Quantum circuit for the fast Fourier transform
@article{Asaka2020QuantumCF, title={Quantum circuit for the fast Fourier transform}, author={Ryo Asaka and Kazumitsu Sakai and Ryoko Yahagi}, journal={Quantum Information Processing}, year={2020}, volume={19}, pages={1-20} }
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…
10 Citations
Gravitational wave matched filtering by quantum Monte Carlo integration and quantum amplitude amplification
- Physics, Computer Science
- 2022
An exponential reduction of the qubit number is achieved compared with Gao et al.
Two-level Quantum Walkers on Directed Graphs II: An Application to qRAM
- Computer Science
- 2022
A quantum random access memory (qRAM) is physically implemented using a multi-particle continuous-time quantum walk with two internal states to process 2 n m -qubit data and, by simply passing quantum walkers through binary trees, data can be automatically extracted in a quantum superposition state.
Scaling up and down of 3-D floating-point data in quantum computation
- Computer ScienceScientific reports
- 2022
A quantum scaling up and down scheme for floating-point data by using trilinear interpolation method in 3-D space is presented and the quantum scaling circuits of3-D floating- point data are designed.
Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
- Physics
- 2021
In the present paper, the first in a series of two, we propose a universal quantum computation via a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states. A dual-rail…
Truncated phase-based quantum arithmetic: error propagation and resource reduction
- Computer Science
- 2021
This work presents a modification of the Draper adder which eliminates smallangle rotations to highly coarse levels, matched with some strategic corrections, and shows that the inherited loss of fidelity is directly given by the rate of carry and borrow bits in the computation.
Scaling Up and Down of 3-D Floating-point Data in Quantum Computation
- Computer Science
- 2021
This paper proposes trilinear interpolation of floating-point numbers in 3-D space to achieve quantum algorithms of scaling up and down for3-D floating- point data, and the circuits of quantum scaling up-and-down for 3- D floating-points data are designed.
Quanta in sound, the sound of quanta: a voice-informed quantum theoretical perspective on sound
- PhysicsArXiv
- 2021
The Quantum Vocal Theory of Sounds can give a quantum-theoretic explanation to some auditory streaming phenomena, eventually leading to practical solutions of relevant sound-processing problems, or it can be creatively exploited to manipulate superpositions of sonic elements.
High-dimensional quantum Fourier transform of twisted light
- Computer SciencePhysical Review A
- 2021
This paper presents an alternative design that uses the orbital angular momentum as a carrier of information and needs only O ( √ d log d ) elements, rendering the path-encoded design inefficient.
Quantum random access memory via quantum walk
- PhysicsQuantum Science and Technology
- 2021
A novel concept of quantum random access memory employing a quantum walk is provided, which relies on a bucket brigade scheme to access the memory cells, and only O(n) steps are required to access and retrieve data in the form of quantum superposition states.
Intelligent control of mobile robot with redundant manipulator & stereovision: quantum / soft computing toolkit
- Computer Science
- 2020
The advantages of the approach based on quantum/soft computing are demonstrated in comparison with the structures of control systems based on soft computing for unforeseen control situations with sensor system.
References
SHOWING 1-10 OF 40 REFERENCES
QRDA: Quantum Representation of Digital Audio
- Physics
- 2016
Multimedia refers to content that uses a combination of different content forms. It includes two main medias: image and audio. However, by contrast with the rapid development of quantum image…
Reversible logic and quantum computers.
- PhysicsPhysical review. A, General physics
- 1985
The construction of a quantum-mechanical Hamiltonian describing a computer generates a dynamical evolution which mimics a sequence of elementary logical steps if each logical step is locally reversible (global reversibility is insufficient).
NEQR: a novel enhanced quantum representation of digital images
- PhysicsQuantum Inf. Process.
- 2013
Performance comparisons with FRQI reveal that NEQR can achieve a quadratic speedup in quantum image preparation, increase the compression ratio of quantum images by approximately 1.5X, and retrieve digital images from quantum images accurately.
SQR: a simple quantum representation of infrared images
- PhysicsQuantum Inf. Process.
- 2014
A basic way to express infrared images in quantum computer using SQR, and the performance comparison with the latest flexible representation of quantum images reveals that SQR can achieve a quadratic speedup in quantum image preparation.
Image storage, retrieval, compression and segmentation in a quantum system
- PhysicsQuantum Inf. Process.
- 2013
An algorithm by which an image of image of N pixels and different colors is stored in a quantum system just using 2N+m qubits to find all solutions in the expected times in O(t\sqrt{N} )$$ is proposed.
An algorithm for the machine calculation of complex Fourier series
- Computer Science
- 1965
Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Factoring wavelet transforms into lifting steps
- Mathematics
- 1998
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple…
Architectures for a quantum random access memory
- Computer Science
- 2008
Two different RAM architectures are analyzed and some proof-of-principle implementations are proposed which show that in principle only O(n) two-qubit physical interactions need take place during each qRAM call, which could give rise to the construction of large qRAMs that could operate without the need for extensive quantum error correction.
Quantum random access memory.
- Physics, Computer SciencePhysical review letters
- 2008
An architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional RAM designs, which yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing.