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Quantum Fourier Transform Circuit Simulator

Víctor H. Téllez, Antonio Campero, Cristina Iuga, Gonzalo Duchen, Chemical Departament

Published Jun 1, 2008• 1 citation
OpenAlex

Abstract

Quantum Fourier transform is of primary importance in many quantum algorithms. This paper presents the development of a Quantum Fourier Transform Circuit Simulator system that processes classical analog signals and presents the results of the processing data. The data is acquired by an analog to digital classical converter, on a classical computer. The data stored is processed by computer using an algorithm that executes a Quantum Fast Fourier Transform (QFT).

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Quantum Fourier transform is of primary importance in many quantum algorithms. This paper presents the development of a Quantum Fourier Transform Circuit Simulator system that processes classical analog signals and presents the results of the processing data. The data is acquired by an analog to digital classical converter, on a classical computer. The data stored is processed by computer using an algorithm that executes a Quantum Fast Fourier Transform (QFT).
This survey presents a comprehensive analysis of the quantum Fourier transform (QFT), a fundamental tool in quantum computing, in comparison to its classical counterpart, the fast Fourier transform (FFT). The study begins with an introduction to the classical Fourier transform, which is widely used in different disciplines such as signal and image processing. The article introduces the QFT as a quantum version of the Fourier transform, detailing how it leverages quantum parallelism and superposition to reduce the time complexity of the operation, and highlighting its crucial role in quantum algorithms like Shor’s algorithm for integer factorization. The analysis also addresses the mathematical foundations of the QFT, its implementation in quantum circuits, and the key advantages and challenges associated with its use, such as measurement precision and quantum decoherence. Finally, it concludes with an exploration of the current and potential applications of QFT in quantum computing.
Abstract We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector spaces. Namely, our FFT is defined as a transformation of the tensor product of quantum states. It is essentially different from the so-called quantum Fourier transform (QFT) defined to be a linear transformation of the amplitudes for the superposition of quantum states. The quantum circuit for the FFT consists of several circuits for elementary arithmetic operations such as a quantum adder, subtractor and shift operations, which are implemented as effectively as possible. Namely, our circuit does not generate any garbage bits. The advantages of our method compared to the QFT are its high versatility, and data storage efficiency in terms, for instance, of the quantum image processing.
Quantum Computing is a computational paradigm that takes into account the laws of Quantum Physics in the steps of the computation which advantages were verified both in Computation and Communications. No scalable quantum computer was developed so far and to execute, to test, and to create new quantum algorithms the simulation of quantum computers on classical computers plays an important role. In this work, we show the design, tools and results obtained for the simulation of the Quantum Fourier Transform algorithm. As a result, we developed an open-source tool, called FTSimulator, and we could simulate up to 12 qubits according to the procedures specified by an experimental test.
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the noisy intermediate-scale quantum era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.
We introduce QFT→\rightarrow→FFT, a family of HPC FFT libraries that compute the discrete Fourier transform by executing a quantum Fourier transform (QFT) circuit on classical quantum computer simulators. Input arrays are mapped directly to state amplitudes with explicit normalization/indexing, making QFT a drop-in replacement for FFT primitives. A backend-agnostic planner builds a fused-gate schedule and memory layout adapters to increase arithmetic intensity and reduce memory data movement. We implement this design on top of Google's C++ \texttt{qsim} and evaluate OpenMP, AVX, and CUDA backends. On an AMD EPYC Zen2 processor, our AVX performance is on par with that of multithreaded FFTW, utilizing 64 threads. On an NVIDIA A100, the CUDA backend achieves more than 4×4\times4× lower time than both AVX and FFTW on AMD EPYC Zen2 at larger sizes. We also employ an approximate QFT (AQFT) that truncates small-angle controlled rotations beyond a cutoff kkk, reducing circuit depth and runtime while preserving accuracy.
For discussing the solving methods of NP problems in classical computers and studying the circuit model which is the most representative in quantum computing to simulate the compute processes, this article discussed how to simulate the quantum Fourier transform by using the quantum logic gates, implemented the quantum Fourier transform and constructed the quantum information and compute simulation platform. The experiment introduced the quantum register structure to be the storage medium, which is better than the form of matrix in space. The operation processes adopted the bit manipulation to avoid the mass time for matrix multiplications. The results presented the changes of quantum amplitudes and probabilities of quantum states according to the quantum effect and compared with the approximate quantum Fourier transform. The experimental platform provided a groundwork for the further simulations of other important quantum algorithms and quantum circuits.