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We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…

Quantum Physics · Physics 2024-08-22 William M. Kirby , Frederick W. Strauch

We aim to advance the state-of-the-art in Quadratic Unconstrained Binary Optimization formulation with a focus on cryptography algorithms. As the minimal QUBO encoding of the linear constraints of optimization problems emerges as the…

Cryptography and Security · Computer Science 2026-04-16 Gregory Morse , Tamás Kozsik , Oskar Mencer , Peter Rakyta

We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead (QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary…

Quantum Physics · Physics 2013-04-03 Thomas G. Draper , Samuel A. Kutin , Eric M. Rains , Krysta M. Svore

Exchange-only (EO) qubits, implemented in triple-quantum-dot systems, offer a compelling platform for scalable semiconductor-based quantum computing by enabling universal control through purely exchange interactions. While high-fidelity…

Quantum Physics · Physics 2025-11-14 Jiahao Wu , Guanjie He , Wenyuan Zhuo , Quan Fu , Xin Wang

Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit…

Quantum Physics · Physics 2026-02-10 Apurav , Jaskaran Singh

We present normal forms for elliptic curves over a field of characteristic $2$ analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient…

Number Theory · Mathematics 2016-01-15 David Kohel

Resource constraints in smart devices demand an efficient cryptosystem that allows for low power and memory consumption. This has led to popularity of comparatively efficient Elliptic curve cryptog-raphy (ECC). Prior to this paper, much of…

Cryptography and Security · Computer Science 2015-02-09 Yasir Malik

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…

Quantum Physics · Physics 2009-10-30 Cesar Miquel , Juan Pablo Paz , Roberto Perazzo

Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package…

Quantum Physics · Physics 2022-07-18 A. V. Antipov , E. O. Kiktenko , A. K. Fedorov

As sensor nodes are deployed anywhere in a wireless sensor network, hence their communication can be easily monitored. In these networks, message protection and node identification are very issues. Hence, security of large scale such…

Cryptography and Security · Computer Science 2013-04-04 S. Ahmed , N. Javaid , S. H. Bouk , A. Javaid , M. A. Khan , Z. A. Khan

This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout…

Quantum Physics · Physics 2007-05-23 Austin G. Fowler

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

The semidirect discrete logarithm problem (SDLP) in finite groups was proposed as a foundation for post-quantum cryptographic protocols, based on the belief that its non-abelian structure would resist quantum attacks. However, recent…

Cryptography and Security · Computer Science 2025-11-04 Mohammad Ferry Husnil Arif , Muhammad Imran

We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…

The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a…

Mesoscale and Nanoscale Physics · Physics 2019-08-15 M. J. Gullans , J. R. Petta

In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…

Cryptography and Security · Computer Science 2025-10-23 Abel C. H. Chen

Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…

Quantum Physics · Physics 2022-07-28 Tao Chen , Zheng-Yuan Xue , Z. D. Wang

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…

The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms-including Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) multiplication, as well as…

Number Theory · Mathematics 2013-10-22 Benjamin Smith