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

Discrete Mathematics and Applications

On quantum realisation of Boolean functions by the fingerprinting technique

Farid Mansurovich Ablayev, A. V. Vasilyev

Published Jan 1, 2009• 17 citations
Publisher

Abstract

In this paper, we develop the fingerprinting technique of calculation of Boolean functions in quantum calculation models. The use of the fingerprinting technique is demonstrated on the example of calculation of the function MOD m in the class of quantum OBDD (oblivious read-once branching programs). Next, the potentialities of the fingerprinting technique are demonstrated in the example of realisation of the ‘equality’ function in the quantum model of communication with a referee (the SMP communication model) and in examples of recognition of languages in quantum automata. All given realisations of Boolean functions in various quantum calculation models (OBDD, SMP communication model, and a finite automaton) are asymptotically optimal. The authors thank Juhani Karhumäki for the invitation to the University of Turku and fruitful discussions of this research.

DOI
10.1515/dma.2009.037

Related papers

Algorithms for Quantum Branching Programs Based on Fingerprinting

Farid Mansurovich Ablayev, Alexander Vasiliev

In the paper we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on fingerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as Equality, Palindrome, and Permutation Matrix Test. We also propose a generalization of our method and apply it to the Boolean variant of the Hidden Subgroup Problem.

arXiv:0911.2317•Electronic Proceedings in Theoretical Computer Science•Nov 15, 2009•29 citations

On the Computation of Boolean Functions by Quantum Branching Programs via Fingerprinting

Farid Mansurovich Ablayev, Alexander Vasiliev

We develop quantum fingerprinting technique for constructing quantum branching pro-grams (QBPs), which are considered as circuits with an ability to use classical bits as control variables. We demonstrate our approach constructing optimal quantum ordered binary decision diagram (QOBDD) for MODm Boolean function. The construction of our technique also allows to extend the recent result of Ambainis and Nahimovs it is based on. In addition we show how our technique works for encoding quantum information for the equality problem in the simultaneous message passing model. 1

Electronic colloquium on computational complexity•Jan 1, 2008•9 citations

On Complexity of Quantum Branching Programs Computing Equality-like Boolean Functions

Farid Mansurovich Ablayev, Airat Khasianov, Alexander Vasiliev

We consider the Hidden Subgroup, and Equality-related problems in the context of quantum Ordered Binary Decision Diagrams. For the decision versions of considered problems we show polynomial upper bounds in terms of quantum OBDD width. We apply a new modification of the fingerprinting technique and present the algorithms in circuit notation. Our algorithms require at most logarithmic number of qubits. 1

Electronic colloquium on computational complexity•Jan 1, 2008•11 citations

On Computational Power of Quantum Read-Once Branching Programs

Farid Mansurovich Ablayev, Alexander Vasiliev

In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting technique, we show that any Boolean function with linear polynomial presentation can be computed by a quantum read-once branching program using a relatively small (usually logarithmic in the size of input) number of qubits. Then we show that the described class of Boolean functions is closed under the polynomial projections.

arXiv:1103.2809•Electronic Proceedings in Theoretical Computer Science•Mar 8, 2011•5 citations

Shallow implementation of quantum fingerprinting with application to quantum finite automata

Mansur Ziatdinov, Aliya Khadieva, Kamil Ravilevich Khadiev

Quantum fingerprinting is a technique that maps a classical input word to a quantum state. The obtained quantum state is much shorter than the original word, and its processing uses fewer resources, making it useful in quantum algorithms, communication, and cryptography. One of the examples of quantum fingerprinting is the quantum automata algorithm for M O D p = { a i · p ∣ i ≥ 0 } languages, where p is a prime number. However, implementing such an automaton on current quantum hardware is not efficient. Quantum fingerprinting maps a word x ∈{0, 1} n of length n to a state |ψ( x )〉 of O (log n ) qubits, and uses O ( n ) unitary operations. Computing quantum fingerprint using all available qubits of the current quantum computers is infeasible due to many quantum operations. To make quantum fingerprinting practical, we should optimize the circuit for depth instead of width, in contrast to the previous works. We propose explicit methods of quantum fingerprinting based on tools from additive combinatorics, such as generalized arithmetic progressions (GAPs), and prove that these methods provide circuit depth comparable to a probabilistic method. We also compare our method to prior work on explicit quantum fingerprinting methods. We provide a series of numerical experiments with implementation of the quantum automata for MOD 17 language on noisy simulators of IBMQ quantum devices. We show that shallow implementation based on GAPs produces results with much smaller computational error compared to standard deep circuit implementation. Despite the fact that on the ideal quantum computational device, the opposite situation arises. We show that the shallow circuit for the quantum automaton is better for near-future quantum computational devices.

