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A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…

Quantum Physics · Physics 2024-07-08 Matan Ben Dov , David Shnaiderov , Adi Makmal , Emanuele G. Dalla Torre

Efficient block encoding of many-body Hamiltonians is a central requirement for quantum algorithms in scientific computing, particularly in the early fault-tolerant era. In this work, we introduce new explicit constructions for block…

Quantum Physics · Physics 2025-10-13 Diyi Liu , Shuchen Zhu , Guang Hao Low , Lin Lin , Chao Yang

We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform…

Quantum Physics · Physics 2007-05-23 Samuel A. Kutin , David Petrie Moulton , Lawren M. Smithline

Recent developments in qudit-based quantum computing, in particular with trapped ions, open interesting possibilities for scaling quantum processors without increasing the number of physical information carriers. In this work, we propose a…

Quantum Physics · Physics 2024-07-02 Anastasiia S. Nikolaeva , Evgeniy O. Kiktenko , Aleksey K. Fedorov

An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…

Quantum Physics · Physics 2023-09-18 Sergey Bravyi , David Gosset , Yinchen Liu

In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds…

Emerging Technologies · Computer Science 2018-07-18 Srijit Dutta , Debjyoti Bhattacharjee , Anupam Chattopadhyay

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…

Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum…

Quantum Physics · Physics 2025-10-14 Alejandro Villoria , Henning Basold , Alfons Laarman

We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic…

Quantum Physics · Physics 2021-09-28 Ryan L. Mann

We examine the fundamental problem of constructing depth-optimum circuits for binary addition. More precisely, as in literature, we consider the following problem: Given auxiliary inputs $t_0, \dotsc, t_{m-1}$, so-called generate and…

Discrete Mathematics · Computer Science 2020-12-11 Ulrich Brenner , Anna Hermann , Jannik Silvanus

Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence…

Quantum state preparation, also known as encoding or embedding, is a crucial initial step in many quantum algorithms and often constrains theoretical quantum speedup in fields such as quantum machine learning and linear equation solvers.…

Quantum Physics · Physics 2025-12-04 Vittorio Pagni , Gary Schmiedinghoff , Kevin Lively , Michael Epping , Michael Felderer

Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…

Quantum Physics · Physics 2026-03-25 Yuxuan Yan , Zhenyu Du , Junjie Chen , Xiongfeng Ma

In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…

Quantum Physics · Physics 2026-05-18 Hanyu Wang , Mingfei Yu , Xinrui Wu , Jason Cong

The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…

Quantum Physics · Physics 2026-03-19 Christine Li , Lia Yeh

Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum…

Quantum Physics · Physics 2026-05-07 Folkert de Ronde , Stephan Wong , Sebastian Feld

We present a novel and efficient in terms of circuit depth design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) Draper's adders to build…

Quantum Physics · Physics 2013-11-05 Archimedes Pavlidis , Dimitris Gizopoulos

We present a constructive method to create quantum circuits that implement oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low $T$-count. In our method…

Quantum Physics · Physics 2019-08-06 Giulia Meuli , Mathias Soeken , Earl Campbell , Martin Roetteler , Giovanni De Micheli

Resource consumption is an important issue in quantum information processing, particularly during the present NISQ era. In this paper, we investigate resource optimization of implementing multiple controlled operations, which are…

Quantum Physics · Physics 2024-02-08 Junhong Nie , Wei Zi , Xiaoming Sun

Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families of states. This work introduces a method for preparing…

Quantum Physics · Physics 2026-03-26 Baptiste Claudon , Alexis Lucas , Jean-Philip Piquemal , César Feniou , Julien Zylberman