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Related papers: Halving the width of Toffoli based constant modula…

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In this paper, we consider the optimized implementation of Multi Controlled Toffoli (MCT) using the Clifford $+$ T gate sets. While there are several recent works in this direction, here we explicitly quantify the trade-off (with concrete…

Quantum Physics · Physics 2025-02-12 Suman Dutta , Siyi Wang , Anubhab Baksi , Anupam Chattopadhyay , Subhamoy Maitra

Bit addition arises virtually everywhere in digital circuits: arithmetic operations, increment/decrement operators, computing addresses and table indices, and so on. Since bit addition is such a basic task in Boolean circuit synthesis, a…

Computational Complexity · Computer Science 2025-09-25 Mikhail Goncharov , Alexander S. Kulikov , Georgie Levtsov

The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318 (2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$ additional…

Quantum Physics · Physics 2023-05-25 Jian Leng , Fan Yang , Xiang-Bin Wang

We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…

Quantum Physics · Physics 2013-08-21 David Gosset , Vadym Kliuchnikov , Michele Mosca , Vincent Russo

Quantum circuits of many qubits are extremely difficult to realize; thus, the number of qubits is an important metric in a quantum circuit design. Further, scalable and reliable quantum circuits are based on Clifford + T gates. An efficient…

Quantum Physics · Physics 2017-06-19 Edgard Muñoz-Coreas , Himanshu Thapliyal

The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic operations on quantum data, e.g., reversible arithmetic circuits. In physical implementations, however, TOFFOLI gates are decomposed into six CNOT gates…

Quantum Physics · Physics 2011-11-03 Vivek V. Shende , Igor L. Markov

In this paper, we present Clifford+T gates based quantum circuit design of integer division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring division algorithm. The proposed quantum circuit of integer division…

Quantum Physics · Physics 2016-09-06 Himanshu Thapliyal , T. S. S. Varun , Edgard Munoz-Coreas

We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…

Quantum Physics · Physics 2013-06-14 Vadym Kliuchnikov

We present a novel Clifford+T decomposition of a Toffoli gate. Our decomposition requires no SWAP gates in order to be implemented on 2D square lattices of qubits. This decomposition enables shallower, more fault-tolerant quantum…

Quantum Physics · Physics 2023-11-22 Alexandru Paler , Evan E. Dobbs , Joseph S. Friedman

Physical implementation of scalable quantum architectures faces an immense challenge in form of fragile quantum states. To overcome it, quantum architectures with fault tolerance is desirable. This is achieved currently by using surface…

Emerging Technologies · Computer Science 2019-12-25 Laxmidhar Biswal , Debjyoti Bhattacharjee , Anupam Chattopadhyay , Hafizur Rahaman

We propose protocols for calculating inner product, matrix addition and matrix multiplication based on multiqubit Toffoli-type and the simplest one-qubit operations and employ ancilla measurements to remove all garbage of calculations. The…

Quantum Physics · Physics 2024-11-22 Alexander I. Zenchuk , Wentao Qi , Asutosh Kumar , Junde Wu

In order for quantum computations to be done as efficiently as possible it is important to optimise the number of gates used in the underlying quantum circuits. In this paper we find that many gate optimisation problems for approximately…

Quantum Physics · Physics 2024-08-13 John van de Wetering , Matt Amy

We present a new linear-depth ripple-carry quantum addition circuit. Previous addition circuits required linearly many ancillary qubits; our new adder uses only a single ancillary qubit. Also, our circuit has lower depth and fewer gates…

Quantum Physics · Physics 2007-05-23 Steven A. Cuccaro , Thomas G. Draper , Samuel A. Kutin , David Petrie Moulton

When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are…

An $(n+1)$-bit Toffoli gate is mainly utilized to construct other quantum gates and operators, such as Fredkin gates, arithmetical adders, and logical comparators, where $n \geq 2$. Several researchers introduced different methods to…

Quantum Physics · Physics 2025-11-03 Shanyan Chen , Ali Al-Bayaty , Xiaoyu Song , Marek Perkowski

We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…

Quantum Physics · Physics 2023-12-20 Vadym Kliuchnikov , Kristin Lauter , Romy Minko , Adam Paetznick , Christophe Petit

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 present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as…

Quantum Physics · Physics 2022-06-16 Pamela Rambow , Mingzhen Tian

There are two important, and potentially interconnecting, avenues to the realisation of large-scale quantum algorithms: improvement of the hardware, and reduction of resource requirements demanded by algorithm components. In focusing on the…

Quantum Physics · Physics 2024-07-02 G. A. L. White , C. D. Hill , L. C. L. Hollenberg

We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for…

Quantum Physics · Physics 2013-08-06 Cody Jones