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Unitary operations are expressed in the quantum circuit model as a finite sequence of elementary gates, such as controlled-not gates and single qubit gates. We prove that the simplified Toffoli gate by Margolus, which coincides with the…

Quantum Physics · Physics 2007-05-23 Guang Song , Andreas Klappenecker

We present quantum circuits for comparison and increment operations that achieve an asymptotically optimal gate count of $\Theta(n)$ and depth of $\Theta(\log n)$ over the Clifford+Toffoli gate set, while using a provably minimal number of…

Quantum Physics · Physics 2026-03-16 Vivien Vandaele

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…

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…

Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…

Quantum Physics · Physics 2024-07-26 Vladimir V. Arsoski

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

Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the…

Quantum Physics · Physics 2022-03-31 Wen-Qiang Liu , Hai-Rui Wei , Leong-Chuan Kwek

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

As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the…

Optimization and Control · Mathematics 2025-07-10 Jihye Jung , Kevin Dalmeijer , Pascal Van Hentenryck

A method, termed controlled-injection, is proposed for compiling three-qubit controlled gates within the non-abelian Fibonacci anyon model. Building on single-qubit compilation techniques with three Fibonacci anyons, the approach showcases…

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

Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…

Quantum Physics · Physics 2025-10-09 David Gosset , Robin Kothari , Chenyi Zhang

Quantum image processing is one of the promising fields of quantum information. The complexity overhead to design circuits to represent quantum images is a significant problem. So, we proposed a new method to minimize the total number…

Quantum Physics · Physics 2020-01-01 Younatan Matthew , Ghose Shohini

The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…

Quantum Physics · Physics 2024-07-09 Taghreed Ahmed , Ahmed Younes , and Islam Elkabani

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

The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information -…

Quantum Physics · Physics 2007-05-23 Sandu Popescu , Berry Groisman , Serge Massar

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

A Toffoli gate ($C^{n}$-NOT gate) is regarded as an important unitary gate in quantum computation, and is simulated by a quantum circuit composed of $C^{2}$-NOT gates. This paper presents a quantum circuit with a new configuration of…

Quantum Physics · Physics 2007-05-23 Masanari Asano , Chikara Ishii

Recently, reversible circuit synthesis has been intensively studied. One of the problems that has not been solved for a long time was exact minimization of gate count (GC) in 4-bit circuits. Finally, last year a tool of practical usage for…

Quantum Physics · Physics 2011-10-24 Marek Szyprowski , Pawel Kerntopf

The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…

Quantum Physics · Physics 2024-11-15 Gregory D. Kahanamoku-Meyer , Norman Y. Yao