The article continues research on the creation of digital quantum coprocessors. A quantum computer has a heterogeneous structure. The quantum (probabilistic) part of a quantum computer is considered as a coprocessor in relation to a classical computer (as its accelerator). The digital quantum coprocessor itself has a heterogeneous structure. It consists of a probabilistic part, which implements the actual quantum computations, and a digital part, which performs complex mathematical calculations necessary for the implementation of quantum algorithms. Organization of modular multiplication and exponentiation, which is used in Shor's algorithm, is discussed in this article. It is proposed to perform modular multiplication and exponentiation using well-known logic circuits, namely, sequential multi-bit multipliers. The structure of a serial modular multiplier and its components is considered. The technical characteristics of the components of the modular multiplier are presented. Further work is outlined in the direction of creating a modular multiplier for implementing Shor's algorithm in a digital quantum coprocessor.
The article continues research on the creation of digital quantum coprocessors. A quantum computer has a heterogeneous structure. The quantum (probabilistic) part of a quantum computer is considered as a coprocessor in relation to a classical computer (as its accelerator). The digital quantum coprocessor itself has a heterogeneous structure. It consists of a probabilistic part, which implements the actual quantum computations, and a digital part, which performs complex mathematical calculations necessary for the implementation of quantum algorithms. Organization of modular multiplication and exponentiation, which is used in Shor's algorithm, is discussed in this article. It is proposed to perform modular multiplication and exponentiation using well-known logic circuits, namely, sequential multi-bit multipliers. The structure of a serial modular multiplier and its components is considered. The technical characteristics of the components of the modular multiplier are presented. Further work is outlined in the direction of creating a modular multiplier for implementing Shor's algorithm in a digital quantum coprocessor.
It is shown that true quantum computers are analog and probabilistic computers and, in fact,they play the role of coprocessors in relation to classical computers. A digital quantum coprocessor consists of digital qubits. Each digital qubit is a finite state machine, the state changes of which is described in the same way as the state changes of an analog qubit. A digital qubit is a chain of digital quantum gates. Each digital quantum gate is digital unit, the state changes of which is described in the same way as the state changes of an analog quantum gate. The main difference between digital qubit and digital quantum gate from analog ones is the presence of memory (more precisely, the possibility of its introduction into their circuit) and its use for organizing calculations. A digital qubit without feedbacks - a digital quantum gate that can be controlled using a classic computer, is a single step of a pipeline with a measurement unit (comparator), a pipeline register and a pipeline trigger at the output. The quantum Fourier transform (QFT) is part of many quantum algorithms, in particular the Shor'sfactorization algorithm. The structures of digital quantum gates, digital qubits, and a digital quantumcoprocessor capable of performing the QFT are presented. The results of the QFT of a multi-qubit digital quantum coprocessor implemented on one FPGA are presented. For this, a IP core generator of multi-qubit quantum coprocessors was created, cores work was simulated. Models were implemented in FPGAs and their time and hardware characteristics were determined. The execution time of one quantum Fourier transform does not depend on the number of qubits in the digital quantum coprocessor and is commensurate with the time of change of the electron spin. The hardware complexity linearly depends on the number of qubits. With an increase in the number of qubits, the rate of true results of QFT decreases, at 64 qubits it is 1.5%, the decrease is nonlinear
Recently, interest is growing towards real quantum computers, which are analog and probabilistic devices by nature. Theinterest is also growing to their digital version, both software and hardware. One approach to the construction of real quantum computers is to use quantum chips. The hardware implementation of digital quantum computers involves the use offield programmable gate arrays.A digital quantum coprocessor has already been createdwhich has over a thousand digital qubitsand can perform such complex algorithms as a quantum Fourier transformation. The created and working digital quantum coprocessorcan already be used to work out various quantum algorithms, algorithms for the interaction of a classic computer and its quantum coprocessor, as well as for research various options for building digital qubits.The purpose of this work is to study the effect of the accuracy of the presentation of the state of digital qubit on the probability of obtaining the correct results of the digitalquantum coprocessor.For the study, a heterogeneous digital quantum coprocessor with thirty two digital qubits is selected, which will perform the Fourier quantum transformation. The article describes the basics of building digital quantum coprocessors.Schemes that illustrate the interaction of a classic computer and a quantum coprocessor, the architecture of the coprocessor and the possible structures of its digital qubitsare given. Two variants of the coprocessor, homogeneous one with one pseudo-random codes generator and one comparator, and heterogeneous one, with a generator and a comparator in each digital quantum cell, from which digital qubits consist, are shown.Two options for comparators are also shown -with a direct functional converter and with reverse one.In this work, the influence of the length of the qubit state codes of heterogeneous digital quantum coprocessors on the probability of the correct results formation is investigated.It was shown that the probability of obtaining the correct results at the output of the digital heterogeneous coprocessor is sharply (up to fifty percent) improved with a decrease of the qubit state code length, that is, with a decrease in the coprocessor hardware cost.With a length of a code equal to twobits, the quality of the operation of the heterogeneous coprocessor becomes commensurate with the quality of the homogeneous one. The need for additional research in this direction, including with homogeneous coprocessors, is shown.
