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Related papers: Algebraic Characterization of CNOT-Based Quantum C…

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Quantum circuit optimization is a central task in Quantum Computing, as current Noisy Intermediate Scale Quantum devices suffer from error propagation that often scales with the number of operations. Among quantum operations, the CNOT gate…

Artificial Intelligence · Computer Science 2026-04-16 Jacopo Cossio , Daniele Lizzio Bosco , Riccardo Romanello , Giuseppe Serra , Carla Piazza

We consider the implementation of two-qubit unitary transformations by means of CNOT gates and single-qubit unitary gates. We show, by means of an explicit quantum circuit, that together with local gates three CNOT gates are necessary and…

Quantum Physics · Physics 2009-11-10 G. Vidal , C. M. Dawson

A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter…

Quantum Physics · Physics 2007-05-23 Robert R. Tucci

Quantum computing has transformative computational power to make classically intractable computing feasible. As the algorithms that achieve practical quantum advantage are beyond manual tuning, quantum circuit optimization has become…

Programming Languages · Computer Science 2025-06-26 Zihan Chen , Henry Chen , Yuwei Jin , Minghao Guo , Enhyeok Jang , Jiakang Li , Caitlin Chan , Won Woo Ro , Eddy Z. Zhang

The quantum circuit synthesis problem bridges quantum algorithm design and quantum hardware implementation in the Noisy Intermediate-Scale Quantum (NISQ) era. In quantum circuit synthesis problems, diagonal unitary synthesis plays a crucial…

Quantum Physics · Physics 2024-12-04 Wenqi Zhang , Jinyang Liu , Zixiang Zhou , Shuai Yang

We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…

Quantum Physics · Physics 2023-11-15 Alexandre Clément , Nicolas Heurtel , Shane Mansfield , Simon Perdrix , Benoît Valiron

Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…

Quantum Physics · Physics 2007-05-23 P. B. M. Sousa , R. V. Ramos

Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some…

Quantum Physics · Physics 2023-04-20 Tom Peham , Lukas Burgholzer , Robert Wille

Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of non-iterative energy corrections, based on the method of…

Chemical Physics · Physics 2023-05-03 Ilias Magoulas , Francesco A. Evangelista

Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…

Quantum Physics · Physics 2025-06-13 Yuchen Guo , Shuo Yang

We present a framework for the synthesis of phase polynomials that addresses both cases of full connectivity and partial connectivity for NISQ architectures. In most cases, our algorithms generate circuits with lower CNOT count and CNOT…

Quantum Physics · Physics 2023-02-15 Vivien Vandaele , Simon Martiel , Timothée Goubault de Brugière

The development of prototype quantum information processors has progressed to a stage where small instances of logical qubit systems perform better than the best of their physical constituents. Advancing towards fault-tolerant quantum…

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…

Quantum Physics · Physics 2015-05-30 Yudong Cao , Anmer Daskin , Steven Frankel , Sabre Kais

In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for…

Quantum Physics · Physics 2026-01-05 Kamil Khadiev , Aliya Khadieva , Vadim Sagitov , Kamil Khasanov

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a…

Quantum Physics · Physics 2009-11-10 Jennifer L. Dodd , Timothy C. Ralph , G. J. Milburn

Quantum gates are the building blocks of quantum circuits, which in turn are the cornerstones of quantum information processing. In this work, we theoretically investigate a single-step implementation of both a universal two- (CNOT) and…

Quantum Physics · Physics 2024-07-01 Luiz O. R. Solak , Daniel Z. Rossatto , Celso J. Villas-Boas

In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X (CX) gates, using the generating set of quantum gates [X, T, CX, CS]. We…

Quantum Physics · Physics 2020-12-10 Shelly Garion , Andrew W. Cross

We focus on the depth optimization of CNOT circuits on hardwares with limited connectivity. We adapt the algorithm from Kutin et al. that implements any $n$-qubit CNOT circuit in depth at most $5n$ on a Linear Nearest Neighbour (LNN)…

Quantum Physics · Physics 2023-03-14 Timothée Goubault de Brugière , Simon Martiel

Single qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. While high fidelity single qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT…

Quantum Physics · Physics 2018-02-02 D. M. Zajac , A. J. Sigillito , M. Russ , F. Borjans , J. M. Taylor , G. Burkard , J. R. Petta

Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…

Quantum Physics · Physics 2025-12-16 Jason Hanson