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Related papers: Primitive Quantum Gates for an $SU(2)$ Discrete Su…

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We provide two sufficient conditions to guarantee that the round functions of a translation based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and…

Group Theory · Mathematics 2019-04-26 Riccardo Aragona , Marco Calderini , Antonio Tortora , Maria Tota

A qubit, or quantum bit, is conventionally defined as "a physical system for storing information that is capable of existing in either of two quantum states or in a superposition of both". In this paper, we examine the simple question of…

Quantum Physics · Physics 2026-03-19 Zhuoran Bao , Daniel F. V. James

We establish and analyse the performance and resource requirements of an end-to-end fault-tolerant quantum algorithm for computing the absorption spectrum and population dynamics of photoexcited pyrazine. The quantum circuit construction…

Quantum Physics · Physics 2026-03-17 Xiaoning Feng , Hans Hon Sang Chan , David P. Tew

We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a…

Computational Complexity · Computer Science 2016-10-03 Mateus de Oliveira Oliveira

In this paper, we offer and discuss three efficient structural solutions for the hardware-oriented implementation of discrete quaternion Fourier transform basic operations with reduced implementation complexities. The first solution: a…

Data Structures and Algorithms · Computer Science 2017-03-21 Aleksandr Cariow , Galina Cariowa , Marina Chicheva

We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…

Quantum Physics · Physics 2018-01-04 Rich Rines , Isaac Chuang

We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits…

Quantum Physics · Physics 2023-11-27 Andreas Klappenecker , Martin Roetteler

Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…

Quantum Physics · Physics 2025-04-30 Chengsi Mao , Changhao Yi , Huangjun Zhu

Atomic Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes from atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which define the distance between two unitary…

Quantum Physics · Physics 2021-12-28 Javad Sharifi

We detail a quantum circuit capable of efficiently encoding analytical approximations to gravitational wave signal waveforms of compact binary coalescences into the amplitudes of quantum bits using both quantum arithmetic operations and…

Quantum Physics · Physics 2023-06-21 Fergus Hayes , Sarah Croke , Chris Messenger , Fiona Speirits

It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built…

Geometric Topology · Mathematics 2019-02-20 Michel Planat , Raymond Aschheim , Marcelo M. Amaral , Klee Irwin

Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega^dagger H, and S. All of these gates have matrix entries in the ring Z[1/2,i], the smallest subring of the complex numbers containing 1/2 and i.…

Quantum Physics · Physics 2021-09-14 Xiaoning Bian , Peter Selinger

In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called C-path gate with which the realization of all possible bipartite POVMs of two-photon polarization states can be simpler and nearly…

Quantum Physics · Physics 2009-02-26 Qing Lin , Jian Li

The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…

Quantum Physics · Physics 2017-02-22 Kishore Thapliyal , Anirban Pathak

Quantum computing has been attracting tremendous efforts in recent years. One prominent application is to perform quantum simulations of electron correlations in large molecules and solid-state materials, where orbital degrees of freedom…

Quantum Physics · Physics 2021-12-10 Hongmian Shui , Shengjie Jin , Zhihan Li , Fansu Wei , Xuzong Chen , Xiaopeng Li , Xiaoji Zhou

For a positive integer $m$, a (positive definite integral) quadratic form is called primitively $m$-universal if it primitively represents all quadratic forms of rank $m$. It was proved in arXiv:2202.13573 that there are exactly $107$…

Number Theory · Mathematics 2023-09-06 Byeong-Kweon Oh , Jongheun Yoon

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

Representation Theory · Mathematics 2007-05-23 Ruedi Suter

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use a smaller, fixed number of qubits at the cost of systematic errors. We systematize this approach by deriving the single…

High Energy Physics - Lattice · Physics 2023-06-12 Yao Ji , Henry Lamm , Shuchen Zhu

Leakage errors damage a qubit by coupling it to other levels. Over the years, several theoretical approaches to dealing with such errors have been developed based on perturbation arguments. Here we propose a different strategy: we use a…

Quantum Physics · Physics 2017-12-18 Yifan Sun , Junyi Zhang , Lian-Ao Wu

This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…

Quantum Physics · Physics 2024-10-01 Zhong-Yi Ni , Yu-Sheng Zhao , Jin-Guo Liu