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The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…

Computational Complexity · Computer Science 2026-02-06 Wenhao Li , Anastasis Kratsios , Hrad Ghoukasian , Dennis Zvigelsky

Optimal control of closed quantum systems is a well studied geometrically elegant set of computational theory and techniques that have proven pivotal in the implementation and understanding of quantum computers. The design of a circuit…

Quantum Physics · Physics 2024-04-29 Johannes Aspman , Vyacheslav Kungurtsev , Jakub Marecek

The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…

Quantum Physics · Physics 2025-12-12 Adrián Pérez-Salinas , Mahtab Yaghubi Rad , Alice Barthe , Vedran Dunjko

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…

Logic in Computer Science · Computer Science 2014-09-16 Sicun Gao

Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…

Logic in Computer Science · Computer Science 2026-05-25 Dan R. Ghica , George Kaye , David Sprunger

Bosonic encoding is an approach for quantum information processing, promising lower hardware overhead by encoding in the many levels of a harmonic oscillator mode. Scaling to multiple modes requires weak interaction for independent control,…

Quantum Physics · Physics 2024-04-04 Asaf A. Diringer , Eliya Blumenthal , Avishay Grinberg , Liang Jiang , Shay Hacohen-Gourgy

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…

Quantum Physics · Physics 2007-05-23 Juha J. Vartiainen , Mikko Mottonen , Martti M. Salomaa

The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…

Quantum Physics · Physics 2024-01-26 Mattias T. Johnsson , Daniel Burgarth

The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic…

Quantum Physics · Physics 2026-05-21 Abhoy Kole , Till Schnittka , Rolf Drechsler

We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum…

Quantum Physics · Physics 2023-03-24 Wei Zi , Qian Li , Xiaoming Sun

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so…

Quantum Physics · Physics 2011-09-19 Alberto Castro , I. V. Tokatly

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…

Quantum Physics · Physics 2016-09-20 Theodore J. Yoder , Ryuji Takagi , Isaac L. Chuang

Reversible logic synthesis is a crucial component in quantum electronic design automation. While rule-based methodologies have gained prominence in reversible circuit optimization, the completeness of the transformation rule systems is a…

Quantum Physics · Physics 2026-02-16 Shiguang Feng , Lvzhou Li

Quantum resource analysis is crucial for designing quantum circuits as well as assessing the viability of arbitrary (error-corrected) quantum computations. To this end, we introduce QUANTIFY, which is an open-source framework for the…

Quantum Physics · Physics 2020-07-22 Oumarou Oumarou , Alexandru Paler , Robert Basmadjian

Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems…

Quantum Physics · Physics 2025-12-05 Christiane P. Koch

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…

Quantum Physics · Physics 2021-11-05 Luca Mondada

The Toffoli gate serving as a basic building block for reversible quantum computation, has manifested its great potentials in improving the error-tolerant rate in quantum communication. While current route to the creation of Toffoli gate…

Atomic Physics · Physics 2020-01-15 Dongmin Yu , Yichun Gao , Weiping Zhang , Jinming Liu , Jing Qian

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…

Quantum Physics · Physics 2007-05-23 S. Virmani , Susana F. Huelga , Martin B. Plenio

Quantum unitaries of the form $\Sigma_{c}\ket{c}\bra{c}\otimes U_{c}$ are ubiquitous in quantum algorithms. This class encompasses not only standard uniformly controlled gates (UCGs) but also a wide range of circuits with uniformly…

Quantum Physics · Physics 2025-12-11 Chengzhuo Xu , Xiao Chen , Xi Li , Zhihao Liu , Zhigang Li
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