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Related papers: On the CNOT-complexity of CNOT-PHASE circuits

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We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Compared to IBM's Qiskit compiler, it improves the fidelity of a…

Quantum Physics · Physics 2024-05-31 Dohun Kim , Minyoung Kim , Sarah Meng Li , Michele Mosca

Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…

Quantum Physics · Physics 2026-03-20 Priyanka Mukhopadhyay , Alexandru Gheorghiu , Hari Krovi

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…

Quantum Physics · Physics 2022-08-24 Sahel Ashhab , Naoki Yamamoto , Fumiki Yoshihara , Kouichi Semba

This paper examines QAOA in the context of parity network synthesis. We propose a pair of algorithms for parity network synthesis and linear circuit inversion. Together, these algorithms can build the diagonal component of the QAOA circuit,…

Quantum Physics · Physics 2024-02-20 Colin Campbell , Edward D Dahl

We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…

Quantum Physics · Physics 2024-10-25 Sahel Ashhab , Fumiki Yoshihara , Miwako Tsuji , Mitsuhisa Sato , Kouichi Semba

Blocks composed of {CNOT, Rz} are ubiquitous in modern quantum applications, notably in circuits such as QAOA ansatzes and quantum adders. After compilation, many of them exhibit large CNOT counts or depths, which lowers fidelity.…

Quantum Physics · Physics 2025-11-25 Xinpeng Li , Ji Liu , Shuai Xu , Paul Hovland , Vipin Chaudhary

In this paper, we give a mathematical proof that bounds the number of CNOT gates required to synthesize an $n$ qubit phase polynomial with $g$ terms to be at least $O(\frac{gn}{\max (\log g, 1)})$ and at most $O(gn)$. However, when…

Quantum Physics · Physics 2026-04-22 Arianne Meijer-van de Griend

We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives, since they are widely-used components in quantum algorithms and also have attracted much experimental interest in recent…

Quantum Physics · Physics 2024-06-11 Shihao Zhang , Junda Wu , Lvzhou Li

Quantum Approximate Optimization Algorithm (QAOA) is studied primarily to find approximate solutions to combinatorial optimization problems. For a graph with $n$ vertices and $m$ edges, a depth $p$ QAOA for the Max-cut problem requires…

NISQ devices have inherent limitations in terms of connectivity and hardware noise. The synthesis of CNOT circuits considers the physical constraints and transforms quantum algorithms into low-level quantum circuits that can execute on…

Quantum Physics · Physics 2025-06-03 Xinyu Chen , Mingqiang Zhu , Xueyun Cheng , Zhijin Guan , Shiguang Feng , Pengcheng Zhu

Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…

Quantum Physics · Physics 2014-11-18 Matthew Amy , Dmitri Maslov , Michele Mosca

A CNOT circuit is the key gadget for entangling qubits in quantum computing systems. However, the qubit connectivity of noisy intermediate-scale quantum (NISQ) devices is constrained by their {limited connectivity architecture}. To improve…

Quantum Physics · Physics 2023-02-03 Bujiao Wu , Xiaoyu He , Shuai Yang , Lifu Shou , Guojing Tian , Jialin Zhang , Xiaoming Sun

Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…

Quantum Physics · Physics 2023-06-05 Tom Peham , Nina Brandl , Richard Kueng , Robert Wille , Lukas Burgholzer

This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…

Quantum Physics · Physics 2024-07-16 Liam Madden , Albert Akhriev , Andrea Simonetto

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

Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…

Quantum Physics · Physics 2024-06-05 Afrin Sultana , Edgard Muñoz-Coreas

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that…

Quantum Physics · Physics 2023-05-10 Nikita A. Nemkov , Evgeniy O. Kiktenko , Ilia A. Luchnikov , Aleksey K. Fedorov

In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence…

Quantum Physics · Physics 2009-11-10 Farrokh Vatan , Colin Williams

The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. In this work, we…

Quantum Physics · Physics 2026-03-24 Spyros Tserkis , Muhammad Umer , Dimitris G. Angelakis

We apply the quantum optimal control theory based on the Krotov method to implement single-qubit $X$ and $Z$ gates and two-qubit CNOT gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and…

Quantum Physics · Physics 2014-07-16 Shang-Yu Huang , Hsi-Sheng Goan