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Efficient Quantum Circuit Encoding of Object Information in 2D Ray Casting

Seungjae Lee, Suhui Jeong, Jiwon Seo

TL;DR

The work tackles efficient quantum encoding of primitive indices and their 2D rectangle parameters $ (m_x,M_x,m_y,M_y) $ for a simplified ray casting problem, addressing NISQ constraints with a generalized Boolean-to-quantum mapping. It employs logic optimization via the Quine–McCluskey algorithm and Petrick’s method to minimize the number of products, terms, and auxiliary qubits, given index size $ register = \log_{2}{N} $ and parameter sizes $ \log_{2}{b_x} $ and $ \log_{2}{b_y} $, enabling a circuit that maps indices to parameters. Simulation shows substantial reductions in depth and gate count (e.g., for 4 primitives, depth from 68 to 41 and gates from 126 to 64) while preserving correctness; hardware experiments on IBM's platform demonstrate improved fidelity under optimization and reduced resource usage. This work demonstrates a viable near-term quantum approach to ray casting by optimizing circuit structure to maintain functional accuracy within NISQ limitations, potentially accelerating intersection verification tasks in rendering.

Abstract

Quantum computing holds the potential to solve problems that are practically unsolvable by classical computers due to its ability to significantly reduce time complexity. We aim to harness this potential to enhance ray casting, a pivotal technique in computer graphics for simplifying the rendering of 3D objects. To perform ray casting in a quantum computer, we need to encode the defining parameters of primitives into qubits. However, during the current noisy intermediate-scale quantum (NISQ) era, challenges arise from the limited number of qubits and the impact of noise when executing multiple gates. Through logic optimization, we reduced the depth of quantum circuits as well as the number of gates and qubits. As a result, the event count of correct measurements from an IBM quantum computer significantly exceeded that of incorrect measurements.

Efficient Quantum Circuit Encoding of Object Information in 2D Ray Casting

TL;DR

The work tackles efficient quantum encoding of primitive indices and their 2D rectangle parameters for a simplified ray casting problem, addressing NISQ constraints with a generalized Boolean-to-quantum mapping. It employs logic optimization via the Quine–McCluskey algorithm and Petrick’s method to minimize the number of products, terms, and auxiliary qubits, given index size and parameter sizes and , enabling a circuit that maps indices to parameters. Simulation shows substantial reductions in depth and gate count (e.g., for 4 primitives, depth from 68 to 41 and gates from 126 to 64) while preserving correctness; hardware experiments on IBM's platform demonstrate improved fidelity under optimization and reduced resource usage. This work demonstrates a viable near-term quantum approach to ray casting by optimizing circuit structure to maintain functional accuracy within NISQ limitations, potentially accelerating intersection verification tasks in rendering.

Abstract

Quantum computing holds the potential to solve problems that are practically unsolvable by classical computers due to its ability to significantly reduce time complexity. We aim to harness this potential to enhance ray casting, a pivotal technique in computer graphics for simplifying the rendering of 3D objects. To perform ray casting in a quantum computer, we need to encode the defining parameters of primitives into qubits. However, during the current noisy intermediate-scale quantum (NISQ) era, challenges arise from the limited number of qubits and the impact of noise when executing multiple gates. Through logic optimization, we reduced the depth of quantum circuits as well as the number of gates and qubits. As a result, the event count of correct measurements from an IBM quantum computer significantly exceeded that of incorrect measurements.
Paper Structure (8 sections, 4 equations, 3 figures, 3 tables)

This paper contains 8 sections, 4 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Geometric Setup
  3. Quantum Circuit Implementation
  4. Logic Optimization
  5. Results
  6. Results from Simulator
  7. Results from Quantum Computer
  8. Conclusion

Figures (3)

  • Figure 1: Geometric configuration with $b_{x}=b_{y}=4$ and four primitives (i.e., axis-aligned rectangles in red, blue, purple, green) parameterized as $(0,1,0,1)$, $(0,3,2,2)$, $(1,1,3,3)$, $(3,3,3,3)$, respectively. This setup follows the configuration of Alves2019:Quantum.
  • Figure 2: Measurement results of the optimized quantum circuit for the configuration with $b_x=b_y=4$, as obtained from the simulator. The histogram indicates the event count of each input (i.e., primitive index $i$) and output (i.e., parameters) pair, denoted as $i : (m_x,M_x,m_y,M_y)$.
  • Figure 3: Measurement results from a quantum computer when (a) the logic optimization was applied and (b) not applied. The histogram indicates the event count of each input (i.e., primitive index $i$) and output (i.e., parameter $m_x$) pair, denoted as $i : m_x$. Incorrect results are indicated by red color.