English
Related papers

Related papers: Optimized circuits for windowed modular arithmetic…

200 papers

Multiplication of quantum states is a frequently used function or subroutine in quantum algorithms and applications, making quantum multipliers an essential component of quantum arithmetic. However, quantum multiplier circuits suffer from…

Quantum Physics · Physics 2025-06-24 Bhaskar Gaur , Himanshu Thapliyal

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…

Quantum Physics · Physics 2020-02-12 E. O. Kiktenko , A. S. Nikolaeva , Peng Xu , G. V. Shlyapnikov , A. K. Fedorov

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…

Quantum Physics · Physics 2013-05-29 Vivek V. Shende , Igor L. Markov , Stephen S. Bullock

With the development of quantum computing, quantum processor demonstrates the potential supremacy in specific applications, such as Grovers database search and popular quantum neural networks (QNNs). For better calibrating the quantum…

Quantum Physics · Physics 2024-11-26 Yuhong Song , Edwin Hsing-Mean Sha , Longshan Xu , Qingfeng Zhuge , Zili Shao

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point…

Quantum Physics · Physics 2017-11-01 Martin Roetteler , Michael Naehrig , Krysta M. Svore , Kristin Lauter

In some quantum algorithms, arithmetic operations are of utmost importance for resource estimation. In binary quantum systems, some efficient implementation of arithmetic operations like, addition/subtraction, multiplication/division,…

Quantum Physics · Physics 2022-06-01 Amit Saha , Turbasu Chatterjee , Anupam Chattopadhyay , Amlan Chakrabarti

Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation…

Quantum Physics · Physics 2023-03-08 Qingfeng Wang , Ze-Pei Cian , Ming Li , Igor L. Markov , Yunseong Nam

Numerous scientific developments in this NISQ-era (Noisy Intermediate Scale Quantum) have raised the importance for quantum algorithms relative to their conventional counterparts due to its asymptotic advantage. For resource estimates in…

Quantum Physics · Physics 2023-09-13 Amit Saha , Anupam Chattopadhyay , Amlan Chakrabarti

This work presents an algorithm to generate depth, quantum gate and qubit optimized circuits for $GF(2^m)$ squaring in the polynomial basis. Further, to the best of our knowledge the proposed quantum squaring circuit algorithm is the only…

Quantum Physics · Physics 2017-06-19 Edgard Muñoz-Coreas , Himanshu Thapliyal

In fault-tolerant quantum computing, the cost of calculating Hamiltonian eigenvalues using the quantum phase estimation algorithm is proportional to the constant scaling the Hamiltonian matrix block-encoded in a unitary circuit. We present…

Quantum Physics · Physics 2024-12-03 Konrad Deka , Emil Zak

Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum…

Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy…

We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls applying $n$ single-qubit arbitrary phase rotations from $4n b+\mathcal{O}(\sqrt{cn b})$ to $2n b+\mathcal{O}(\sqrt{cn…

Quantum Physics · Physics 2021-10-27 Guang Hao Low

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 a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation,…

Quantum Physics · Physics 2023-03-22 Paul D. Nation , Matthew Treinish

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…

Quantum Physics · Physics 2024-03-14 A. M. Krol , A. Sarkar , I. Ashraf , Z. Al-Ars , K. Bertels

Rapid progress in the design of scalable, robust quantum computing necessitates efficient quantum circuit implementation for algorithms with practical relevance. For several algorithms, arithmetic kernels, in particular, division plays an…

Quantum Physics · Physics 2024-03-05 Siyi Wang , Eugene Lim , Anupam Chattopadhyay

Submodular functions are set functions mapping every subset of some ground set of size $n$ into the real numbers and satisfying the diminishing returns property. Submodular minimization is an important field in discrete optimization theory…

Data Structures and Algorithms · Computer Science 2020-01-16 Yassine Hamoudi , Patrick Rebentrost , Ansis Rosmanis , Miklos Santha

Decoded Quantum Interferometry (DQI) provides a framework for superpolynomial quantum speedups by reducing certain optimization problems to reversible decoding tasks. We apply DQI to the Optimal Polynomial Intersection (OPI) problem, whose…

In 2004, Cuccaro et al found a quantum-quantum adder with $O(n)$ gate cost and $O(1)$ ancilla qubits. Since then, it's been an open question whether classical-quantum adders can achieve the same asymptotic complexity. These costs are…

Quantum Physics · Physics 2025-08-01 Craig Gidney