 95% across a range of track densities, from 50 to 200 total tracks. Benchmarking on the IBM Heron and Quantinuum H2 systems revealed that the trapped-ion architecture, with its all-to-all connectivity and lower error rates, provided improved solution fidelity for small systems.

1-Bit Filter Enables Complex Particle Tracking The development

The development of the 1-Bit Quantum Filter represents a significant advancement in quantum algorithms for particle tracking. Researchers have successfully reformulated the tracking problem from a computationally intensive matrix inversion to a more efficient binary ground-state filtering process. This adaptation of the Harrow-Hassidim-Lloyd algorithm achieves an asymptotic gate complexity of O(√N logN), where N represents the Hamiltonian dimension, demonstrating a substantial reduction in required quantum resources. Validation through simulations of LHCb Vertex Locator events confirms the algorithm’s ability to handle event sizes previously inaccessible to quantum methods.

This work establishes a resource-efficient approach to track reconstruction, showing robustness against the noise profiles of current generation quantum hardware, particularly those with high connectivity. Simulations utilising both Quantinuum H2 and IBM Heron processor noise models indicate the algorithm’s feasibility within the constraints of the Noisy Intermediate Scale Quantum era. The authors acknowledge limitations stemming from discrepancies between simulated noise and actual hardware noise, as well as variations in noise mitigation strategies between different quantum platforms.