Implementing a Quantum Finite Automaton in IBMQ using Custom Control Pulses

TL;DR

This work tackles decoherence and gate‑level errors in implementing a MO1QFA for the MOD^p problem on IBMQ superconducting hardware. It introduces pulse‑level programming to calibrate a fast square control pulse that realizes the MO1QFA rotations more efficiently than default gate decompositions. The results show substantial gains: the custom pulse yields a fourfold reduction in gate duration and can extend the maximum computable word length by about 12× at a 10% error threshold and by more than 7× at a 20% threshold, with several lengths exceeding 1000 symbols. This demonstrates the viability of MO1QFA implementations on real quantum devices and highlights pulse‑level gate engineering as a practical route to improve quantum automata performance.

Abstract

Quantum finite automata can be used for pattern recognition. Present implementations on actual quantum devices face decoherence issues, which compromise the quality of long strings computation. In this work, we focus on the Measure Once 1-way Quantum Finite Automata (MO1QFA) model for addressing the MOD^p problem, investigating how quantum errors may affect the quality of the computation in this model when implemented in IBM-Q superconducting environment. To improve the performance of the implementation, we use pulse-level programming for calibrating a fast single-qubit gate designed specifically for the automaton implementation. The demonstrations conducted on the Jakarta quantum computer show that using custom pulses significantly reduces errors during extended word computations. While realizing improvements in error variations and predictability -- with a fourfold reduction in circuit latency -- the proposed solution demonstrates a substantial increase in the supported computation length of the automaton. When considering thresholds of 10% and 20% in absolute errors of acceptance probabilities, the solution has the potential to increase the maximum word length by 12 and 7+ times, respectively, compared to the default Qiskit gate.

Figures (5)

• Figure 1: MO1QFA automaton diagram for $MOD^p$ problem. $\ket{0}$ is the initial state (indicated by the horizontal arrow) and also the final one (represented in the double circle), and $\ket{1}$ is an intermediate state of the computation process. After reading a symbol $a$ of the string, the result of the computation will depend on the amplitudes of remaining in the same state $\cos(2\pi/p)$ or changing to another state $-i\sin(2\pi/p)$, which are described above or under the arrows.
• Figure 2: Comparison between expected probability for word lengths congruent to 0 and 3 modulo 11 and acceptance probability with optimization level 0 run on ibm_jakarta.
• Figure 3: Transpiled quantum circuit for $R_x(4\pi/11)$ gate.
• Figure 4: $2\pi$ Rabi rates calibration for Jakarta.
• Figure 5: Expected and obtained acceptance probabilities for the $17.8$$ns$ square pulse for word lengths congruent to 0 and 3 modulo 11.

Theorems & Definitions (2)

• Definition 1
• Definition 2