arXiv subjects

Farid Ablayev

Publications and source records attributed to Farid Ablayev.

17 recordsLinked to original sources

arXiv2026

Quantum algorithm for Ewald summation based computation of long-range electrostatics

In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate computation of the Coulomb electrostatic energy for a system of point charges. The algorithm employs the Ewald method based decomposition of electrostatic energy into several energy terms, of which the "Fourier component" (long-range electrostatics) computed on a quantum device, utilizing the power of Quantum Fourier Transform (QFT). We demonstrate that the algorithm complexity is $N \log M$ and that the quantum advantage for a system of point charges in the three-dimensional space is achieved when the number of grid points $M^3$ exceeds the number of charges $N$. The numerical error is small $<10^{-3}$. The algorithm can be implemented to run the all-atom Molecular Dynamics simulations on a quantum device requiring 15 qubits, thereby expanding the scope of applications of QFT-based methods to computational chemistry and biophysics.

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arXiv2024

Quantum search in a dictionary based on fingerprinting-hashing

In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that the algorithm is based on the quantum fingerprinting-hashing technique, which (a) provides a first level of amplitude amplification before applying the sequence of Grover amplitude amplification operators and (b) makes the algorithm more efficient in terms of memory use -- it requires $O(\log n + \log m)$ qubits. Note that previously developed algorithms by other researchers without hashing require $O(\log n + m)$ qubits.

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arXiv2023

Hybrid classical-quantum text search based on hashing

The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time, Grover's quantum search provides a quadratic speedup in the complexity of the query and gives the correct result with a high probability. We propose a hybrid classical-quantum algorithm (hybrid random-quantum algorithm to be more precise), that implements Grover's search to find a given substring in a text. As expected, the algorithm works a) with a high probability of obtaining the correct result and b) with a quadratic query acceleration compared to the classical one. What's new is that our algorithm uses the uniform hash family functions technique. As a result, our algorithm is much more memory efficient (in terms of the number of qubits used) compared to previously known quantum algorithms.

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arXiv2020

Quantum Algorithms for String Processing

In the paper, we investigate two problems on strings. The first one is the String matching problem, and the second one is the String comparing problem. We provide a quantum algorithm for the String matching problem that uses exponentially less quantum memory than existing ones. The algorithm uses the hashing technique for string matching, quantum parallelism, and ideas of Grover's search algorithm. Using the same ideas, we provide two algorithms for the String comparing problem. These algorithms also use exponentially less quantum memory than existing ones. Additionally, the second algorithm works exponentially faster than the existing one.

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arXiv2017

Lower Bounds and Hierarchies for Quantum Memoryless Communication Protocols and Quantum Ordered Binary Decision Diagrams with Repeated Test

We explore multi-round quantum memoryless communication protocols. These are restricted version of multi-round quantum communication protocols. The "memoryless" term means that players forget history from previous rounds, and their behavior is obtained only by input and message from the opposite player. The model is interesting because this allows us to get lower bounds for models like automata, Ordered Binary Decision Diagrams and streaming algorithms. At the same time, we can prove stronger results with this restriction. We present a lower bound for quantum memoryless protocols. Additionally, we show a lower bound for Disjointness function for this model. % As an application of communication complexity results, we consider Quantum Ordered Read-$k$-times Branching Programs ($k$-QOBDD). Our communication complexity result allows us to get lower bound for $k$-QOBDD and to prove hierarchies for sublinear width bounded error $k$-QOBDDs, where $k=o(\sqrt{n})$. Furthermore, we prove a hierarchy for polynomial size bounded error $k$-QOBDDs for constant $k$. This result differs from the situation with an unbounded error where it is known that an increase of $k$ does not give any advantage.

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arXiv2016

Model of a Programmable Quantum Processing Device

We propose a model of a programmable quantum processing device realizable with existing nanophotonic technologies and which can be viewed as a basis for new high performance hardware architectures. We present protocols and their physical implementation on the controlled photon transfer for executing basic single-qubit and multi-qubit gates. The possible operation of this quantum computer scheme is analyzed. The physical architecture is then formalized by a mathematical model of the Quantum Processing Unit (QPU), which is used as a basis for the Quantum Programming Framework that makes it possible to perform universal quantum computations in a multitasking environment.

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arXiv2015

On the Concept of Cryptographic Quantum Hashing

In the paper we define a notion of quantum resistant ($(ε,δ)$-resistant) hash function which combine together a notion of pre-image (one-way) resistance ($ε$-resistance) property we define in the paper and the notion of collision resistance ($δ$-resistance) properties. We show that in the quantum setting a one-way resistance property and collision resistance property are correlated: the "more" a quantum function is one-way resistant the "less" it collision resistant and vice versa. We present an explicit quantum hash function which is "balanced" one-way resistant and collision resistant and demonstrate how to build a large family quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a "phase constructions" technique to express quantum hashing constructions, which is good to map hash states to coherent states in a superposition of time-bin modes. The later is ready to be implemented with current optical technology.

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arXiv2015

Quantum Hashing via Classical $ε$-universal Hashing Constructions

In the paper, we define the concept of the quantum hash generator and offer design, which allows to build a large amount of different quantum hash functions. The construction is based on composition of classical $ε$-universal hash family and a given family of functions -- quantum hash generator. The proposed construction combines the properties of robust presentation of information by classical error-correcting codes together with the possibility of highly compressed presentation of information by quantum systems. In particularly, we present quantum hash function based on Reed-Solomon code, and we proved, that this construction is optimal in the sense of number of qubits needed.

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arXiv2014

Very narrow quantum OBDDs and width hierarchies for classical OBDDs

We present several results on comparative complexity for different variants of OBDD models. - We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2 but any classical OBDD (deterministic or stable bounded error probabilistic) needs width 2k+1. - We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient than classical one. In particular, an explicit function is presented which is computed by a quantum nondeterministic OBDD with constant width but any classical nondeterministic OBDD for this function needs non-constant width. - We also present new hierarchies on widths of deterministic and non-deterministic OBDDs. We focus both on small and large widths.

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arXiv2013

Quantum Hashing

We present a version of quantum hash function based on non-binary discrete functions. The proposed quantum procedure is "classical-quantum", that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance), in addition it has the properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. This function can be naturally used in a quantum digital signature protocol.

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arXiv2011

Quantum Computing on Multi-atomic Ensembles in Quantum Electrodynamics Cavity

We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and swapping-based operations that together provide implementation of any encoded single-qubit operation by three elementary gates and the encoded controlled-NOT operation is performed in a single step. This approach simplifies a physical realization of universal quantum computing and adds the immunity to a number of errors. We also demonstrate that the proposed architecture of quantum computer satisfies DiVincenzo criteria.

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arXiv2011

Encoded Universality of Quantum Computations on the Multi-Atomic Ensembles in the QED Cavity

We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity. We use the two-qubit encoding and swapping-based operations to simplify a physical realization of universal quantum computing and add the immunity to a number of errors. This approach allows to implement any encoded single-qubit operation by three elementary gates and the encoded controlled- NOT operation can be performed in a single step. The considerable advantages are also shown for implementing some commonly used controlled gates.

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arXiv2011

On Computational Power of Quantum Read-Once Branching Programs

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.

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arXiv2011

Proceedings CSR 2010 Workshop on High Productivity Computations

This volume contains the proceedings of the Workshop on High Productivity Computations (HPC 2010) which took place on June 21-22 in Kazan, Russia. This workshop was held as a satellite workshop of the 5th International Computer Science Symposium in Russia (CSR 2010). HPC 2010 was intended to organize the discussions about high productivity computing means and models, including but not limited to high performance and quantum information processing.

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arXiv2009

Algorithms for Quantum Branching Programs Based on Fingerprinting

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.

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arXiv2004

Quantum and Stochastic Branching Programs of Bounded Width

In this paper we show that one qubit polynomial time computations are at least as powerful as $\NC^1$ circuits. More precisely, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show any $\NC^1$ language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless $\NC^1=\ACC$. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in $\NC^1$. The change in the revised version is the addition of the syntactic condition.

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arXiv2003

On Computational Power of Quantum Branching Programs

In this paper we study a model of a Quantum Branching Program (QBP) and investigate its computational power. We prove a general lower bound on the width of read-once QBPs, which we show to be almost tight on certain symmetric function.

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