QCxSimulation: Scatter-Aware X-Ray Projection Radiography via Discrete-Time Quantum Walks

1 Introduction

• Virtual projections support cost-effective scan-setting exploration when physical experiments are constrained by cost and safety.Source: §1 · p. 1
• The proposed quantum encoding represents photon trajectories and Rayleigh and Compton events, while superposition tracks potential scattering paths simultaneously.Source: §1 · p. 1

1.1 X-ray Radiography Simulation

• Higher-order scattering reduces tissue contrast and fine detail, while XSimulation runtime rises from 57 ms for primary-only to 28 s for first-order and 23 min for second-order scatter.Source: §1.1 · p. 2, Figure 1 · p. 2
• Monte Carlo, analytical, and hybrid simulators face rapidly increasing runtime with specimen size and scatter order, limiting large parameter-space exploration and virtual CT studies.Source: §1.1 · p. 2

1.2 Quantum Computing

• A discrete-time quantum walk uses position and internal-mode registers with coin and shift operators; repeated steps propagate amplitudes for all admissible paths in superposition.Source: §1.2 · p. 3
• Quantum radiative-transport approaches include hybrid ray-intersection or visibility methods, quantum path tracing, and grid-based walks, though some face encoding, depth, or hardware constraints.Source: §1.2 · pp. 3–4

2 Method

• The quantum walk encodes admissible multi-scatter photon paths in a state over position, direction, and other descriptors, with amplitudes representing the paths.Repeated interaction and shift operations propagate this state through the discretized medium.Source: §2 · p. 4

2.1 Physical Problem and Discretization

• Photoelectric absorption removes photons, Rayleigh scattering changes direction without energy transfer, and Compton scattering changes direction and degrades energy according to its angle.Rayleigh angles are approximated by uniform sampling over 4π, and secondary electrons from absorption are disregarded.Source: §2.1 · pp. 4–5
• Fourteen directions and four energy levels balance transport resolution against circuit resources, capturing leading-order Compton anisotropy and typical spectral evolution.The angular discretization is described as sufficient for total transmission and scatter-to-primary ratios; with six steps, histories typically contain at most three deflected Compton scatters.Source: §2.1 · pp. 6–7

2.2 X-ray Simulation: Per-Step Quantum Circuit

• Each circuit step applies material-local interaction blocks and then a global shift, with boundary checks marking photons absorbed, detected, or lost.Interaction probabilities and redistribution use material- and energy-dependent cross sections; deflected Compton events decrement the energy level, while forward-like scatters leave it unchanged.Source: §2.2 · pp. 7–8
• Aggregated measurement shots provide primary and scatter projections, scatter-to-primary ratios, and energy-resolved images.Each shot records final position, direction, energy, survival status, and per-step Compton and Rayleigh flags.Source: §2.2 · pp. 7–8

3 Results

• Results use a 5 × 5 × 5 grid, six quantum-walk steps, and 10,000 measurement shots, with detector projections separated into primary and scattering-history categories.Reported categories include Compton 1x, Compton 2x, all Compton, and all detected photons.Source: §3 · p. 8

3.1 Use Case 1

• With the aluminium phantom, point-source Compton counts spread beyond the central primary pixel, the 3 × 3 source fills the central region, and full-field illumination reaches surrounding air voxels.The simulations use an 80 keV beam and a 3 × 3 × 2 voxel aluminium block.Source: §3.1 · pp. 8–9, Figure 3 · p. 9

3.1 Use Case 1; 3.2 Use Case 2

• QCxSimulation and GEANT4 show qualitatively similar all-detected projections for all three source geometries and all three photon energies.The remaining differences are attributed to physical discretization, which slightly changes scattering intensities without changing the main spatial structure.Source: Figure 4 · p. 10, §3.1 · p. 10, §3.2 · p. 11

3.2 Use Case 2

• From 80 to 400 keV, copper primary transmission increases while Compton scatter broadens and becomes more uniform as the aluminium–copper cross-section difference decreases.At 80 keV, photoelectric attenuation strongly suppresses the primary signal in copper; at 400 keV, Compton scattering dominates for both materials.Source: §3.2 · pp. 10–11, Figure 6 · p. 11

3.3 Use Case 3

• The normalized nine-run sum matches the 3 × 3 source in spatial structure, with primary-pixel errors below expected shot-noise uncertainty and no systematic discrepancy.The 3 × 3 run allocates 10,000 shots across nine positions (~1,111 each), yielding ~3% expected relative uncertainty.Source: §3.3 · p. 12

4 Discussion

• Across three use cases, the walk reproduces dominant spatial and energetic features and handles varied source geometries, multi-material phantoms, and spectral ranges.Source: §4 · p. 12

4.1 Physical Accuracy and Modelling Approximations

• GEANT4 comparisons reproduce dominant radiographic behavior, with 14 propagation directions and four energy levels approximating continuous transport physics.Source: §4.1 · p. 13
• Discretisation can slightly shift scattering intensities, but finite scattering histories bound accumulated error and leave projection spatial structure unchanged.Source: §4.1 · p. 13
• Each measurement yields one photon outcome, so activating more source positions shares a fixed shot budget rather than increasing total counts.With 10,000 shots across nine positions, each position receives approximately 1,111 effective measurements; classical simulations likewise redistribute a fixed photon budget unless photons per position are held fixed.Source: §4.1 · pp. 13–14
• The forward-leap directions traverse two grid layers per step, shortening detector-reaching paths but killing photons that overshoot from the final layer.Source: §4.1 · p. 14

4.2 Scalability and Quantum Advantage

• The circuit can adapt to grid size, material assignments, source geometry, and finer direction or energy resolution, with added qubits for finer resolution.Source: §4.2 · p. 14
• Classical path counts grow exponentially with scatter order, whereas the walk advances admissible paths in superposition with polynomial circuit cost.Source: §4.2 · p. 14
• Quantum amplitude estimation could reduce measurement repetitions quadratically, but integrating it requires a deeper unitary walk and fault-tolerant hardware beyond current NISQ capabilities.The current implementation measures scattering at each walk step, which is incompatible with amplitude estimation's unitary-walk requirement.Source: §4.2 · pp. 14–15

• The quantum-walk simulation reproduces energy-dependent angular distributions of first- and second-order Compton scattering and multi-material contrast validated against GEANT4.Source: §5 · p. 15
• All simulations ran on a classical statevector simulator because current NISQ hardware remains insufficient.Source: §5 · p. 15
• The work establishes a physically validated framework positioned as a future alternative to classical Monte Carlo methods as fault-tolerant hardware becomes more available.Source: §5 · p. 15