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The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…

Quantum Physics · Physics 2018-08-31 James R. Wootton , Daniel Loss

In this paper, we first define the quantum discrete logarithm problem (QDLP)which is similar to classical discrete logarithm problem. But, this problem cannot be solved by Shor's quantum algorithm. Based on quantum discrete logarithm…

Quantum Physics · Physics 2007-05-23 Chien-Yuan Chen , Chih-Cheng Hsueh

Quantum computing is a new technology that is expected to revolutionize the computation paradigm in the next few years. Qubits exploit the quantum physics proprieties to increase the parallelism and speed of computation. Unfortunately,…

Emerging Technologies · Computer Science 2022-04-12 Daniel Oliveira , Edoardo Giusto , Emanuele Dri , Nadir Casciola , Betis Baheri , Qiang Guan , Bartolomeo Montrucchio , Paolo Rech

Recently, quantum computing experiments have for the first time exceeded the capability of classical computers to perform certain computations -- a milestone termed "quantum computational advantage." However, verifying the output of the…

Quantum Physics · Physics 2023-09-13 Gregory D. Kahanamoku-Meyer

High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…

Quantum Physics · Physics 2021-05-05 Samuel Jaques , Thomas Häner

We present a novel one-way quantum key distribution protocol based on 3-dimensional quantum state, a qutrit, that encodes two qubits in its 2-dimensional subspaces. The qubits hold the classical bit information that has to be shared between…

Quantum Physics · Physics 2012-02-03 R. Kumar , R. Demkowicz-Dobrzanski , K. Banaszek

We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the…

Quantum Physics · Physics 2022-01-05 Henrik Dreyer , Mircea Bejan , Etienne Granet

Quantum no-Hiding theorem, first proposed by Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)], was verified experimentally by Samal et al. [Phys. Rev. Lett. 186, 080401 (2011)] using NMR quantum processor. Till then, this…

Elliptic curves over finite fields GF(2^n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this…

Quantum Physics · Physics 2013-12-05 Brittanney Amento , Rainer Steinwandt , Martin Roetteler

We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…

Quantum Physics · Physics 2016-09-08 Stephane Beauregard

This paper presents a simple, but efficient class of non-interactive protocols for quantum authentication of $m$-length clas sical messages. The message is encoded using a classical linear algebraic code $C[n,m,t]$. We assume that Alice and…

Quantum Physics · Physics 2007-05-23 Rex A. C. Medeiros , Francisco M. de Assis , Bernardo L. Júior , Aércio F. Lima

We present improved quantum circuits for elliptic curve scalar multiplication, the most costly component in Shor's algorithm to compute discrete logarithms in elliptic curve groups. We optimize low-level components such as reversible…

Quantum Physics · Physics 2020-01-28 Thomas Häner , Samuel Jaques , Michael Naehrig , Martin Roetteler , Mathias Soeken

We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes…

Quantum Physics · Physics 2021-07-27 Giacomo Nannicini , Lev S Bishop , Oktay Gunluk , Petar Jurcevic

Analysis and verification of quantum circuits are highly challenging, given the exponential dependence of the number of states on the number of qubits. For analytical derivation, we propose a new quantum polynomial representation (QPR) to…

Quantum Physics · Physics 2025-03-14 Yu-Ting Kao , Hao-Yu Lu , Yeong-Jar Chang , Darsen Lu

Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…

Whilst many key exchange and digital signature systems still rely on NIST P-256 (secp256r1) and secp256k1, offering around 128-bit security, there is an increasing demand for transparent and reproducible curves at the 256-bit security…

Cryptography and Security · Computer Science 2026-04-21 Víctor Duarte Melo , William J. Buchanan

Quantum secret sharing is a cryptographic scheme that enables a secure storage and reconstruction of quantum information. While the theory of secret sharing is mature in its development, relatively few studies have explored the performance…

Quantum Physics · Physics 2025-11-04 Jay Graves , Mike Nelson , Eric Chitambar

Circuit cutting allows quantum circuits larger than the available hardware to be executed. Cutting techniques split circuits into smaller subcircuits, run them on the hardware, and recombine results through classical post-processing.…

Quantum Physics · Physics 2024-11-28 Songqinghao Yang , Prakash Murali

Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…

Quantum Physics · Physics 2018-01-23 Sergio Boixo , Sergei V. Isakov , Vadim N. Smelyanskiy , Hartmut Neven

In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…

Quantum Physics · Physics 2023-03-14 Hyeonhak Kim , Seokhie Hong