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Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…

Quantum Physics · Physics 2024-07-26 Vladimir V. Arsoski

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…

Quantum Physics · Physics 2009-10-28 V. Vedral , A. Barenco , A. Ekert

Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…

Quantum Physics · Physics 2024-08-23 David Rogerson , Ananda Roy

Prior studies have largely focused on quantum algorithms, often reducing parallel computing designs to abstract models or overly simplified circuits. This has contributed to the misconception that most applications are feasible only through…

Quantum Physics · Physics 2025-06-23 Yu-Ting Kao , Yeong-Jar Chang , Ying-Wei Tseng

We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generally, any elliptic curve over F\_{p^2} with a low-degree…

Number Theory · Mathematics 2019-02-20 François Morain , Charlotte Scribot , Benjamin Smith

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…

Quantum Physics · Physics 2007-05-23 Stephen D. Bartlett , Hubert de Guise , Barry C. Sanders

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose.…

In many practical applications, quantum algorithms require several qubits, significantly more than those available with current noisy intermediate-scale quantum processors. Distributed quantum computing (DQC) is considered a scalable…

Quantum Physics · Physics 2026-03-02 Michele Bandini , Davide Ferrari , Stefano Carretta , Michele Amoretti

This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit…

Quantum Physics · Physics 2020-07-29 Steven Herbert

Efficient scalar multiplication is critical for enhancing the performance of elliptic curve cryptography (ECC), especially in applications requiring large-scale or real-time cryptographic operations. This paper proposes an M-ary…

Cryptography and Security · Computer Science 2025-05-06 Tongxi Wu , Xufeng Liu , Jin Yang , Yijie Zhu , Shunyang Zeng , Mingming Zhan

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

Quantum Physics · Physics 2024-12-30 Boris Arseniev , Dmitry Guskov , Richik Sengupta , Igor Zacharov

We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical…

Quantum Physics · Physics 2021-02-17 Lucas Kocia , Mohan Sarovar

While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design.…

Quantum Physics · Physics 2007-05-23 George F. Viamontes , Manoj Rajagopalan , Igor L. Markov , John P. Hayes

This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit…

Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…

Optimization and Control · Mathematics 2024-12-23 Zeguan Wu , Pouya Sampourmahani , Mohammadhossein Mohammadisiahroudi , Tamás Terlaky

Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…

Quantum Physics · Physics 2011-01-14 Fabrizio Buscemi

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…

Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources,…

IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…

Emerging Technologies · Computer Science 2022-06-10 Gerhard W. Dueck , Anirban Pathak , Md Mazder Rahman , Abhishek Shukla , Anindita Banerjee

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical…