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Related papers: Optimal Synthesis of Multi-Controlled Qudit Gates

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We use machine learning techniques to design a 50 ns three-qubit flux-tunable controlled-controlled-phase gate with fidelity of >99.99% for nearest-neighbor coupled transmons in circuit quantum electrodynamics architectures. We explain our…

We propose the theory of Cayley graphs as a framework to analyse gate counts and quantum costs resulting from reversible circuit synthesis. Several methods have been proposed in the reversible logic synthesis literature by considering…

Discrete Mathematics · Computer Science 2012-09-17 A. C. Ribeiro , C. M. H. de Figueiredo , F. L. Marquezino , L. A. B. Kowada

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate…

Optimization and Control · Mathematics 2010-12-06 Srinivas Sridharan , Mile Gu , Matthew R. James , William M. McEneaney

Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…

Quantum Physics · Physics 2026-04-27 Mathias Weiden , Justin Kalloor , John Kubiatowicz , Ed Younis , Costin Iancu

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 propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and…

Logic in Computer Science · Computer Science 2011-11-09 Guowu Yang , William N. N. Hung , Xiaoyu Song , Marek Perkowski

Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement,…

Quantum Physics · Physics 2023-01-12 Kevin Mato , Martin Ringbauer , Stefan Hillmich , Robert Wille

The matrices that can be exactly represented by a circuit over the Toffoli-Hadamard gate set are the orthogonal matrices of the form $M/ \sqrt{2}{}^k$, where $M$ is an integer matrix and $k$ is a nonnegative integer. The exact synthesis…

Quantum Physics · Physics 2023-05-22 Matthew Amy , Andrew N. Glaudell , Sarah Meng Li , Neil J. Ross

Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…

Quantum Physics · Physics 2025-03-20 Mark Webster , Stergios Koutsioumpas , Dan E Browne

In fault-tolerant quantum computing, errors in unitary gate synthesis is comparable with noise inherent in the gates themselves. While mixed synthesis can suppress such coherent errors quadratically, there is no clear understanding on its…

Quantum Physics · Physics 2025-07-10 Nobuyuki Yoshioka , Seiseki Akibue , Hayata Morisaki , Kento Tsubouchi , Yasunari Suzuki

We present numerical results which show how two-bit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a…

Condensed Matter · Physics 2007-05-23 David P. DiVincenzo , John Smolin

Three-qubit quantum gates are key ingredients for quantum error correction and quantum information processing. We generate quantum-control procedures to design three types of three-qubit gates, namely Toffoli, Controlled-Not-Not and Fredkin…

Quantum Physics · Physics 2016-11-17 Ehsan Zahedinejad , Joydip Ghosh , Barry C. Sanders

In some quantum algorithms, arithmetic operations are of utmost importance for resource estimation. In binary quantum systems, some efficient implementation of arithmetic operations like, addition/subtraction, multiplication/division,…

Quantum Physics · Physics 2022-06-01 Amit Saha , Turbasu Chatterjee , Anupam Chattopadhyay , Amlan Chakrabarti

Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…

Quantum Physics · Physics 2026-02-19 Lukas Theißinger , Thore Gerlach , David Berghaus , Christian Bauckhage

In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in…

Quantum Physics · Physics 2016-06-28 Mona Arabzadeh , Mahboobeh Houshmand , Mehdi Sedighi , Morteza Saheb Zamani

We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to…

Quantum Physics · Physics 2009-10-30 Wojciech Hubert Zurek , Raymond Laflamme

How to implement quantum oracle with limited resources raises concerns these days. We design two ancilla-adjustable and efficient algorithms to synthesize SAT-oracle, the key component in solving SAT problems. The previous work takes 2m-1…

Quantum Physics · Physics 2022-06-10 Shuai Yang , Wei Zi , Bujiao Wu , Cheng Guo , Jialin Zhang , Xiaoming Sun

Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on…

Quantum Physics · Physics 2016-12-06 M. B. Hastings

We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…

Quantum Physics · Physics 2013-03-18 Cody Jones

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches…

Quantum Physics · Physics 2015-06-05 Kaveh Khodjasteh , Hendrik Bluhm , Lorenza Viola