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The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…

Quantum Physics · Physics 2020-04-09 Yunseong Nam , Yuan Su , Dmitri Maslov

Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…

Quantum Physics · Physics 2023-03-09 Michael McGuigan

This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…

Quantum Physics · Physics 2025-06-23 Shuangbao Paul Wang , Jianzhou Mao , Eric Sakk

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…

Quantum Physics · Physics 2009-11-10 Runyao Duan , Zhengfeng Ji , Yuan Feng , Mingsheng Ying

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…

The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…

Quantum Physics · Physics 2020-01-27 Alastair A. Abbott

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision…

Quantum Physics · Physics 2013-06-12 Hamed Ahmadi , Chen-Fu Chiang

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…

Quantum Physics · Physics 2017-05-03 Lidia Ruiz-Perez , Juan Carlos Garcia-Escartin

We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $\Theta(n \log n)$ gates, and the…

Quantum Physics · Physics 2025-02-11 Ronit Shah

In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…

Quantum Physics · Physics 2022-05-03 Shlomo Kashani , Maryam Alqasemi , Jacob Hammond

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical…

The Cosmic Microwave Background (CMB) data analysis and the map-making process rely heavily on the use of spherical harmonics. For suitable pixelizations of the sphere, the (forward and inverse) Fourier transform plays a crucial role in…

The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…

Quantum Physics · Physics 2025-12-16 Gianfranco Cariolaro , Edi Ruffa , Amir Mohammad Yaghoobianzadeh , Jawad A. Salehi

Quantum phase estimation is an important routine in many quantum algorithms, particularly for estimating the ground state energy in quantum chemistry simulations. This estimation involves applying powers of a unitary to the ground state,…

Quantum Physics · Physics 2026-01-26 Kaur Kristjuhan , Dominic W. Berry

The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a…

Quantum Physics · Physics 2015-03-24 Shruti Dogra , Arvind , Kavita Dorai

The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…

Quantum Physics · Physics 2007-05-23 Lisa R. Hales

We construct a quantum algorithm that performs function-dependent phase transform and requires no initialization of an ancillary register. The algorithm recovers the initial state of an ancillary register regardless of whether its state is…

Quantum Physics · Physics 2007-05-23 Dong Pyo Chi , Jinsoo Kim , Soojoon Lee

Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…

The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…

Quantum Physics · Physics 2025-06-26 Francesco Di Colandrea , Nazanin Dehghan , Alessio D'Errico , Ebrahim Karimi

To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT…

Quantum Physics · Physics 2017-12-25 Fu Xiang-qun , Bao Wan-su , Huang He-liang , Li Tan , Shi Jian-hong , Wang Xiang , Zhang Shuo , Li Feng-guang