arXiv:2412.18823•Frontiers in Computer Science•May 16, 2025•9 citations

GAPs for Shallow Implementation of Quantum Finite Automata

Mansur Ziatdinov, Aliya Khadieva, Abuzer Yakaryılmaz

Quantum fingerprinting is a technique that maps classical input word to a quantum state.The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms, communication, and cryptography.One of the examples of quantum fingerprinting is quantum automata algorithms for MOD p = {a i•p | i ≥ 0} languages, where p is a prime number.However, implementing such an automaton on the current quantum hardware is not efficient.Quantum fingerprinting maps a word x ∈ {0, 1} n of length n to a state |ψ(x) of O(log n) qubits, and uses O(n) unitary operations.Computing quantum fingerprint using all available qubits of the current quantum computers is infeasible due to a large number of quantum operations.To make quantum fingerprinting practical, we should optimize the circuit for depth instead of width in contrast to the previous works.We propose explicit methods of quantum fingerprinting based on tools from additive combinatorics, such as generalized arithmetic progressions (GAPs), and prove that these methods provide circuit depth comparable to a probabilistic method.We also compare our method to prior work on explicit quantum fingerprinting methods.

arXiv:2304.12868•Electronic Proceedings in Theoretical Computer Science•Sep 3, 2023•10 citations
In this paper, we develop the fingerprinting technique of calculation of Boolean functions in quantum calculation models. The use of the fingerprinting technique is demonstrated on the example of calculation of the function MOD m in the class of quantum OBDD (oblivious read-once branching programs). Next, the potentialities of the fingerprinting technique are demonstrated in the example of realisation of the ‘equality’ function in the quantum model of communication with a referee (the SMP communication model) and in examples of recognition of languages in quantum automata. All given realisations of Boolean functions in various quantum calculation models (OBDD, SMP communication model, and a finite automaton) are asymptotically optimal. The authors thank Juhani Karhumäki for the invitation to the University of Turku and fruitful discussions of this research.
In the paper we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on fingerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as Equality, Palindrome, and Permutation Matrix Test. We also propose a generalization of our method and apply it to the Boolean variant of the Hidden Subgroup Problem.
We develop quantum fingerprinting technique for constructing quantum branching pro-grams (QBPs), which are considered as circuits with an ability to use classical bits as control variables. We demonstrate our approach constructing optimal quantum ordered binary decision diagram (QOBDD) for MODm Boolean function. The construction of our technique also allows to extend the recent result of Ambainis and Nahimovs it is based on. In addition we show how our technique works for encoding quantum information for the equality problem in the simultaneous message passing model. 1
In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting technique, we show that any Boolean function with linear polynomial presentation can be computed by a quantum read-once branching program using a relatively small (usually logarithmic in the size of input) number of qubits. Then we show that the described class of Boolean functions is closed under the polynomial projections.
Quantum fingerprinting is a technique that maps a classical input word to a quantum state. The obtained quantum state is much shorter than the original word, and its processing uses fewer resources, making it useful in quantum algorithms, communication, and cryptography. One of the examples of quantum fingerprinting is the quantum automata algorithm for M O D p = { a i · p ∣ i ≥ 0 } languages, where p is a prime number. However, implementing such an automaton on current quantum hardware is not efficient. Quantum fingerprinting maps a word x ∈{0, 1} n of length n to a state |ψ( x )〉 of O (log n ) qubits, and uses O ( n ) unitary operations. Computing quantum fingerprint using all available qubits of the current quantum computers is infeasible due to many quantum operations. To make quantum fingerprinting practical, we should optimize the circuit for depth instead of width, in contrast to the previous works. We propose explicit methods of quantum fingerprinting based on tools from additive combinatorics, such as generalized arithmetic progressions (GAPs), and prove that these methods provide circuit depth comparable to a probabilistic method. We also compare our method to prior work on explicit quantum fingerprinting methods. We provide a series of numerical experiments with implementation of the quantum automata for MOD 17 language on noisy simulators of IBMQ quantum devices. We show that shallow implementation based on GAPs produces results with much smaller computational error compared to standard deep circuit implementation. Despite the fact that on the ideal quantum computational device, the opposite situation arises. We show that the shallow circuit for the quantum automaton is better for near-future quantum computational devices.
Quantum fingerprinting is a technique that maps classical input word to a quantum state.The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms, communication, and cryptography.One of the examples of quantum fingerprinting is quantum automata algorithms for MOD p = {a i•p | i ≥ 0} languages, where p is a prime number.However, implementing such an automaton on the current quantum hardware is not efficient.Quantum fingerprinting maps a word x ∈ {0, 1} n of length n to a state |ψ(x) of O(log n) qubits, and uses O(n) unitary operations.Computing quantum fingerprint using all available qubits of the current quantum computers is infeasible due to a large number of quantum operations.To make quantum fingerprinting practical, we should optimize the circuit for depth instead of width in contrast to the previous works.We propose explicit methods of quantum fingerprinting based on tools from additive combinatorics, such as generalized arithmetic progressions (GAPs), and prove that these methods provide circuit depth comparable to a probabilistic method.We also compare our method to prior work on explicit quantum fingerprinting methods.