2000 character limit reached
Efficient Quantum Circuit Encoding of Object Information in 2D Ray Casting (2405.16132v1)
Published 25 May 2024 in quant-ph and cs.GR
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.
- R. P. Feynman, “Simulating physics with computers,” Feynman and Computation, pp. 133–153, 1982.
- D. Deutsch, “Quantum theory, the Church–Turing principle and the universal quantum computer,” Proc. R. Soc. Lond. A, vol. 400, pp. 97–117, 1985.
- P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput., vol. 26, no. 5, pp. 1484–1509, 1997.
- D. Coppersmith, “An approximate Fourier transform useful in quantum factoring,” arXiv:quant-ph/0201067, 2002.
- A. Y. Kitaev, “Quantum measurements and the Abelian stabilizer problem,” arXiv:quant-ph/9511026, 1995.
- C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, “Strengths and weaknesses of quantum computing,” SIAM J. Comput., vol. 26, no. 5, pp. 1510–1523, 1997.
- J. Preskill, “Quantum computing in the NISQ era and beyond,” Quantum, vol. 2, p. 79, 2018.
- M. Brooks, “Beyond quantum supremacy: The hunt for useful quantum computers,” Nature, vol. 574, no. 7776, pp. 19–21, Oct. 2019.
- D. C. Marinescu, “The promise of quantum computing and quantum information theory - quantum parallelism,” in Proc. IEEE IPDPS, 2005, p. 112.
- L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proc. ACM STOC, 1996, pp. 212–219.
- C. Alves, L. P. Santos, and T. Bashford-Rogers, “A quantum algorithm for ray casting using an orthographic camera,” in Proc. ICGI, 2019, pp. 56–63.
- A. Glassner, “Quantum computing, part 3,” IEEE Comput. Graphics Appl., vol. 21, no. 6, pp. 72–82, 2001.
- S. Kim and J. Seo, “Machine-learning-based classification of GPS signal reception conditions using a dual-polarized antenna in urban areas,” in Proc. IEEE/ION PLANS, Apr. 2023, pp. 113–118.
- S. Kim, J. Byun, and K. Park, “Machine learning-based GPS multipath detection method using dual antennas,” in Proc. ASCC, May 2022, pp. 691–695.
- H. Lee, J. Seo, and Z. Kassas, “Urban road safety prediction: A satellite navigation perspective,” IEEE Intell. Transp. Syst. Mag., vol. 14, no. 6, pp. 94–106, Nov.-Dec. 2022.
- S. Kim, S. Park, and J. Seo, “Single antenna based GPS signal reception condition classification using machine learning approaches,” J. Position. Navig. Timing, vol. 12, no. 2, pp. 149–155, 2023.
- Y. Lee, Y. Hwang, J. Y. Ahn, J. Seo, and B. Park, “Seamless accurate positioning in deep urban area based on mode switching between DGNSS and multipath mitigation positioning,” IEEE Trans. Intell. Transp. Syst., vol. 24, no. 6, pp. 5856–5870, Jun. 2023.
- H. Lee, S. Pullen, J. Lee, B. Park, M. Yoon, and J. Seo, “Optimal parameter inflation to enhance the availability of single-frequency GBAS for intelligent air transportation,” IEEE Trans. Intell. Transp. Syst., vol. 23, no. 10, pp. 17 801–17 808, Oct. 2022.
- A. K. Sun, H. Chang, S. Pullen, H. Kil, J. Seo, Y. J. Morton, and J. Lee, “Markov chain-based stochastic modeling of deep signal fading: Availability assessment of dual-frequency GNSS-based aviation under ionospheric scintillation,” Space Weather, vol. 19, no. 9, pp. 1–19, Sep. 2021.
- S. Kim, H. Lee, and K. Park, “GPS multipath detection based on carrier-to-noise-density ratio measurements from a dual-polarized antenna,” in Proc. ICCAS, 2021, pp. 1099–1103.
- M. Jia, H. Lee, J. Khalife, Z. M. Kassas, and J. Seo, “Ground vehicle navigation integrity monitoring for multi-constellation GNSS fused with cellular signals of opportunity,” in Proc. IEEE ITSC, 2021, pp. 3978–3983.
- K. Park and J. Seo, “Single-antenna-based GPS antijamming method exploiting polarization diversity,” IEEE Trans. Aerosp. Electron. Syst., vol. 57, no. 2, pp. 919–934, Apr. 2021.
- H. Lee, S. Kim, J. Park, S. Jeong, S. Park, J. Yu, H. Choi, and J. Seo, “A survey on new parameters of GPS CNAV/CNAV-2 and their roles,” J. Position. Navig. Timing, vol. 13, no. 1, pp. 45–52, 2024.
- L. P. Santos, T. Bashford-Rogers, J. Barbosa, and P. Navratil, “Towards quantum ray tracing,” IEEE Trans. Visual Comput. Graphics, 2024, in press.
- E. h. Shaik and N. Rangaswamy, “Implementation of quantum gates based logic circuits using IBM Qiskit,” in Proc. ICCCS, 2020, pp. 1–6.
- A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A, vol. 52, p. 3457, 1995.
- E. J. McCluskey, “Minimization of Boolean functions,” Bell Labs Tech. J., vol. 35, no. 6, pp. 1417–1444, 1956.
- S. R. Petrick, “A direct determination of the irredundant forms of a Boolean function from the set of prime implicants,” USAF Cambridge Research Center, Bedford, Mass., AFCRC Technical Report TR-56-100, April 1956.
- A. K. Chandra and G. Markowsky, “On the number of prime implicants,” Discrete Math., vol. 24, no. 1, pp. 7–11, 1978.
- R. Rudell and A. Sangiovanni-Vincentelli, “Multiple-valued minimization for PLA optimization,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., vol. 6, no. 5, pp. 727–750, 1987.