[Paper Review] On the Power of Quantum Queue Automata in Real-time

Amandeep Singh Bhatia, Ajay Kumar|arXiv (Cornell University)|Oct 29, 2018

Quantum Computing Algorithms and Architecture20 references4 citations

TL;DR

This paper introduces real-time quantum queue automata (rtQQA), a quantum variant of classical queue automata using unitary transitions. It proves that rtQQA can recognize languages undecidable by real-time deterministic and non-deterministic classical queue automata, demonstrating a strict computational advantage via quantum superposition and interference in real-time processing.

ABSTRACT

This paper proposed a quantum analogue of classical queue automata by using the definition of the quantum Turing machine and quantum finite-state automata. However, quantum automata equipped with storage medium of a stack has been considered, but the concept of quantum queue automata has not been introduced so far. The classical Turing machines can be simulated by classical queue automata. Motivated by the efficiency of the quantum Turing machine and nature of classical queue automata, we have introduced the notion of quantum queue automata using unitary criteria. Our contributions are as follows. We have also introduced a generalization of real-time deterministic queue automata, the real-time quantum queue automata which work in real-time i.e. the input head can move towards the right direction only and takes exactly one step per input symbol. We have shown that real-time quantum queue automata is more superior than its real-time classical variants by using quantum transitions. We have proved the existence of the language that can be recognized by real-time quantum queue automata and cannot be recognized by real-time deterministic (reversible) queue automata. Further, we have shown that there is a language that can be recognized by real-time quantum queue automata but not by real-time non-deterministic queue automata.

Motivation & Objective

• To formalize a quantum analogue of classical queue automata using quantum Turing machine principles and unitary evolution.
• To investigate the computational power of real-time quantum queue automata (rtQQA) compared to classical real-time variants.
• To demonstrate that quantum transitions enable recognition of languages beyond the reach of classical real-time deterministic and non-deterministic queue automata.
• To establish a hierarchy of language recognition capabilities between classical and quantum queue automata in real-time models.

Proposed method

• Define quantum queue automata using unitary transition functions over quantum states, queue symbols, and head positions.
• Introduce real-time quantum queue automata (rtQQA) with a single right-moving input head and unitary evolution per input symbol.
• Construct a quantum automaton for the language $L_{xy} = \{w \in \{a,b,0,1,c,\$\}^* \mid w = xcyx^R\}$ using superposition to explore multiple computation paths in parallel.
• Implement quantum transitions that simultaneously enqueue symbols (A/B for a/b or 0/1) and later compare them via queue operations, leveraging quantum interference.
• Use amplitude amplification and destructive interference to ensure acceptance with probability ≥ 2/3 for valid inputs and rejection with probability ≥ 2/3 for invalid ones.
• Define well-formedness conditions for transition functions to ensure unitarity and valid quantum evolution across all configurations.

Experimental results

Research questions

• RQ1 Can a quantum variant of queue automata be formally defined using unitary transitions, and how does it differ from classical queue automata?
• RQ2 Is real-time quantum queue automata more powerful than real-time deterministic queue automata in terms of language recognition?
• RQ3 Can real-time quantum queue automata recognize languages that are not recognizable by real-time non-deterministic queue automata?
• RQ4 What is the role of quantum superposition and interference in enabling recognition of non-context-free or non-regular languages in real-time?

Key findings

• A language $L_{xy} = \{xcyx^R \mid x,y \in \{a,b\}^*\}$ can be recognized by real-time quantum queue automata with acceptance probability ≥ 2/3.
• This same language cannot be recognized by any real-time deterministic queue automaton, proving a strict computational advantage of rtQQA over classical deterministic variants.
• There exists a language that is recognizable by real-time quantum queue automata but not by any real-time non-deterministic queue automaton, demonstrating that rtQQA surpasses even non-deterministic classical counterparts.
• The quantum automaton achieves recognition through superposition of multiple computation paths, with interference ensuring high-probability acceptance or rejection based on input structure.
• The construction uses unitary transition functions that preserve quantum state normalization and enable coherent evolution across queue operations.
• The results confirm that quantum transitions in real-time models significantly enhance the language recognition power of queue automata beyond classical limits.