Multidimensional Quantum Fourier Transformation

• URL: http://arxiv.org/abs/2301.13835v1
• Date: Tue, 31 Jan 2023 18:25:40 GMT
• Title: Multidimensional Quantum Fourier Transformation
• Authors: Philipp Pfeffer
• Abstract summary: In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. An example on current hardware is depicted by a 6 qubit 2D-QFT with an IBM quantum computer.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The complexity of the algorithm is $\mathcal{O}( \log^2(M)/d )$ for an array with $M=(2^n)^d$ elements $(n \in \mathbb{N})$ equally separated along $d$ dimensions. Relevant properties for application are discussed. An example on current hardware is depicted by a 6 qubit 2D-QFT with an IBM quantum computer.

Related papers

• A Novel Finite Fractional Fourier Transform and its Quantum Circuit Implementation on Qudits [0.0]
  We present a new number theoretic definition of discrete fractional Fourier transform (DFrFT) The DFrFT is defined as the $N times N$ dimensional unitary representation of the generator of the arithmetic rotational group $SO_2[mathbbZ_pn]$.
  arXiv  Detail & Related papers  (2024-09-09T16:15:53Z)
• Quantum hashing algorithm implementation [0.0]
  We implement a quantum hashing algorithm which is based on a fingerprinting technique presented by Ambainis and Frievalds, 1988, on gate-based quantum computers. 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.
  arXiv  Detail & Related papers  (2024-07-14T09:41:16Z)
• Efficient implementation of discrete-time quantum walks on quantum computers [0.0]
  We propose an efficient and scalable quantum circuit implementing the discrete-time quantum walk (DTQW) model. For $t$ time-steps of the DTQW, the proposed circuit requires only $O(n2 + nt)$ two-qubit gates compared to the $O(n2 t)$ of the current most efficient implementation.
  arXiv  Detail & Related papers  (2024-02-02T19:11:41Z)
• Polynomial-depth quantum algorithm for computing matrix determinant [46.13392585104221]
  We propose an algorithm for calculating the determinant of a square matrix, and construct a quantum circuit realizing it. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems.
  arXiv  Detail & Related papers  (2024-01-29T23:23:27Z)
• A two-circuit approach to reducing quantum resources for the quantum lattice Boltzmann method [41.66129197681683]
  Current quantum algorithms for solving CFD problems use a single quantum circuit and, in some cases, lattice-based methods. We introduce the a novel multiple circuits algorithm that makes use of a quantum lattice Boltzmann method (QLBM) The problem is cast as a stream function--vorticity formulation of the 2D Navier-Stokes equations and verified and tested on a 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• On sampling determinantal and Pfaffian point processes on a quantum computer [49.1574468325115]
  DPPs were introduced by Macchi as a model in quantum optics the 1970s. Most applications require sampling from a DPP, and given their quantum origin, it is natural to wonder whether sampling a DPP on a classical computer is easier than on a classical one. Vanilla sampling consists in two steps, of respective costs $mathcalO(N3)$ and $mathcalO(Nr2)$ operations on a classical computer, where $r$ is the rank of the kernel matrix.
  arXiv  Detail & Related papers  (2023-05-25T08:43:11Z)
• Quantum Fourier Addition, Simplified to Toffoli Addition [92.18777020401484]
  We present the first systematic translation of the QFT-addition circuit into a Toffoli-based adder. Instead of using approximate decompositions of the gates from the QFT circuit, it is more efficient to merge gates.
  arXiv  Detail & Related papers  (2022-09-30T02:36:42Z)
• Improving Quantum Simulation Efficiency of Final State Radiation with Dynamic Quantum Circuits [1.3375143521862154]
  We make use of a new quantum hardware capability called dynamical quantum computing to improve the scaling of the QPS algorithm. We modify the quantum parton shower circuit to incorporate mid-circuit qubit measurements, resets, and quantum operations conditioned on classical information.
  arXiv  Detail & Related papers  (2022-03-18T15:31:19Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.