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Academician O.B. Lupanov International Scientific Seminar "Discrete Mathematics and Its Applications"

Optimisation of circuit for quantum automata

Aliya Khadieva

Published Jan 1, 2022• 0 citations
Publisher

Abstract

he paper considers the implementation of a finite quantum automaton, recognizing the unary language MOD_p using the qiskit library and the language python programming. We also present an optimization of the quantum schemes for implementing the distributed controlled algorithm rotation used in the implementation of the aforementioned quantum machine.

DOI
10.20948/dms-2022-23

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he paper considers the implementation of a finite quantum automaton, recognizing the unary language MOD_p using the qiskit library and the language python programming. We also present an optimization of the quantum schemes for implementing the distributed controlled algorithm rotation used in the implementation of the aforementioned quantum machine.
We implement a quantum hashing algorithm which is based on a fingerprinting technique presented by Ambainis and Frievalds, 1988, on gate-based quantum computers. This algorithm is based on a quantum finite automaton for a unary language MODp\mathtt{MOD_p}MODp​, where $ \mathtt{MOD_p} = \{ a^{i \cdot p} \mid i \geq 0 \} $, for any prime number ppp. We consider 16-qubit and 27-qubit IBMQ computers with the special graphs of qubits representing nearest neighbor architecture that is not Linear Nearest Neighbor (LNN) one. We optimize quantum circuits for the quantum hashing algorithm with respect to minimizing the number of control operators as the most expensive ones. We apply the same approach for an optimized circuit implementation of Quantum Fourier Transform (QFT) operation on the aforementioned machines because QFT and hashing circuits have common parts.
The study of quantum finite automata (QFA's) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as MODp={aj ∣ j≡0mod  p}\mathtt{MOD}_{\rm p} = \{a^{j}~ |~ j \equiv 0 \mod p\}MODp​={aj ∣ j≡0modp}, where ppp is a prime number. In this paper, we present a modified MCQFA algorithm for the language MODp\mathtt{MOD}_{\rm p}MODp​, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using less basis gates compared to the implementation of the original algorithm given in the literature.
The study of quantum finite automata (QFAs) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as MODp={aj∣j≡0mod  p}\mathtt{MOD}_p = \{ a^{j} \mid j \equiv 0 \mod p\}MODp​={aj∣j≡0modp}, where ppp is a prime number. In this paper, we present a modified MCQFA algorithm for the language MODp\mathtt{MOD}_pMODp​, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using fewer basis gates compared to the implementation of the original algorithm given in the literature.
For many practical applications, Quantum computers offer major speed-ups over traditional machines. The production of quantum chips has recently made tremendous strides, with the quantity of Qubits increasing and fidelity increasing. The smallest unit of information is the binary digit i.e. bit in general computing. In Quantum Computing the term Qubit (Quantum Bit) is used for the same purpose. In order to differentiate between a classical bit and a Qubit, Bra-Ket or Dirac notation is used. So, the Qubits are represented as |0〉 and |1〉 and are often read as Ket 0 for zero state and Ket 1 for one state. In this paper mainly programming and application sides of Quantum Computing are focused. For that, Qiskit module and its tools are used in Python programming language. General circuit optimization scheme is given. The Quantum circuits with the concept of Quantum Gates implemented are stronger compared to the optimizing algorithm and with faster execution time. In addition, for prime factorization, access to IBM's Quantum computer is carried out successfully.
In the contemporary era we dwell in, every now and then, new technologies are developed by master brains such as researchers and scientists. This also paves the way to discover replacements to classical computers. One such progression among the great inventions is the essence of quantum computing. They are brought to light for the purpose of solving problems and scenarios solved by classical computers but in a more effective way and in the least span of time. The study of quantum computing focuses on finding new ways to compute by using quantum physics phenomena. A qubit, in contrast to a typical computer bit, can be either 0 or 1, or it can be a superposition of both 0 and 1. Quantum theory commemorates with automata theory, thereby formulating quantum finite automata. Quantum finite automaton, or basically a deterministic finite automaton, is one of the simplest models of computation, which is an input-driven model, which takes an input, and according to the input, we just read the machine, and it changes its state. This proves that any quantum finite automata are completely capable of recognizing languages like Tally with given cut point too. Such languages recognized by a cut point, by quantum finite automata, are called stochastic languages. It further collaborates with the chemical industry with its qubit power over molecular collide, interactive models, and collaborative string processing using nonregular languages.
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.