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A Representative Framework for Implementing Quantum Finite Automata on Real Devices

Aliya Khadieva, Özlem Salehi, Abuzer Yakaryılmaz

TL;DR

The paper tackles implementing quantum finite automata for the language $MOD_p$ on gate-based quantum computers in the NISQ era. It develops device-independent circuit decompositions for uniformly controlled rotations and hardware-aware adaptations to IBM Quantum backends, including pseudo-rotations and linear-nearest-neighbor optimizations. Key contributions include tunable trade-offs between CNOT-cost and rotation-precision (e.g., $2^t + \frac{d}{2}(192(\log_2 d - t) - 768)$ for $0<t<\log_2 d - 4$) and practical demonstrations showing substantial reductions in CNOT counts and circuit depth, along with improved discrimination between members and non-members for $MOD_p$ (e.g., $p=11$, $p=37$). The findings offer actionable guidance for deploying QFA on NISQ devices and underscore the importance of topology-aware transpilation and basis-gate alignment.

Abstract

We present a framework for the implementation of quantum finite automata algorithms designed for the language $ MOD_p = \{ a^{i\cdot p } \mid i \geq 0 \}$ on gate-based quantum computers. First, we compile the known theoretical results from the literature to reduce the number of CNOT gates. Second, we demonstrate techniques for modifying the algorithms based on the basis gates of available quantum hardware in order to reduce circuit depth. Lastly, we explore how the number of CNOT gates may be reduced further if the topology of the qubits is known.

A Representative Framework for Implementing Quantum Finite Automata on Real Devices

TL;DR

The paper tackles implementing quantum finite automata for the language on gate-based quantum computers in the NISQ era. It develops device-independent circuit decompositions for uniformly controlled rotations and hardware-aware adaptations to IBM Quantum backends, including pseudo-rotations and linear-nearest-neighbor optimizations. Key contributions include tunable trade-offs between CNOT-cost and rotation-precision (e.g., for ) and practical demonstrations showing substantial reductions in CNOT counts and circuit depth, along with improved discrimination between members and non-members for (e.g., , ). The findings offer actionable guidance for deploying QFA on NISQ devices and underscore the importance of topology-aware transpilation and basis-gate alignment.

Abstract

We present a framework for the implementation of quantum finite automata algorithms designed for the language on gate-based quantum computers. First, we compile the known theoretical results from the literature to reduce the number of CNOT gates. Second, we demonstrate techniques for modifying the algorithms based on the basis gates of available quantum hardware in order to reduce circuit depth. Lastly, we explore how the number of CNOT gates may be reduced further if the topology of the qubits is known.
Paper Structure (9 sections, 1 theorem, 8 equations, 12 figures)

This paper contains 9 sections, 1 theorem, 8 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Device independent implementations
  4. Using Möttönen et al. approach
  5. Optimization
  6. Pseudo rotations approach
  7. Implementations on real hardware
  8. Experimental results
  9. Conclusion

Key Result

theorem thmcountertheorem

For the input string $a^j$, the circuit proposed in this subsection for recognizing $\mathtt{MOD_p}$ language uses $(2+3(n-3))j+2$ CNOT gates when executed on an $n$-qubit device with linear-nearest neighbor topology.

Figures (12)

  • Figure 1: QFA construction for $\mathtt{MOD_p}$ language.
  • Figure 2: Multi-qubit controlled rotation operation decomposition.
  • Figure 3: Efficient decomposition of the uniformly controlled rotation gate mottonen2006decompositions.
  • Figure 4: Proposed decomposition for a pair of rotations.
  • Figure 5: Multi-qubit controlled gate decompositions from barenco1995elementary.
  • ...and 7 more figures

Theorems & Definitions (2)

  • proof
  • theorem thmcountertheorem