Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
91 tokens/sec
GPT-4o
12 tokens/sec
Gemini 2.5 Pro Pro
o3 Pro
5 tokens/sec
GPT-4.1 Pro
15 tokens/sec
DeepSeek R1 via Azure Pro
33 tokens/sec
Gemini 2.5 Flash Deprecated
12 tokens/sec
2000 character limit reached

Quantum Backtracking in Qrisp Applied to Sudoku Problems (2402.10060v3)

Published 15 Feb 2024 in quant-ph, cs.DS, and cs.PL

Abstract: The quantum backtracking algorithm proposed by Ashley Montanaro raised considerable interest, as it provides a quantum speed-up for a large class of classical optimization algorithms. It does not suffer from Barren-Plateaus and transfers well into the fault-tolerant era, as it requires only a limited number of arbitrary angle gates. Despite its potential, the algorithm has seen limited implementation efforts, presumably due to its abstract formulation. In this work, we provide a detailed instruction on implementing the quantum step operator for arbitrary backtracking instances. For a single controlled diffuser of a binary backtracking tree with depth n, our implementation requires only $6n+14$ CX gates. We detail the process of constructing accept and reject oracles for Sudoku problems using our interface to quantum backtracking. The presented code is written using Qrisp, a high-level quantum programming language, making it executable on most current physical backends and simulators. Subsequently, we perform several simulator based experiments and demonstrate solving 4x4 Sudoku instances with up to 9 empty fields. This is, to the best of our knowledge, the first instance of a compilable implementation of this generality, marking a significant and exciting step forward in quantum software engineering.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (46)
  1. “Quantum optimization: Potential, challenges, and the path forward” (2023). arXiv:2312.02279.
  2. “Beating the random assignment on constraint satisfaction problems of bounded degree” (2015). arXiv:1505.03424.
  3. Ewin Tang. “A quantum-inspired classical algorithm for recommendation systems”. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. STOC ’19. ACM (2019).
  4. “Grover’s algorithm offers no quantum advantage” (2023). arXiv:2303.11317.
  5. “Does provable absence of barren plateaus imply classical simulability? or, why we need to rethink variational quantum computing” (2023). arXiv:2312.09121.
  6. “Disentangling hype from practicality: On realistically achieving quantum advantage” (2023). arXiv:2307.00523.
  7. “Focus beyond quadratic speedups for error-corrected quantum advantage”. PRX Quantum 2, 010103 (2021).
  8. Ashley Montanaro. “Quantum-walk speedup of backtracking algorithms”. Theory of Computing 14, 1–24 (2018).
  9. Ashley Montanaro. “Quantum speedup of branch-and-bound algorithms”. Physical Review Research 2, 013056 (2020).
  10. “Quantum algorithms: A survey of applications and end-to-end complexities” (2023). arXiv:2310.03011.
  11. “Practical implementation of a quantum backtracking algorithm”. Page 597–606. Springer International Publishing.  (2020).
  12. Qiskit contributors. “Qiskit: An open-source framework for quantum computing”. [Software]. Available from https://github.com/Qiskit (2023).
  13. “t|ket⟩: a retargetable compiler for NISQ devices”. Quantum Science and Technology 6, 014003 (2020).
  14. “Pennylane: Automatic differentiation of hybrid quantum-classical computations” (2022). arXiv:1811.04968.
  15. Cirq Developers. “Cirq”. [Software]. Available from https://github.com/quantumlib/Cirq (2022).
  16. “Qibo: a framework for quantum simulation with hardware acceleration”. Quantum Science and Technology 7, 015018 (2021).
  17. “A new quantum ripple-carry addition circuit” (2004). arXiv:quant-ph/0410184.
  18. Craig Gidney. “Halving the cost of quantum addition”. Quantum 2, 74 (2018).
  19. “A higher radix architecture for quantum carry-lookahead adder” (2023). arXiv:2304.02921.
  20. “Efficient floating point arithmetic for quantum computers”. IEEE Access 10, 72400–72415 (2022).
  21. “Quantum algorithm for tree size estimation, with applications to backtracking and 2-player games”. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing. STOC ’17. ACM (2017).
  22. “Quantum lattice enumeration and tweaking discrete pruning”. Cryptology ePrint Archive, Paper 2018/546 (2018). https://eprint.iacr.org/2018/546.
  23. “Quantum speedup of the traveling-salesman problem for bounded-degree graphs”. Phys. Rev. A 95, 032323 (2017).
  24. “Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems”. New Journal of Physics 18, 073003 (2016).
  25. “Applying quantum algorithms to constraint satisfaction problems”. Quantum 3, 167 (2019).
  26. “Silq: a high-level quantum language with safe uncomputation and intuitive semantics”. In Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation. Page 286–300. New York, NY, USA (2020). Association for Computing Machinery.
  27. “Qunity: A unified language for quantum and classical computing”. Proceedings of the ACM on Programming Languages 7, 921–951 (2023).
  28. “ProjectQ: an open source software framework for quantum computing”. Quantum 2, 49 (2018).
  29. “Q#: Enabling scalable quantum computing and development with a high-level dsl”. In Proceedings of the Real World Domain Specific Languages Workshop 2018. RWDSL2018. ACM (2018).
  30. “Quipper: a scalable quantum programming language”. In Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation. Page 333–342. PLDI ’13New York, NY, USA (2013). Association for Computing Machinery.
  31. “isQ: Towards a practical software stack for quantum programming” (2023). arXiv:2205.03866.
  32. “Tower: data structures in quantum superposition”. Proc. ACM Program. Lang.6 (2022).
  33. “Quantum types: going beyond qubits and quantum gates” (2024). arXiv:2401.15073.
  34. “Unqomp: synthesizing uncomputation in quantum circuits”. In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. Page 222–236. New York, NY, USA (2021). Association for Computing Machinery.
  35. “Uncomputation in the Qrisp high-level quantum programming framework”. Page 150–165. Springer Nature Switzerland.  (2023).
  36. Lov K. Grover. “A fast quantum mechanical algorithm for database search” (1996).
  37. “Logic synthesis for quantum computing” (2017). arXiv:1706.02721.
  38. “Reversible pebbling game for quantum memory management” (2019). arXiv:1904.02121.
  39. Piotr Porwik. “Efficient calculation of the Reed-Muller form by means of the Walsh transform”. International Journal of Applied Mathematics and Computer Science 12, 571–579 (2002). url: http://eudml.org/doc/207613.
  40. “On the controlled-not complexity of controlled-not–phase circuits”. Quantum Science and Technology 4, 015002 (2018).
  41. “Automatic generation of Grover quantum oracles for arbitrary data structures”. Quantum Science and Technology 8, 025003 (2023).
  42. “Efficient constructions for simulating multi controlled quantum gates”. In Computational Science – ICCS 2022. Pages 179–194. Springer International Publishing (2022).
  43. “Synthesis of quantum-logic circuits”. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25, 1000–1010 (2006).
  44. “Local, expressive, quantum-number-preserving VQE ansätze for fermionic systems”. New Journal of Physics 23, 113010 (2021).
  45. “A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits”. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 32, 818–830 (2013).
  46. Dmitri Maslov. “Advantages of using relative-phase Toffoli gates with an application to multiple control Toffoli optimization”. Physical Review A 93, 022311 (2016).
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now