Quantum computers consist of two parts - a classical computer and its quantum coprocessor or accelerator. The functioning of the main elements of a quantum coprocessor is described by a wave function. You can create digital elements in FPGAs, the operation of which will be described by the wave function, so called digital qubits. Due to the high computational complexity of quantum computing such as Shor’s algorithm of factorization VHDL-descriptions of digital quantum units must be created for their implementation in FPGA. The article estimates the computational complexity of operations that must be performed according to the Shor’s algorithm. Also the article describes a multilevel generator of VHDL-descriptions for quantum Fourier transform implementation. The generator creates descriptions of both homogeneous and heterogeneous coprocessors. In addition, the generator creates test circuits to check the generated coprocessors. This makes it possible to study the created coprocessors, compare results of their functioning with ones of real quantum coprocessors and analyze them.
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared with their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, researchers remain keen to develop novel designs and improve existing ones. In this review article, we aim to provide a systematically organized and easily comprehensible overview of the current state of the art in quantum arithmetic circuits. Specifically, this study covers fundamental operations such as addition, subtraction, multiplication, division and modular exponentiation. We delve into the detailed quantum implementations of these prominent designs and evaluate their efficiency considering various objectives. We also discuss potential applications of the presented arithmetic circuits and suggest future research directions.This article is part of the theme issue 'Emerging technologies for future secure computing platforms'.
Quantum computers are analog and probabilistic computers and, in fact, they play the role of coprocessors in relation to classical computers. The components of quantum coprocessors are called qubits. Their behavior should be described by a wave function. In particular, qubits can be discrete objects - finite states machines. Such qubits will be called digital. Quantum coprocessors and quantum computers built on their basis will also be called digital. External influences on digital qubits are fed through digital quantum gates. So a digital qubit is a unique chain of digital quantum gates. Digital quantum coprocessor can be implemented in FPGA as several chains of digital quantum.The article explores FPGA-based digital quantum coprocessor. It consists of 32 qubits. The structures of digital quantum gates, digital qubits, and a digital quantum coprocessor capable of performing the quantum Fourier transform are presented. Digital qubits were implemented for the case of real amplitudes of the wave functions.The results of the quantum Fourier transform of a 32-qubit digital quantum coprocessor implemented on one FPGA are presented.The execution time of one quantum Fourier transform does not depend on the number of qubits in the digital quantum coprocessor and is commensurate with the time of electron spin change (near 10 ns). But the time complexity of the quantum Fourier transform is probabilistic polynomial in time. The measured ratio of correct results for a 32-qubit coprocessor is approximately 1700 ppm.
Quantum computers are analog and probabilistic computers and, in fact, they play the role of coprocessors in relation to classical computers. The components of quantum coprocessors are called qubits. In particular, qubits can be discrete objects - finite states machines or series of quantum gates. Such qubits will be called digital. Digital quantum coprocessor can be implemented in FPGA as set of digital quantum qubits. The PRNG is an important part of digital qubit. A homogeneous digital quantum coprocessor uses one PRNG for all digital qubits. In a heterogeneous digital quantum coprocessor, each qubit has its own pseudo random number generator (PRNG). The article compares the performance of a homogeneous and heterogeneous digital quantum coprocessor. A 32-qubit digital quantum coprocessor was selected for study; it will perform the quantum Fourier transform during the study.