Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International journal of unconventional computing

Quantum finite state machines - A circuit based approach

Martin Lukáč, Michitaka Kameyama, Marek A. Perkowski

Published May 1, 2013• 4 citations
OpenAlex

Abstract

We present a model of Quantum Finite State Machines (QFSM) based on the quantum circuit representation. In this model, properties of quantum bits are exploited in order to implement Quantum Finite State Machines without an explicit external memory. We show that because of the the natural ability of quantum systems to retain the quantum state, quantum circuits can be directly used to implement some classes of the quantum finite state machines. In particular, the circuit model allows to remove the logic-memory distinction as it is used in the classically established model of finite state machines. Rather, the quantum register implementing the QFSM as a circuit is alternatively used as memory and as logic. In order to allow such behavior the quantum circuit (processor) is controlled by a classical circuit that provides the necessary timing of the quantum operations as well as the interface between the quantum and the classical world. Moreover, additional mechanism for preserving unknown quantum qubit state is used and a novel computational protocol allowing the implementation of the QFSM is proposed. This framework is is called the Classically Controlled Quantum Computer (CCQC). The CCQC thus combines a quantum processor with a classical controller in such manner that computation is carried from the classical inputs, through quantum processing to classical outputs. We discuss a high level synthesis approach to quantum sequence detection based on the synthesis of quantum sequential circuits. Such machines can find many applications for instance in robotics; for example a robot is required to recognize certain sequences of input sensor values.

Related papers

Quantum Finite State Machines as Sequential Quantum Circuits

Martin Lukáč, Marek A. Perkowski

In this paper we present the synthesis process of quantum finite state machines for sequence detection based on the synthesis of quantum sequential circuits. Such machines have many applications for instance in robotics. We show the relation between the quantum circuit and the natural ability of quantum systems to retain the quantum state. We consider cases where a single qubit in a circuit represents a quantum state and another is used as the input qubit. We analyze some of the well known circuits as sequence detectors and describe their behaviors. We show that the standard quantum logic synthesis can be used for both the synthesis of quantum circuits as well as for quantum finite state machines used as sequence detectors.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•Jan 1, 2009•16 citations

Comparison of state assignment methods for “quantum circuit” model of permutative quantum state machines

Manjith Kumar, Samy Boshra-riad, Yasodha Nachimuthu +1 more

The design of state machines for quantum algorithms remains a largely unexplored topic. The abstract models for quantum computation proposed by Feynman [1], Deutsch [2] etc have been related to the theory of Quantum Turing Machines (QTM) and the work was later expanded by Bernstein and Vazirani [3] to lay the foundations of quantum complexity theory. However, no papers deal with the following problem: “how to realize the quantum state machine in hardware as an operational quantum circuit that the internal states of which can be measured and used as inputs in a system of such machines”. This is an equivalent to the fundamental problem of “structural synthesis of FSM”. This paper creates models of quantum state machines that are useful from an engineering perspective. The objective of the paper is to propose models that can be used for circuit-level implementation. We restrict our study to binary logic realized in quantum, the so-called binary permutative quantum circuits; the “permutative machines”. The presented synthesis procedure is analogous to classical logic circuits synthesis and is a necessary step in the entire design procedure of quantum automata. Thus state minimization, state assignment and excitation function realization aspects are also of interest and some preliminary experimental results are presented.

IEEE Congress on Evolutionary Computation (CEC)•Jul 1, 2010•6 citations

Analysis of Reversible and Quantum Finite State Machines Using Homing, Synchronizing and Distinguishing Input Sequences

M. Lukac, Michitaka Kameyama, Marek A. Perkowski +1 more

We present an analysis of the Reversible and Quantum Finite State Machines (QFSM) realized as Quantum Circuits using the three well known sequences applied in the analysis of the classical Finite State Machines (FSM). The synchronizing, the homing and the distinguishing sequences are applied to both strictly Reversible FSM (RFSM) and QFSM in order to determine the power of these new techniques in the above mentioned new models of sequential devices. In particular, care is taken to demonstrate these classical techniques on the RFSM and the one-way QFSMs. We show certain properties of the RFSM/QFSM with respect to these sequences and we show what are the restrictions and advantages.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2013•2 citations

Quantum Circuit Components for Cognitive Decision-Making

Dominic Widdows, Jyoti Rani, Emmanuel M. Pothos

This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.

arXiv:2302.03012•Entropy•Mar 23, 2023•28 citations

Equivalence Checking of Sequential Quantum Circuits

Qisheng Wang, Riling Li, Mingsheng Ying

We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalization of Mealy machines. A major difficulty in checking quantum circuits (but not present in checking classical circuits) is that the state spaces of quantum circuits are continuums. This difficulty is resolved by our main theorem showing that equivalence checking of two quantum Mealy machines can be done with input sequences that are taken from some chosen basis (which are finite) and have a length quadratic in the dimensions of the state Hilbert spaces of the machines. Based on this theoretical result, we develop an (and to the best of our knowledge, the first) algorithm for checking equivalence of sequential quantum circuits with running time$\mathcal {O}(2^{3m+5l}(2^{3m}{\,+\,}2^{3l}))$, where$m$and$l$denote the numbers of input and internal qubits, respectively. The complexity of our algorithm is comparable with that of the known algorithms for checking classical sequential circuits in the sense that both are exponential in the number of (qu)bits. Several case studies and experiments are presented.

arXiv:1811.07722•IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems•Oct 5, 2021•22 citations

Quantum Sequential Circuits

D. -S. Wang

This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based architectures, QSCs employ symmetry-protected topological junctions where quantum gates are encoded as Choi states via channel-state duality and activated through bulk measurements, utilizing ebits to realize the functional analog of feedback loops in classical sequential circuits. This framework establishes a universal model for quantum computation that inherently incorporates memory and temporal sequencing, complementing existing combinational quantum circuit model. Our work advances the conceptual bridge towards a quantum von Neumann architecture, underscoring the potential of hybrid and modular design principles for the development of large-scale, integrated quantum information processors.

quant-pharXiv:2602.05166•Feb 6, 2026•0 citations
We present a model of Quantum Finite State Machines (QFSM) based on the quantum circuit representation. In this model, properties of quantum bits are exploited in order to implement Quantum Finite State Machines without an explicit external memory. We show that because of the the natural ability of quantum systems to retain the quantum state, quantum circuits can be directly used to implement some classes of the quantum finite state machines. In particular, the circuit model allows to remove the logic-memory distinction as it is used in the classically established model of finite state machines. Rather, the quantum register implementing the QFSM as a circuit is alternatively used as memory and as logic. In order to allow such behavior the quantum circuit (processor) is controlled by a classical circuit that provides the necessary timing of the quantum operations as well as the interface between the quantum and the classical world. Moreover, additional mechanism for preserving unknown quantum qubit state is used and a novel computational protocol allowing the implementation of the QFSM is proposed. This framework is is called the Classically Controlled Quantum Computer (CCQC). The CCQC thus combines a quantum processor with a classical controller in such manner that computation is carried from the classical inputs, through quantum processing to classical outputs. We discuss a high level synthesis approach to quantum sequence detection based on the synthesis of quantum sequential circuits. Such machines can find many applications for instance in robotics; for example a robot is required to recognize certain sequences of input sensor values.
In this paper we present the synthesis process of quantum finite state machines for sequence detection based on the synthesis of quantum sequential circuits. Such machines have many applications for instance in robotics. We show the relation between the quantum circuit and the natural ability of quantum systems to retain the quantum state. We consider cases where a single qubit in a circuit represents a quantum state and another is used as the input qubit. We analyze some of the well known circuits as sequence detectors and describe their behaviors. We show that the standard quantum logic synthesis can be used for both the synthesis of quantum circuits as well as for quantum finite state machines used as sequence detectors.
The design of state machines for quantum algorithms remains a largely unexplored topic. The abstract models for quantum computation proposed by Feynman [1], Deutsch [2] etc have been related to the theory of Quantum Turing Machines (QTM) and the work was later expanded by Bernstein and Vazirani [3] to lay the foundations of quantum complexity theory. However, no papers deal with the following problem: “how to realize the quantum state machine in hardware as an operational quantum circuit that the internal states of which can be measured and used as inputs in a system of such machines”. This is an equivalent to the fundamental problem of “structural synthesis of FSM”. This paper creates models of quantum state machines that are useful from an engineering perspective. The objective of the paper is to propose models that can be used for circuit-level implementation. We restrict our study to binary logic realized in quantum, the so-called binary permutative quantum circuits; the “permutative machines”. The presented synthesis procedure is analogous to classical logic circuits synthesis and is a necessary step in the entire design procedure of quantum automata. Thus state minimization, state assignment and excitation function realization aspects are also of interest and some preliminary experimental results are presented.
We present an analysis of the Reversible and Quantum Finite State Machines (QFSM) realized as Quantum Circuits using the three well known sequences applied in the analysis of the classical Finite State Machines (FSM). The synchronizing, the homing and the distinguishing sequences are applied to both strictly Reversible FSM (RFSM) and QFSM in order to determine the power of these new techniques in the above mentioned new models of sequential devices. In particular, care is taken to demonstrate these classical techniques on the RFSM and the one-way QFSMs. We show certain properties of the RFSM/QFSM with respect to these sequences and we show what are the restrictions and advantages.
This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.
We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalization of Mealy machines. A major difficulty in checking quantum circuits (but not present in checking classical circuits) is that the state spaces of quantum circuits are continuums. This difficulty is resolved by our main theorem showing that equivalence checking of two quantum Mealy machines can be done with input sequences that are taken from some chosen basis (which are finite) and have a length quadratic in the dimensions of the state Hilbert spaces of the machines. Based on this theoretical result, we develop an (and to the best of our knowledge, the first) algorithm for checking equivalence of sequential quantum circuits with running timeO(23m+5l(23m + 23l))\mathcal {O}(2^{3m+5l}(2^{3m}{\,+\,}2^{3l}))O(23m+5l(23m+23l)), wheremmmandllldenote the numbers of input and internal qubits, respectively. The complexity of our algorithm is comparable with that of the known algorithms for checking classical sequential circuits in the sense that both are exponential in the number of (qu)bits. Several case studies and experiments are presented.
This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based architectures, QSCs employ symmetry-protected topological junctions where quantum gates are encoded as Choi states via channel-state duality and activated through bulk measurements, utilizing ebits to realize the functional analog of feedback loops in classical sequential circuits. This framework establishes a universal model for quantum computation that inherently incorporates memory and temporal sequencing, complementing existing combinational quantum circuit model. Our work advances the conceptual bridge towards a quantum von Neumann architecture, underscoring the potential of hybrid and modular design principles for the development of large-scale, integrated quantum information processors.